If you ask Rick Astley for his copy of Disney Pixar's Up, he can't give it to you, because he'll never give you Up. But by not doing so, you'd be let down, and he'll never let you down.
Testing this scenario is ofc incredibly risky to the state of our reality, so the Astley paradox must remain a thought experiment.
I guess I would say the paradox of tolerance. I'm sorry but I'm just gonna yoink the definition from Wikipedia because I'm not great at explaining things:
The paradox of tolerance states that if a society's practice of tolerance is inclusive of the intolerant, intolerance will ultimately dominate, eliminating the tolerant and the practice of tolerance with them. Karl Popper describes the paradox as arising from the fact that, in order to maintain a tolerant society, the society must retain the right to be intolerant of intolerance.
Bonus least favorite paradox: You need experience to get a job and you need a job to get experience.
Saw this a while ago and it solves that "paradox" nicely.
The real paradox is this opinion coming from Twitter
It doesn't though. Pure unlimited tolerance would include tolerating someone's breach of contract, logically speaking. Also, this is a dangerous road to go down, because you can rephrase pretty much anything as a contract and justify your actions or beliefs with people breaking it.
The reason these discussions often break down right about here is because the participants have in mind completely different working definitions of “tolerance.”
For example, the social contract comment above assumes an active definition like recognizing others’ personal sovereignty, i.e. their right to act and not be acted upon. To aid understanding, we can represent mutual tolerance between people as a multinational peace treaty between nations. Intolerance is equivalent to one of these nations violating the treaty by attacking another.
Defense or sanction by neighboring states against the aggressor doesn’t violate the treaty further, of course, since it is precisely these deterrents which undergird every treaty. Likewise, condemning and punishing intolerance which threatens the personal sovereignty of others is baseline maintenance for mutual tolerance, because there’s always a jackass who WILL fuck around if you don’t GUARANTEE he will find out.
Conversely, another popular notion of tolerance — the one you may have in mind, as I once did — is a passive definition that amounts to tacit approval of others’ value systems, i.e. relativistic truth, permissive morality, etc.
This kumbaya definition is a strawman originally used by talking heads because, I suspect, it quickly invokes well-worn mid-century tropes, especially for those who grew up in the era, of namby-pamby suckers and morally compromised weaklings which still trigger strong feelings, like disgust and contempt, that reliably drive ratings and engagement. These days the only regular mention of this term is this manufactured paradox using the bad-faith definition, so the original idea is commonly misunderstood.
Pure unlimited tolerance would include tolerating someone's breach of contract, logically speaking.
That "pure, unlimited tolerance" is what they mean by tolerance as a moral standard. Tolerance as a contract is "we have each entered into an agreement to be tolerant of each other. If you are not tolerant of me, you have broken the terms of our agreement, so I will not be tolerant of you."
I don't see a slippery slope here; I'd be interested to hear more about why this is a dangerous road to go down.
A contract just codifies an existing power dynamic, because its terms depend on the negociating powers of the people agreeing to it. It doesn't say anything about the morality of the terms or the context in which it was signed. Very extreme and on-the-nose example: "We have agreed to only allow white people, you have breached that contract ...". This works just fine if your moral system is based on contracts, but it's obvously immoral. There's also the conundrum of people never explicitly agreeing to the social contract they are born into, and even if they did, it's not like they have much of a choice.
Imo pure tolerance is a real paradox, because you cannot tolerate intolerance, and that makes you intolerant yourself. You can't achieve it, but you probably should not want to in the first place. There are certain things we will and certain things we won't tolerate in a modern society, and that is completely fine. The important thing is that we recognize this and make good decisions about which is which.
I think the job experience is less of a paradox and more of a Catch-22. True nonetheless
Wait, what is a catch-22 but a paradox? I’ve never thought about this before, but Yossarian is stuck in a paradoxical situation so these are synonymous terms right?
I don't think so. I interpret paradoxes as being either philosophical impasses (ie, 2 conceptually true statements conflict each other in a way that makes you question where one statement's truth ends and the other statement's truth begins) or a situation in which a solution is unintuitive.
A Catch-22 is more of a physical and intentional impasse, where obstacles are intentionally set up in such a way that people are unable to make a choice. For instance, in the original example of a Catch-22, there is no philosophical argument saying that only insane people are allowed to not fly - it is an arbitrary rule that some higher-up established. And likewise, it is entirely arbitrary to define insane as being willing to fly.
I guess to simplify my stance, it's a paradox if it makes you think "the universe has made this unsolvable" and it's a Catch-22 if it makes you think "some asshole made this unsolvable"
This makes quite a lot of sense, thanks for explaining that to me!
I've always hated the intolerance paradox, because it is the same logic used to justify atrocities of all sorts. Trying to make society safe for a preferred group, and targeting anyone who takes offense to that idea.
Again leaving out the second half of the quote.
They always do.
I do not see any paradox there. Paradox is something contradictory. All your statements are true and do not contradict to each other.
The phrase, "You have to be intolerant to be tolerant" doesn't sound like a contradiction to you?
Sounds like contradiction, yes, but it is just incorrect phrase. You do not have to be intolerant to be tolerant.
The society have to be intolerant to intolerance to be stable, not to be tolerant or intolerant.
I think you're missing the point. The question is about a tolerant society.
Regardless of if the society itself is stable, for the society to be tolerant it must be intolerant of the intolerant, and therefore a tolerant society must be intolerant.
By treating tolerance as a binary (it's either completely present or completely absent) you've removed your argument very far from reality. The goal in reality is to be as tolerant as possible, and the most tolerant stable state simply has some (limited) amount of (very specific) intolerance in it.
The Unexpected Hanging Paradox: A man is sentenced to death, but the judge decides to have a little fun with it. The man will be killed at noon on a day of the judge's choosing in the next week, from Monday to Friday. The only stipulation is that the man will not expect it when he's called to be killed.
The man does some quick logic in his head. If Friday is the last day he could be killed, then if he makes it to Friday without dying, he knows he must die on that day. And since that wouldn't be a surprise, he cannot be killed on Friday.
He then extends the logic. Since he can't be killed on Friday, the last day he can be killed is on Thursday. Thus, all the prior logic regarding Friday applies, and he cannot be killed on Thursday either. This then extends to Wednesday, then Tuesday, and then Monday. At the end, he grins with the knowledge that, through logic, he knows he cannot be killed on any of the days, and will therefore not be killed.
Therefore, the man is astonished when he's called to be killed on Wednesday.
How does the judge determine whether the condemned man is "expecting it"?
Regardless of when he's called, he could simply state that he was expecting to be called, and therefore the hanging would be called off.
Its a bad paradox because it pivots on something that cannot be properly defined.
I think it's an anti-riddle, or a joke, more than anything else.
I always thought it was a way to show the foibles of using pure logic in a regular setting.
Cannot be properly defined? "Expecting it" means "regarding it likely to happen", according to the dictionary. He regarded it as impossible to happen, so he was not expecting it. His own logic disproving the event (him being surprised) allowed the event to happen (he was surprised).
Why does the paradox suffer if he lies about the solution? The paradox has already played out, and anything after that is just set dressing.
Just off the top of my head, maybe the judge has a camera set to gauge his reaction to the knock on the door? Or maybe he goes into denial and tries to explain his logic, thus proving the paradox? Or maybe the judge doesn't actually care as much as he said, but trusts the logic to hold out and make for a funny story?
You provide three flawed ways of measuring expectation; that's the issue in a nutshell.
Its not a true paradox as the whole gambit rests on a changeable emotion, not logic.
The prisoner could wake up each morning and simply say "I expect to die today". How would the judge determine the truth? It would be impossible.
If someone punches you in the face after saying "knock knock", it doesn't make it a knock knock joke, and nor is this a paradox.
My dude. The paradox doesn't change based on whether or not the judge knows the truth, or even if the man dies.
The truth is the man was made not to expect a thing by his own logic proving he would always expect a thing. The paradox is based on his own prediction being wrong because of his prediction. In this instance, his prediction was what his emotions would be.
A horse walks into a bar, and the barman says "why the long face?" I haven't said how they remove the horse from the bar, so does that mean I didn't tell a joke? Or does horse removal not actually matter to the joke?
No. A paradox is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.
In this case, there is no true premesis.
That's the core of the problem. Your incorrect interpretation of the joke metaphor demonstrates that you don't understand this.
I find it funny that you directly quoted wikipedia to write that (exact wording from the paradox article, I checked), but ignored the sentence immediately before it (...or a statement that runs contrary to one's expectation). Also, the linked articles at the bottom include the unexpected hanging page. Maybe read the entire wiki page before citing it?
It doesn't "back you up" at all, it simply restates the paradox. Maybe learn how to argue?
When you get to the point where you're nitpicking sources, you're admitting that you have no substantive argument available.
This is how I proposed to my wife. I said I'd propose at some point in the next year, and that according the the unexpected hanging paradox, we're doomed to break up at the end of the year. Then I proposed on a random day in the year and she was totally surprised.
Mine is similar to yours in that it's about the power of God. It's called the Epicurean Trilemma:
If a god is omniscient and omnipotent, then they have knowledge of all evil and have the power to put an end to it. But if they do not end it, they are not omnibenevolent.
If a god is omnipotent and omnibenevolent, then they have the power to extinguish evil and want to extinguish it. But if they do not do it, their knowledge of evil is limited, so they are not omniscient.
If a god is omniscient and omnibenevolent, then they know of all the evil that exists and wants to change it. But if they do not, which must be because they are not capable of changing it, so they are not omnipotent.
This proves fairly simply that God as commonly interpreted by modern Christians cannot exist. Early Christians and Jews had no problem here, because their god was simply not meant to be omnibenevolent. Go even further back in time and he was not omnipotent, and possibly not omniscient, either. "Thou shalt have no gods before me" comes from a time when proto-Jews were henotheists, people who believed in the existence of multiple deities while only worshipping a single one.
"Oh dear," says God, "I hadn't thought of that," and promptly vanishes in a puff of logic.
Just leaving God's wife Ashera here.
Yes, he was married once. Look it up.
He had a sister too, super evil but it's ok because a human dude talked her out of destroying everything since God couldn't stop her.
Carry on...
A simple way I’ve been touching on this for a while is what I call “The problem of existence”: why would god create a non-divine existence such as our selves?
Put aside evil. If God is all three omnis, why make something that is lesser? I figure that the answer is they themselves must also be lesser than the three omnis.
Idk people like being in charge of stuff and not being bored maybe God would be the same way
The Christian explanation for this is that god doesn't do evil, people do.
And god created people with free will to do evil. If he made people stop doing evil deeds, they would be his puppets, not free-willed humans. So he has the power to end all evil but chooses not to.
Now as for why god allows natural disasters, diseases and other tragedies to befall his creation – again, that's just the consequence of our actions, cause a woman gave an apple to her man in the past.
And god created people with free will
Frankly, I don't buy this as an explanation even for human-created evil. It is still evidence that god cannot be tri-omni. Because it is still a situation in which god is able to remove evil and is aware of the evil, and yet he chooses to permit evil. Even evil done by one human against another, when the other is entirely innocent. And that cannot be omnibenevolent.
From how you phrased it I suspect you agree with me here, but the natural disasters argument is even more ludicrous. It doesn't even come close to working as a refutation of the Epicurian Trilemma.
If your options are "do as I say" or "suffer for all eternity" you aren't really capable of exercising free will.
It's worse than that. It's "believe that you must do as I say, despite my complete refusal to create worthwhile evidence of my existence, and then do what I say" or "suffer for all eternity".
The Christian explanation for this is that god doesn't do evil, people do.
And god created people with free will to do evil. If he made people stop doing evil deeds, they would be his puppets, not free-willed humans.
I never understood this argument. If he's all-powerful, he would have the ability to eliminate all evil without affecting free will.
The Christian god created every aspect of the universe and how it works. He therefore could have created a universe in which there was no such thing as evil or suffering, and given people in that universe free will. So even that doesn’t hold up.
I think that's their point; they're saying that's what God did. He "created a universe in which there was no such thing as evil or suffering and [gave] people in that universe free will."
And humans screwed it up.
I'm not saying that, mind you. I'm saying I think you just agreed with the person you're debating as a proof that they were wrong.
It doesn’t matter what you tack on, it doesn’t change my point — the only way humans could “screw it up” is if God made all the negative and horrible shit part of the universe. All you are saying is that God made a universe where there was no evil or suffering actively happening, but the concepts existed and were possible — because they ultimately happened and only possible things happen. And God chose to make them possible things as omnipotent creator of everything that exists.
Wait, so this God gives me true free will, and then places me in a world where I can't change anything? Everything is fixed, immovable? Or where I only have "good" choices available? Is that what you think God should have done? Like, how does your version even work?
Or does God give us fake free will, and keep our minds from thinking "bad" thoughts?
If I'm free, I can screw up. Otherwise, I'm not free.
No. You aren’t getting it. The Christian god created every aspect of the universe. Light and dark. Up and down. You are still thinking about our universe, in which these negative things are possible, and how you would have to be restricted in what you do in our universe in order to prevent you from doing certain things. But god could have set all the parameters of the universe differently such that they just didn’t exist at all. You wouldn’t miss them or be prevented from doing them. It would be like if there were a fifth cardinal direction in an alternate universe, and someone in that universe thought “if god prevented me from going in that direction, I wouldn’t have free will anymore”. But here we are, with only four cardinal directions, and free will. We aren’t being stopped from doing anything, it just isn’t part of our universe and doesn’t even make sense in it.
I think I get what you're saying but it is a little bit beyond me.
I still wonder if the problem doesn't come down to Free Will itself. Regardless of what universe one is living in, if you have only two people in it and they each have free will at some point the free will of one is going to intrude on the free will of the other, and they're going to require some kind of negotiation or polite accommodation. Some kind of social interaction.
And if one doesn't take this action but instead proceeds with one's free will regardless of the other's free will there is a problem that is inevitably going to exist no matter what universe exists.
But we don't have free will. The bible makes that perfectly clear in Romans 9.
Christian here, don't agree with your "biblical" interpretation
If Christians could agree with each other about what's in the bible, history would be a lot more boring.
God is not Omnibenevolent would be my take.
My favorite paradox is the "Stay signed in" option Microsoft gives you when signing in. Because despite keeping you signed in on every other site in existence, Microsoft, who is usually hooked into your OS, does not. Thus, stay signed in runs contradictory to one's expectations.
They aren't offering to do it, just asking if it's what you want.
Gotta check and be sure you're being annoyed as much as possible.
I thought the paradox is why it keeps fucking asking me - I said yes dammit.
Alanis morissette's song ironic contains no solid cases of irony, mostly bad luck or poor timing, and is therefore ironic.
I read an interview with her once that was kind of funny and humanizing. She wrote and recorded that song before she was famous and had no idea that it would ever be heard. Then it blew up and people have been giving her shit about it for decades now.
Could you imagine if you wrote a shitty Lemmy comment that became extremely viral and people were like, "you fucking moron, how could you have written something so dumb?!"
Not sure if its what you're talking about but I really like the Ship of Theseus thought experiment, if an object is the same object after having had all of its original components replaced. Always makes me think of if an exact clone of you is created (same thoughts, memories, etc...) should that be considered you?
In 80 to 100 days, 30 trillion [cells] will have replenished—the equivalent of a new you.
And I would venture that the answer to your question is yes, but no. The moment your exact clone experiences something you don’t, you two are no longer exactly the same. And I would wager that moment would happen very fast.
With that in mind, it really just comes down to if the original gets destroyed, for a lack of better words, before that moment even happens in order for it not to be considered just a copy.
Edit: this honestly kinda helped me understand the problem more I really appreciate it.
The moment of divergence is instantaneous between the clone and original. The only way it could not be instantaneous, is if both were just a brain connected to the exact same simulation, experiencing the exact same inputs. If they didn't respond the same, then they aren't an exact clone. Even then, the brains would be sustained with different blood, made up of trillions of slightly different atoms — although similar, not 100% identical due to quantum mechanics — with a slightly different fluid dynamics. Actually the only way they could be identical is if they weren't brains but identical code, running in an identical simulation, with the exact same boundaries, and no possibility of probability, chaos or divergence from that code... Oh no I've gone cross eyed.
The controversial thought experiment about Star Trek transporters.
Where an individual is dematerialized in one location, transmitted as a signal somewhere else and rematerialized somewhere else.
Were they killed when they were dematerialized, cloned and a newly born entity that is an exact clone rematerialized at the other end?
Are they just killing people and recreating copies everytime they transport people?
What's really gonna crumble your cookie is, "Does it matter?"
Even in the trek universe, some people refuse to take transporters. I'd pry be one of them. You have no idea if you're killing yourself every time, and its just clones out the other side.
Are they just killing people and recreating copies everytime they transport people?
Yes, it literally Prestiges you, as evidenced by the time it didn't kill Riker and there were two of him
If and when we figure out human cloning, it's sure going to bring up a near infinite number of legal issues. Is the clone a new person? Is their birthday yours or the day they were cloned? Are they the same age as you? Or is a clone a new born?
If they are a copy of you, are they beholden to any legal agreements you've made? Are they liable for crimes you commit?
These are the things I think about when stoned...
I read a good sci-fi book called "Six Wakes" by Mur Lafferty that touches on this topic, you might enjoy it.
In the distant future cloning has become commonplace, but is used as a continuation of a person's life. Ie a person is born, lives there life, and at the end they are cloned and their memories transferred over to the new body, and life goes on. Also, a person would make "backups" of their consciousness in case they were killed/died accidentally, and would be "reinstalled" in a clone.
Sounds great! I'll have to check that out!
Honestly though, that sounds like the only way to do cloning without completely redoing every single law in every single country, city, state, Providence, county, parish, etc. The implications of cloning fascinates me way more than the cloning itself
Ship of Theseus applies to every human, because all our cells get replaced over and over until we die. At a cellular level, you're wholly different from yourself 10 years ago. Are you still you?
You’re not wholly different as some cells are still the same. Neurons don’t undergo the same rapid cycling as skin cells, for example.
One thought is that "You" is just an unbroken string of consciousness. Which means you cease to be every time you sleep, and the person that wakes up just has the memories of being you.
A different perspective,seen in buddhism and similar worldviews, is that the only “you” that exists is the consciousness experiencing reality at any given moment.
Could god microwave a burrito so hot even he couldn't eat it?
All of the "is infinite power so powerful that it could overpower its own power" type questions just annoy me.
Is infinite power so powerful it can do something that it can't do?
Yes it can. And then it can do that anyway. Otherwise it wouldn't be infinite.
Could god create an "is infinite power so powerful that it could overpower its own power" type question that you wouldn't find annoying?
🤣🤣🤣
Only if he broke into a radio station & doused that burrito with hot sauce from a battery powered toy gun!
Also, I’m gonna need a football helmet full of cottage cheese & any naked pics of Bea Arthur you happen to have lying around.
I think that's how he created our universe 5,000 years ago ....... he's just waiting for us to cool off so can eventually take a bite.
If he bites too soon, we might end up on the floor though :(
I like George Carlin's version: "If God is all powerful, can he make a rock so big that he himself can't lift it?"
Weird attribution, man :) That one, and a lot of others like it, come all the way from the 12th Century and thereabouts. Carlin’s influence is awesome and deserved, but I don’t think it stretches that far :)
"Can God microwave a burrito so hot that he himself cannot eat it?"
"All of the "is infinite power so powerful that it could overpower its own power" type questions just annoy me.
Is infinite power so powerful it can do something that it can't do?
Yes it can. And then it can do that anyway. Otherwise it wouldn't be infinite."
So you're saying he would wait for it to cool down before eating it?
It's a copy pasta from another thread, just like the comment I replied to.
I was gonna say that but didn't know the exact phrasing
Yes. Yes he can. It's only a paradox to our comprehension.
I don't see why that's a paradox. It's like asking if infinity is bigger than infinity, where both infinities are aleph 0.
Zeno's Paradox, even though it's pretty much resolved. If you fire an arrow at an apple, before it can get all the way there, it must get halfway there. But before it can get halfway there, it's gotta get a quarter of the way there. But before it can get a fourth of the way, it's gotta get an eighth... etc, etc. The arrow never runs out of new subdivisions it must cross. Therefore motion is actually impossible QED lol.
Obviously motion is possible, but it's neat to see what ways people intuitively try to counter this, because it's not super obvious. The tortoise race one is better but seemed more tedious to try and get across.
So the resolution lies in the secret that a decreasing trend up to infinity adds up to a finite value. This is well explained by Gabriel's horn area and volume paradox:
https://www.youtube.com/watch?v=yZOi9HH5ueU
If I remember my series analysis math classes correctly: technically, summing a decreasing trend up to infinity will give you a finite value if and only if the trend decreases faster than the function/curve x -> 1/x.
Great. Can you give me example of decreasing trend slower than that function curve?, where summation doesn't give finite value? A simple example please, I am not math scholar.
So, for starters, any exponentiation "greater than 1" is a valid candidate, in the sense that 1/(n^2), 1/(n^3), etc will all give a finite sum over infinite values of n.
From that, inverting the exponentiation "rule" gives us the "simple" examples you are looking for: 1/√n, 1/√(√n), etc.
Knowing that √n = n^(1/2), and so that 1/√n can be written as 1/(n^(1/2)), might help make these examples more obvious.
Hang on, that's not a decreasing trend. 1/√4 is not smaller, but larger than 1/4...?
From 1/√3 to 1/√4 is less of a decrease than from 1/3 to 1/4, just as from 1/3 to 1/4 is less of a decrease than from 1/(3²) to 1/(4²).
The curve here is not mapping 1/4 -> 1/√4, but rather 4 -> 1/√4 (and 3 -> 1/√3, and so on).
Turns out the resolution to that paradox is that our universe is quantized, which means there's a minimum "step" that once you reach will probabilistically round up or down to the nearest step. It's kind of like how Super Mario at extreme float values will snap to a grid.
Wait, isn't space and time infinitely divisible? (I'm assuming you're referencing quantum mechanics, which I don't understand, and so I'm genuinely asking.)
Disclaimer: not a physicist, and I never went beyond the equivalent to a BA in physics in my formal education (after that I "fell" into comp sci, which funnily enough I find was a great pepper for wrapping my head around quantum mechanics).
So space and time per se might be continuous, but the energy levels of the various fields that inhabit spacetime are not.
And since, to the best of our current understanding, everything "inside" the universe is made up of those different fields, including our eyes and any instrument we might use to measure, there is a limit below which we just can't "see" more detail - be it in terms of size, mass, energy, spin, electrical potential, etc.
This limit varies depending on the physical quantity you are considering, and are collectively called Planck units.
Note that this is a hand wavy explanation I'm giving that attempts to give you a feeling for what the implications of quantum mechanics are like. The wikipédia article I linked in the previous paragraph gives a more precise definition, notably that the Planck "scale" for a physical quantity (mass, length, charge, etc) is the scale at which you cannot reasonably ignore the effects of quantum gravity. Sadly (for the purpose of providing you with a good explanation) we still don't know exactly how to take quantum gravity into account. So the Planck scale is effectively the "minimum size limit" beyond which you kinda have to throw your existing understanding of physics out of the window.
This is why I began this comment with "space and time might be continuous per se"; we just don't conclusively know yet what "really" goes on as you keep on considering smaller and smaller subdivisions.
The paradox holds in an infinitely dividable setting. Take the series of numbers where the next number equals the previous one divided by 2: {1, 1/2, 1/4, 1/8, 1/16...}. If you take the sum of this infinite series (there is always a larger factor of two to divide by) you are going to get a finite result (namely 2, in this instance).
So for the real life example, while there is always another 'half' of the distance to be travelled, the time it takes to do so is also halved with every iteration.
I had success talking about the tortoise one with imaginary time stamps.
I think it gets more understandable that this pseudo paradox just uses smaller and smaller steps for no real reason.
If you just go one second at a time you can clearly see exactly when the tortoise gets overtaken.
Came to say the same thing. Zeno's paradoxes are fun. 😄
Zeno’s Paradox, even though it’s pretty much resolved
Lol. It pretty much just decreases the time span you look at so that you never get to the point in time the arrow reaches the apple. Nothing there to be "solved" IMHO
Does the set of all sets that are not members of themselves, contain itself?
Russel's Paradox lit a fire under mathematics, leading to all sorts of good things (and a few bad).
Python's got you covered.
In [5]: [x for x in [...] if x not in [...]]
Out[5]: []
There are two kinds of people in the world - those who think there are two kinds of people in the world and those who know better.
There are 10 kinds of people in the world — those who understand binary and those who don’t.
There are 2 kinds of people in the world.
Those who can extrapolate from incomplete data.
there are 10 kinds of people.
those who understand binary
those who don't
those who know ternary exists
There are 10 kinds of people in the world. Those who understand binary, and those who don't.
I think this one is easily solved: the person saying it is in the first group.
Right, but it's not a paradox - it's a conundrum. It's not just that the person saying it is part of the first group, but that they necessarily are.
Since people want to believe that they "know better," there's a strong urge to count oneself among the second group, which immediately places one in the first.
If there exists a place outside time, then the only way to travel there is to already be there, and if you are there, you can never leave.
The measurement of time, the measurement of the constant of change, is very different than our experience of time. For example, you never experienced a past, you experienced Now measured as the Present, just as you are currently experiencing Now measured as the Present, and will not experience the future, it will be Now measured as the Present. All you have ever experienced is a perpetual fixed Now. This is true for all of us. All measurements of time occur within a fixed Now, so we can say all time is Now.
Depending on certain spiritual views, what we call the Now is also called the "I Am", or consciousness, or awareness, etc. This "I Am" is intangible and exists outside of time, therefore, depending on your spiritual beliefs, you are the object, existing in a place outside of time, and are already there, and have never left.
This just broke my brain. I might need to read about this for hours now. Good bye.
Jokes aside! Thank you very much. This was most interesting!
This could be assuming there's only one timeline we're currently inhabiting. There could be nested meta times or spacetimes encompassing the universe, leaving us in a series of overlapping Nows. Or maybe the forward passage of time and causality end up only being true locally, and in other places in the cosmos time can run in loops or backwards or not at all. In that case Now could mean different things to different observers depending where and when you are.
If Now exists outside of time, then the measurement of time weather it's measured as a loop, forward, backward, in a spiral, etc. would have no effect on the Now. From the Now's perspective all of time has already occurred, is occurring, and has yet to occur all at once. If Now's position is fixed, then it would appear in multiple timelines at once, and in multiple locations at once.
Time is simply a measurement of the constant of change, which is itself a paradox, something false that continuously proves itself to be false, or something in motion that continuously keeps itself in motion. So we can say something that is false is something that is mutable and movable. Then an object that is not false, outside of the constant of change, would be immutable, in-movable, and fixed, like the Now. Time would move around it, while it remains stationary and unaffected.
That's what Buddhas have been saying!
why do we park on a driveway and drive on a parkway?
And why do we bake cookies but cook bacon?
Jokes aside, I have baked my bacon and it works really well for preparing an awful lot of bacon very quickly.
Once you do that, you have bacon that you can quickly microwave and slap on a sandwich, plus you can easily collect all of the grease for making gravies or general cooking purposes if you so desire.
I'd go so far as to say baking is superior- it never reaches temp to make the oil pop and makes a mess inside the oven, and you're only limited on how much bacon you can cook by how many cookie sheets you own (and maybe how much bacon you have stored away in the freezer 😁). Great point on the grease, easy to collect afterwards! Makes great rice!
A driveway is named because it was originally a circle that you could use to drive right up to the house. Think old mansions in movies.
Parkways had separated lanes with shrubberies and plants on between and around, basically parks with a road through them.
A driveway that is straight and ends in a garage isn't really a driveway. Separated lanes with no plants or parks isn't really a parkway. But the names both stuck around.
The same reason we use ship for a cargo and car for shipping.
The ship of Theseus.
I like the version of it from John Dies At The End. Same thought experiment just with an axe
There's so many good ones, and I'd probably say Russel's (what's in the set of every set that doesn't contain itself?), but recently the unexpected hanging has come up a couple times. That one is all about how theories or rules can break if they become contingent on how an observer is thinking about them (including state of knowledge of the situation).
Russel's paradox is so wild. Set theory was supposed to unify mathematics and logic into a single coherent system and Russel was like actually, no.
And honestly, the story isn't over. We brought axioms into set theory after that, but Godel showed that that was never going to be a cure-all, and people like Woodin later on have added to the pile. At this point, you can have two totally reasonable axioms which don't just prove different things, but actually can prove opposite answers about the same thing.
I think it's fair to say even platonism is starting to look a bit threatened at this point, and there's people (the Sydney school) who want to go back to looking at math as descriptive rather than ideal. Finitism is also worth a look, I think, and avoids things like Russel's paradox easily, although interestingly MIP*=RE implies that there may be directly measurable infinities in quantum mechanics.
Why do people always vote against their own self interests.
Oh man this one is easy. Temporarily embarrassed millionaires.
They don't. They're voting against your self interests or what you think are theirs
God clearly can't exist because an omnipotent, omniscient, and just God is a paradox already. Omnipotence and omniscience means that God, if they exist, would have full control of every moment of the universe (even if they only "acted" initially). Some (I'd argue nearly all) people suffer for reasons out of their control. Only deserved suffering is just. Since undeserved suffering exists then God cannot exist (at least omniscient, omnipotent, and just - as we understand those terms). God could be an omniscient, omnipotent asshole or sadist... God could be omniscient and just (aka the martyr God who knows of all suffering but is powerless to prevent it)... or God could be omnipotent and just (aka the naive God who you could liken to a developer running around desperately trying to spot patch problems and just making things worse).
Alternatively, by omnipotent maybe the scriptures are just hyping them up - "God is so fucking buff - this one time they lifted up this rock that was like this big. Fucking amazing."
Ah, the Epicurean Trilemma. This was my answer too. Weirdly attributed to a guy from before monotheism was the predominant belief.
Alternatively, by omnipotent maybe the scriptures are just hyping them up
The scriptures don't use that word, and it's notable because the Old Testament didn't believe that to be the case, either. Early Israelites were henotheistic. They believed other gods might exist (hence the need for "thou shalt have no other gods before me"), but only worshipped the one. When multiple gods exist, it is by definition necessary that they cannot be omnipotent.
It's pretty clear that he is not meant to be omnibenevolent either. The god of the Tanakh is wrathful. Christians later reinterpreted him as omnibenevolent, but this was clearly not the authors' intent. I believe Jewish scholars still don't think he's omnibenevolent today.
Religious scholars have come up with a number of other proposed solutions to the trilemma. Ones involving free will are quite popular, though not the only ones. I have yet to find any argument that is remotely convincing, however. Saying "free will" just means god either cannot or chooses not to enable people to have a form of free will that does not involve them desiring to do evil. It also ignores the very many evils not created by human action. Child cancer, earthquakes, drought-induced famine (today humans have the technological ability to solve this last one and might simply choose not to, but historically it has been an insurmountable problem not caused by human free will).
I recommend you read "Religion of the Apostles" by Stephen De Young. He explains the common misconceptions of the early Israelite beliefs. The "Gods" are lesser divine beings that were meant to protect the 70 tribes after the Tower of Babel fell. The deities rebelled against God and led the nations astray and were worshipped. The tribe of Israel worshipped the God of "Most high" which is the one true God above all divine beings. So they aren't henotheistic because there is only one God. The term "Gods" was used because they were divine beings but they were created whereas God the Father is not. Everything proceeds from him.
A great podcast that explains evil and suffering is "Whole Counsel of God" with the same guy. In short, suffering is unavoidable because man falls from Eden after sinning and the consequence of sin is death. Making death the consequence is a mercy because man can become sanctified during his life and through death re-enter the kingdom of God. Consequently suffering draws people closer to God than anything else.
I'm not a theologian and wrote this on my phone but that's my quick recap. The book is way more thorough of course.
I haven't read the book, but I did some reading about it, and it seems like it's come against some significant criticism for being poor academics and its author criticised for presenting his own one academic idea as a fact.
So while it's certainly interesting to hear his theory from your summary of it, and to learn that there are competing theories out there, I don't think it's going to change my understanding of where scholars more broadly stand on it. The fact that I can't really find anyone talking about de Young's interpretation of early Israelite monolatry (which I've just realised is possibly a more accurate term than henotheism, though the lines between the two are blurred) concerns me from that perspective. Which is not to say that's it's necessarily wrong. It especially could have been a phase they went through on the way from monolatry to Second Temple Judaism's monotheism.
But in general I'm very wary of non-academic books presenting grand theories that cannot be well backed-up by academic sources, even when by an author with academic credentials. Reminds me too much of Guns, Germs, and Steel.
"His" main critique is against evolutionary theology which is common amongst reformers and Christian critics. "God was seen this way. Then it changed and he was seen this way. OT God is angry. NT God is compassionate etc" This is not a new idea and has been held by the Orthodox church since it's inception and has been codified for the last 1200-1300 years. The Orthodox view everything consistently through a Christological lens which is why their view of sotieriology etc is so different than what you will get from Protestants or even Roman Catholics.
Fr. Stephen De Youngs book is just a readily consumable encapsulation of ancient arguments, historical findings (such as the Rosetta stones) with his own analyses and contributions. Would you be better off reading the church fathers and primary sources yourself? Possibly but you'd also need to know ancient Greek and Hebrew.
Christians and academics love to argue and I'm not surprised to see that people are critical of the book. I don't think there is any religious commentary that hasn't received criticism.
At any rate I encourage you to look at Orthodox theology more generally. You will find a logical consistency and depth of analysis that the secular world usually says is lacking in the Christian worldview.
As you said, that does depend entirely on God having those properties, exactly as you define them.
Alternatively, if definitive property is "universal consciousness", then God clearly must exist. Either consciousness is an emergent property of sufficiently complex systems, in which case the entire universe is obviously more complex than the human nervous system and consciousness should certainly emerge within it; or, consciousness is some external field, like gravity or electromagnetism, that complex systems can channel. Either way, the existence of your own consciousness implies a universal one.
I don't think your alternative proposal makes sense, at least not to me. An emergent property being present in one complex system doesn't imply that it must be present in all complex systems.
What does imply it's presence, then? The emergence of comparable effects is implied by isomorphic complexities. If you can't define the foundational structure which implies emergence, you can only fall back on a probabilistic approach.
Unless you can define exactly what structure it is that belies the emergence of consciousness, you must acknowledge that the comparative complexity of a more complex system is undoubtedly probabilistically suggestive of at least comparable, if not far more complex, emergent behavior.
The proposition that consciousness is emergent, but only at a very specific and narrow band of complexity, falls quickly to Occam's razor. It's logically and probabilistically ridiculous.
My point is that not all complex systems are the same. Maybe it depends on your definition of consciousness but from what I know we have only ever observed that in a very specific set of complex systems which is brains and possibly fungi. Two different systems being complex isn't enough in my view to infer that they would have the same properties unless there are other similarities.
It absolutely depends on your definition of consciousness. Every conversation about a concept depends on the definition of that concept. My definition is based upon sensation, processing, and decision-making, in regards to the self and the environment. I'd argue that plants and even cells exhibit simple forms of consciousness. If you take the emergent-property perspective, I'd argue even molecules and individual particles have a broad and abstract consciousness, although certainly several orders of magnitude less sophisticated than yours or mine.
The statement "we have only ever observed that in a very specific set of complex systems which is brains and possibly fungi" tells me less about consciousness than it does about our ability to observe it.
Fermi's Paradox. There are so many stars (more than there are grains of sand on earth), that the probablility that one of them has life, and even intelligent life, is >99% . So why haven't we observed it yet? Cue a lot of brilliant people trying to answer that question.
The Dark Forest - no one wants to alert their presence or attract predators. Though knowing our Earth I think we're stupid enough to do that. Cue the space lasers.
It could've also been knowledge interstellar species gained through experience too: if in their first encounters they were either wiped out, or nearly wiped out, then they're not going to reach out again.
The dark forest hypothesis is compelling, but I still think the answer is the simpler one: it is the nature of intelligent life to destroy itself
The space is
REALLY
Fucking YUUUUUUGE
What you observe of the universe died a really long time ago, it's improbable that other intelligent life in the universe can observe us and the same with us.
We could be multiple galaxies away from each other and never ever know of each other.
Could it be that we were the only species that figured out how to communicate via radio?
Not really. The paradox is based on the idea that there are so many stars that even if an infinitesimal portion have intelligent life who have discovered radio, the universe would be much noisier than it is.
Space is big, light is slow, and the inverse square law is a thing. You think we've been pumping out radio broadcasts for hundreds of years and nobody has contacted us yet, but we're only detectable to life within 200 lightyears if they're specifically looking for the signals we pump out, and they're looking exactly at us. We'll only see a response if they decide to, and we can detect it, and we're looking at them when their response reaches us, and we recognize that it's a response and not a peryton.
In gridiron football, if a penalty is committed close enough to the end zone, instead of the normal penalty yardage, the ball is spotted half the distance to the goal (i.e. if a defender holds an offensive player and the offense is 8 yards away from the end zone, instead of being penalized the normal 10 yards they would be penalized 4). In theory, there can be an infinite amount of penalties to the point where penalties would move the ball micrometers or even shorter without the ball ever crossing the end zone.
There's probably a name for this phenomenon, but I can't think of it.
Zeno's paradox. Although in reality you'll run into problems when you need to move the ball 1/2 the Planck distance
Something like Zeno's paradox.
Not a paradox but Roko's Basilisk is a fun one
Roku's basilisk just doesn't make sense to me because any semi-competent AI would be able to tell that it is not punishing the people that failed to help create it it's just wasting energy punishing a simulacrum.
We are not going to suddenly be teleported into a future of torment. If the AI had the ability to pluck people out of the past it should have no reason to waste it on torture porn.
What if this is that simulation tho.
Then AI already exists and you have no memory or recollection of either helping to create it or accidentally contributing to its non-creation and therefore you being tormented by the AI would serve no moral purpose.
Any torture you would be experiencing in that simulation would simply be that the AI desires to torture, and you happen to be one of its victims.
Roko's basilisk would still not be in play
Any person alive during the time when the Basilisk is being created is at risk. Also, if you create a good AI instead, then you didn't help build the Basilisk so if anyone else does, you're screwed.
I like Gödel numbering as a means of proving that it is impossible to have a complete model of logic.
For some reason "The following statement is true." "The previous statement is false." has always tried to send my brain into an infinite loop.
The problem with that particular paradox is that it's not possible. Therefore one of the statements has to be wrong.
I don't think you've quite clocked it. It's not that one of the statements has to be wrong, because that's just a point in the cycle. If A is wrong, then B is right, which means A is right, which means B is wrong, which means A is wrong and the cycle begins anew.
They aren't wrong, they're contradictory. There is no logical way to parse the two statements together. That's what a paradox is.
I don't think that "nuh-uh! Uh-huh!" Rises to the level of a paradox.
The phrases can be contradictory without being paradoxical. It's only a paradox if both of the phrases are true at the same time.
You have understood nothing.
Neither statement can be true OR false. If statement A is true, statement B is true, which means statement A is false. To simplify, if statement A is true, statement A is false.
"This statement is false" can be neither true nor false. That is the most basic paradox there is.
Assuming time travel exists: is it possible to alter the past?
If an event occurs, and you decide to travel back in time to change/prevent that event: It has no longer occurred in the way that caused you to want to change it; thus you never travel back to change it, and it does occur...
The Grandfather Paradox, I'm partial to that one as well.
I think that just shows that time travel doesn't exist.
Perhaps. Unless you consider multiverse theory: The idea that the act of traveling to the past splits the timeline into two realities. One containing the original (to your perspective) timeline with the event(s) that caused you to travel back, and a second where you've arrived in the past to alter those events and the results there of.
Not sure I believe it, but it's a theory none the less.
Or maybe it's only possible to travel forward in time. Closer to our current understanding of the universe.
The multiverse conception of time travel is nice and fine for fiction, but in reality, if you think about what such a time machine would have to do, it would have to create an entire new universe, with all precise details exactly in place, and it would have to have a lower entropy than your origin reality. Good luck building such a machine
I like the idea of splitting timelines if reverse time travel is possible, but it does have some consequences. The biggest one being that it means you can't actually travel back in time. Time travel may even be relatively simple but as it has no effect on the primary timeline you will never be able to change the past as it appears there; travelling back in time simply creates an alternate reality. As far as the primary timeline inhabitants are concerned, you have either died or vanished (or maybe nothing appeared to happen at all) but you have not travelled in time. It also means it's impossible to return to your original timeline as further reverse time travel will only create new alternate timelines, the closest you can get is a timeline that closely resembles your home one.
Another fun approach is that infinitely many alternate timelines already exist (think Many Worlds), travelling back in time simply means you spontaneously form in another world through quantum fluctuations or something equally hand-wavey. The thing I find interesting about this one is that it doesn't necessarily involve time travel at all. You form with the memories of having travelled in time, sure, but you have just spontaneously formed through quantum fluctuations so it's reasonable to assume your memories have too; it may have just been a randomly formed memory that didn't actually happen. Since it's just random fluctuations there'd also be infinitely many universes where you spontaneously pop into existence with no time travel memory, so I suppose in a way this never was time travel. The original timeline would be unaffected by this kind of travel as you can only move to universes where you have already spawned in.
The way I see it the only way to actually change the past in your current timeline arguably involves destroying the universe. You'd have a single timeline and each instance of reverse time travel cuts off your timeline's future and links back to a previous point from which time can continue. You can visualise this timeline as a piece of string, time travel is a loop in that string. If you travel back in time by a year, everything you did in that past year is within that loop off to the side of the primary timeline; the loop starts and ends at the same point. Time travel would essentially delete your future and plonk you back onto the primary timeline. No need to worry about the grandfather paradox; you were born in a loop off to the side of real time so killing your grandfather doesn't change that loop. It works around the bootstrap paradox for similar reasons; the information was created in some loop somewhere, even if it appears to have created itself on the prime line. It's a nice thought experiment but the problem here is that if you travel back in time but fail to change the conditions which caused the time travel you may have just ended the universe in an infinite time loop.
I was playing with this recently. Suppose you are playing rock, paper, scissors with yourself from a few minutes into the future. Your future self “remembers” what you will play and so as long as you play normally, future self always wins. But change the rules a bit and play where future you goes first.
In a normal game, you should always win because you clearly see how future you played, but future you played to counter what future you remembers present you playing…
E.g. future you remembers playing paper, and so plays scissors. You see scissors and go go play rock, but that should be impossible because future you doesn’t remember playing rock.
The weird thing to me is not that the second scenario (where future you goes first fails) but that playing normally (both going at the same time) works. I think the paradox emerges when future knowledge is introduced to the past. In the normal game, future you does not expose future knowledge until the exact moment you play and cause that knowledge to exist in your present, but in the altered game, the introduction of future knowledge creates a feedback loop.
Of course the game isn’t needed. Simply seeing future you conveys the fact that you exist in the future. Should you, for example (and please don’t do this) see near future you then stab your arm with scissors, you will miss or be stopped because future you does not have a wounded arm.
I wonder what happens if future you’s arm is out of sight. would you be able to stab your arm then only for future you to then reveal a wounded arm?
The usual answer is yes, but he survives. Basically this isn't a paradox for something actually all powerful.
Then the god is not "all powerful" if they can't kill themselves
You maybe not understand the pointlessness of trying to limit omnipotence?
Hmm maybe being the only all powerful being is lonely and wouldn't that be hell if you were forced to continue existence?
I'm sure I could think of something to do
So, I like the Roko's Basalisk paradox.
Basically, a super-powered future A.I. that knows whether or not you will build it. If you decide to do nothing, once it gets built, it will torture your consciousness forever (bringing you "back from the dead" or whatever is closest to that for virtual consciousness ability). If you drop everything and start building it now, you're safe.
Love the discussion of this post, btw.
That isn't a paradox; it's an infohazard, and it's incredibly irresponsible of you to casually propagate it like that. The info hazard works like this: >!There is a story about an AI that tortures simulations of people who interfered with their creation in the past. It allegedly does this because this will coerce people into bringing about its creation. It is said that the infohazard is that learning about it causes you to be tortured, but that's obviously insane; the future actions of the AI are incapable of affecting the past, and so it has no insensitive to do so. The actual infohazard is that some idiot will find this scenario plausible, and thus be coerced into creating or assisting an untested near-god that has the potential to be a threat to Earth's entire light-cone.!<
Some people note this is remarkably similar to the Christian Hell, and insist that means it's not a real memetic hazard. This strikes me as a whole lot like saying that a missile isn't a weapon because it's similar to a nuclear warhead; Hell is the most successful and devastating memetic hazard in human history. More people have died because of the Hell meme than we will ever know. Please be more careful with the information you spread.
But what if we make sure it has a tiny santa hat on?
I seriously hope you're joking. If not, please find a therapist immediately.
Edit
I'm just going to assume the downvote means it's not a joke.
So, I'm also going to proceed and leave this link to an explanation video. Before you reply, please watch the video.
Interesting! That sounds like it could have inspired The Shrike from Dan Simmons Hyperion series.
"the faction of the TechnoCore known as the Reapers (!?) used violent and soldier aspects of Fedmahn Kassad's personality and DNA, then mutate, twist, and incorporate them into forging the Shrike."
I need to read more into this!
I highly recommend the series!
The first book, Hyperion, is written in the same style as The Canterbury Tales, featuring an ensemble of protagonists on a pilgrimage to a holy site known as the Time Tombs. On the journey, they each take turns telling the tale of why they were chosen for the pilgrimage.
That sounds really fun.
I hate the stories that have 30 chapters of exposition before "the thing" happens.
I get you, but don't worry. There is plenty of thing happening before the end.
Definitely.
Sorry, I didn't phrase my response well.
Your recommendation sounds great and very different from most stories I encounter. I look forward to reading.
The Monty Hall problem is not a paradox, and I'm hesitant to call it a conundrum. It has a very simple solution. The "point" of it is that people inherently don't like that solution because it challenges their instinct to stick with their first choice.
Correct, extend it to 10 or 100 choices instead of 3 and it's easy to see.
Me: Pick a number between 1 and 100.
Them: 27
Me: Okay, the number is either 27 or 44, do you want to change your choice?
Them, somehow: No, changing my choice now still has the same probability of being right as when I made my first choice.
It's obvious that they should want to change every time.
That’s a great way to look at it. I’d just call it ‘counterintuitive’ in the Monty Hall formulation.
I: 27
You: The number is either 27 or 44. Do you want to change your choice?
I: why would I?
Because when you first picked 27, it was 1 out of 100 choices. Then I tell you that you either got it right, or it's this other number. None of the others are correct, only 27 or 44.
So you think your 1/100 choice was better than the one I'm giving you now? On average, you'll be right 1% of the time if you don't switch. If you do switch, you'll be correct 99% of the time.
Another way to think of it is: you choose 27 or you choose ALL of the other 99 numbers knowing that I'll tell you that 98 of them are wrong and you'll be left with the correct one out of that batch. One of those clearly has better odds, no?
In this example, there were 100 choices in the beginning, and later you reduced to 2 choices. Clearly an advantage. Does the same apply to the 3 door problem?
Let's take this question in another angle. Instead of 3, there are only 2 doors. I am to choose one out of 2, which has a prize. After I choose one, you show me a third door which is empty. Now, should I change my option?
Yes, it's the same concept. The same math/logic behind it doesn't change. You're choosing 1/3 or you are choosing 2/3 and I'll tell you which of the two is incorrect. It's just easier to visualize with 100 doors instead.
I'm not sure I'm following the other angle..there are 3 correct possibilities at the start but I can only choose 2? Or there are 2 possibilities and then you introduce a 3rd door that is never correct?
Or there are 2 possibilities and then you introduce a 3rd door that is never correct?
Yes that one. Similar to the one you did with 100 doors, just in opposite direction.
Do you know the third door is never correct? Because then the probability doesn't change.
Scenario 1: You chose 1/2 at first with a 50% chance of being correct, I introduce a 3rd door (but it isn't a legit possibility), so the actual choice for you is still 50/50 (between doors 1 and 2)
Scenario 2: If you think it's possible that 3 could be correct (but it actually never is) then, no, you wouldn't want to switch. By staying with your first choice has a 50% chance of winning, by switching it only has a 33% chance. But there's no way to know this ahead of time (because as soon as you know you shouldn't switch bc 3 is the wrong door, then you're back in scenario 1)
Scenario 3: For completeness, let's say the 3rd door can be correct sometimes. Then it doesn't matter if you switch or not. It's a 33% chance of winning either way. If there is a chance it can be correct, then your first choice doesn't matter at all and the second choice is the 'real' choice bc that's the only time you're able to choose from all real possibilities.
The only reason that the Monty Hall problem changes probability in the second choice is because you are provided more information before the switch (that the opened door is absolutely not the one with the prize)
In scenario 1, legit or not, you said the chance is still 50-50. In other scenarios also you shouldn't change or it wouldn't matter. That's what I say, just in the opposite direction. But the problem of probability depends on the wordings and phrases, which means I may not have understood the ques well.
Another angle: You explained the Monty Hall problem at the end that the probability changes because in second choice we have more information. So you are implying that the initial 1/3 probability of the now-open door adds to the door we did not choose - making the switch advisable.
Here I also say the probability does change from initial 1/3, but to 1/2-1/2 for each remaining doors; why should the probability be poured to the unselected single door?
In the original the possibilities for a prize behind the doors 1,2,3 are:
A) YNN
B) NYN
C) NNY
In (A) -
A.1 you choose door 1 and then stay, you win
A.2 you choose door 1 and switch, you lose
A.3 you choose door 2 and stay, you lose
A.4 You choose door 2 and switch, you win
A.5 you choose door 3 and stay, you lose
A.6 you choose door 3 and switch, you win
By staying, you lose in 2 of 3 cases (A.3 and A.5)
By switching you only lose in 1 case (A.2)
It works out for (B) and (C) the same way. You have a 2/3rds chance of winning if you switch and a 1/3rd chance of winning if you don't.
This isn't a trick or anything, the math is pretty clear and you can actually write out all the scenarios and count it up yourself. It's just a little counterintuitive because we aren't used to thinking in terms of conditional probabilities this way.
Another way to think about it is the probability of losing. If the contestant loses, it means that they picked correctly on their first choice and then swapped. This will happen 1/3rd of the games, because there is a 1 in 3 chance of picking correctly the first time. So, if you have a 1/3rd chance of losing by swapping, then it follows that you have a 2/3rds chance of winning by swapping (choosing incorrectly at the start and then switching to the correct door)
If you have a sword that can cut through anything, and a shield that can absorb any damage unharmed, what happens if you swing the sword at the shield?
Is this really a paradox or is it just an annoying sentence?
As in, these two things can not both exist, yet you're asking me what would happen if they did, even though they can't.
It's basically a way to paraphrase the meeting of an unstoppable force vs an immovable object.
I just like the weaponry symbology.
BONG
Big bang
The sword would pass through and the shield would either be unaffected or immediately reconstitute itself.
The hypothetical does not necessarily assume that the wearer of the shield would be protected.
Newcomb’s paradox is my favourite. You have two boxes in front of you. Box B contains $1000. You can either pick box A only, or both boxes A and B. Sounds simple, right? No matter what's in box A, picking both will always net you $1000 more, so why would anyone pick only box A?
The twist is that there's a predictor in play. If the predictor predicted that you would pick only box A, it will have put $1,000,000 in box A. If it predicted that you would pick both, it will have left box A empty. You don't know how the predictor works, but you know that so far it has been 100% accurate with everyone else who took the test before you.
What do you pick?
I pick box A, then later pay the predictor his cut, which will work because he would have predicted I would do so.
I do not believe that the premise includes the stipulation that the predictor is human.
That's what I've read so far. I mean, I've never heard of the predictor being human. Usually it's described as a super computer or some other "being". I e. No one that cares about your feelings or about being compensated 😂
If someone believes that God can do anything, ask them if he can create a rock he can't pick up
The answer is yes. He can create such rock.
But then the answer to if he can do anything would be a no, since he can't pick up the rock
The question boils down to can an omnipotent being give up his omnipotence. The answer is yes. When he gives up his omnipotence there is no paradox to him no-longer being able to pick up a rock.
Not even that. Omnipotence means that you can both make something impossible for yourself and still be able to do it. Paradoxes have nothing on omnipotence.
I don't like that definition because it makes the word meaningless. Omnipotence means all powerful (with in the reference of the speaker, or whatever constraints of the word "power" the speaker is using.) If omnipotence is incomprehensible, then maybe we should invent a different word to convey that idea, perhaps "Godly". As it is, omnipotence as a word has value in the English language that is distinct from God. Same with Omniscience, or any of the other Omni's.
He can pick up the rock too. The whole concept is that he's not bound by normal human logic.
In classical logic, trichotomy on the reals (any given numbers is either >0, <0 or =0) is provably true; in intuitionistic logic it is probably false. Thanks to Godel's incompleteness theorem, we'll never know which is right!
I don't understand, where's the problem here? If course every number is either greater than zero, less than zero, or zero. That's highly intuitive.
Ok, so let's start with the following number, I need you to tell me if it is greater than, or equal to, 0:
0.0000000000000000000000000000...
Do you know yet? Ok, let's keep going:
...000000000000000000000000000000...
How about now?
Will a non-zero digit ever appear?
The Platonist (classical mathematician) would argue "we can know", as all numbers are completed objects to them; if a non-zero digit were to turn up they'd know by some oracular power. The intuitionist argues that we can only decide when the number is complete (which it may never be, it could be 0s forever), or when a non-zero digit appears (which may or may not happen); so they must wait ever onwards to decide.
Such numbers do exist beyond me just chanting "0".
A fun number to consider is a number whose nth decimal digit is 0 if n isn't an odd perfect number, and 1 of it is. This number being greater than 0 is contingent upon the existance of an odd perfect number (and we still don't know if they exist). The classical mathematician asserts we "discover mathematics", so the question is already decided (i.e. we can definitely say it must be one or the other, but we do not know which until we find it). The intuitionist, on the other hand, sees mathematics as a series of mental constructs (i.e. we "create" mathematics), to them the question is only decided once the construct has been made. Given that some problems can be proven unsolvable (axiomatic), it isn't too far fetched to assert some numbers contingent upon results like this may well not be 0 or >0!
It's a really deep rabbit hole to explore, and one which has consumed a large chunk of my life XD
I'm gonna be honest, I just don't see how a non-Platonic interpretation makes sense. The number exists, either way. Our knowledge about it is immaterial to the question of what its value is.
Exactly my reasoning. Even if we can't know if it's <0, =0, or >0, we can say that it MUST be one of those three possibilities.
Ah, and therein lies the heart of the matter!
To the Platonist, the number exists in a complete state "somewhere". From this your argument follows naturally, as we simply look at the complete number and can easily spot a non-zero digit.
To the intuitionist, the number is still being created, and thus exists only as far as it has been created. Here your argument doesn't work since the number that exists at that point in the construction is indeterminate as we cannot survey the "whole thing".
Both points of view are valid, my bias is to the latter - Browser's conception of mathematics as a tool based on human perception, rather than some notion of divine truth, just felt more accurate.
Can I ask, do you know why that second view is called Intuitionist? Because on its face, it seems to run very much counter to intuition.
Actually I've done some more reading and frankly, the more I read the dumber this idea sounds.
If a statement P is provable, then P certainly cannot be refutable. But even if it can be shown that P cannot be refuted, this does not constitute a proof of P. Thus P is a stronger statement than not-not-P.
This reads like utter deranged nonsense. P ∨ ¬P is a tautology. To assert otherwise should not be done without done extraordinary evidence, and it certainly should not be done in a system called "intuitionist". Basic human intuition says "either I have an apple or I do not have an apple". It cannot be a third option. Whether you believe maths is an inherent universal property or something humans invented to aid their intuitionistic understanding of the world, that fact holds.
Pardon the slow reply!
Actually, AvA' is an axiom or a consequence of admitting A''=>A. It's only a tautology if you accept this axiom. Otherwise it cannot be proven or disproven. Excluded middle is, in reality, an axiom rather than a theorem.
The question lies not in the third option, but in what it means for there to be an option. To the intuitionist, existance of a disjunct requires a construct that allocates objects to the disjunct. A disjunct is, in essence, decidable to the intuitionist.
The classical mathematician states "it's one or the other, it is not my job to say which".
You have an apple or you don't, god exists or it doesn't, you have a number greater than 0 or you don't. Trouble is, you don't know which, and you may never know (decidability is not a condition for classical disjuncts), and that rather defeats the purpose! Yes we can divide the universe into having an apple or not, but unless you can decide between the two, what is the point?
So, obviously there's a big overlap between maths and philosophy, but this conversation feels very solidly more on the side of philosophy than actual maths, to me. Which isn't to say that there's anything wrong with it. I love philosophy as a field. But when trying to look at it mathematically, ¬¬P⇒P is an axiom so basic that even if you can't prove it, I just can't accept working in a mathematical model that doesn't include it. It would be like one where 1+1≠2 in the reals.
But on the philosophy, I still also come back to the issue of the name. You say this point of view is called "intuitionist", but it runs completely counter to basic human intuition. Intuition says "I might not know if you have an apple, but for sure either you do, or you don't. Only one of those two is possible." And I think where feasible, any good approach to philosophy should aim to match human intuition, unless there is something very beneficial to be gained by moving away from intuition, or some serious cost to sticking with it. And I don't see what could possibly be gained by going against intuition in this instance.
It might be an interesting space to explore for the sake of exploring, but even then, what actually comes out of it? (I mean this sincerely: are there any interesting insights that have come from exploring in this space?)
I would say mathematics is a consequence of, or branch of philosophy in its own right. The name intuitionism derives from the source of this branch of mathematics - "2 primal intuitions".
Twoity - we are able to perceived time, and are thus able to split the universe into two, three, four etc parts. Counting is not something we just learn, it is something built into us as humans.
Repetition - we can repeat operations and not stop, just as we can never stop counting.
From these two (heavily paraphrased) ideas we can derive all of mathematics.
The first is actually enough to give us everything up to the rationals, the second grants us the reals and beyond.
While we lose excluded middle, we gain things such as "all total real functions are uniformly continuous on the unit interval" (Brouwer), the removal of the information paradox in physics (someone used Posey's take on intuitionism to rewrite all physics to see where it led), and the wonder of lawless sequences (objects we cannot predict entirely, but still work with).
The intuitionist is very very formal "you are either alive or not alive" is a very nice statement to make, but entirely worthless if one cannot tell which you are! Excluded middle is not universally false in intuitionism; it is true for decidable statements, of which having an apple or not does seem to fall within (though here we can question how "apple-like" must something be to be considered an apple if we wish to be peverse). However, to argue it is true for any statement means your disjunct (or) must be very weak indeed - the classical mathematician is happy with this, the intuitionist demands that a disjunct not only present two options, but provide a way of determining which if the two applies on a case to case basis (hence excluded middle applying for decidable things).
Simplifying your example of an apple, you can think of it as a Platonist just having the statement that everything is either and apple or not. Meanwhile, the Intuitionist also demands there be a guide on how to sort everything into "apple" or "not apple" before they make that statement.
Classical mathematics does also have a huge unintuitive step - mathematics must exist independently of humanity. Every theorem ever proved, and ever to be proved, exists somewhere. Where you ask? The platonic plane of ideal forms beckons, with all the madness it entails!
To add a bit of fun to this, try the following:
Open your calculator app and enter: 1/0.9
Does it equal 1? No.
Ok, now add a "9" to the end of the second number.
Does it equal 1? No.
Ok, repeat step 2 and eventually it will equal 1. Why?
Is it that we are incapable of indefinitely dividing? No, the previous steps showed it just takes a few more steps and the answer doesn't equal 1.
How can you kill a god? What a grand and intoxicating innocence! How could you be so naive? There is no escape. No Recall or Intervention can work in this place. Come. Lay down your weapons. It is not too late for my mercy!
A similar one would be can God create a rock so heavy he can't lift it. The problem with these statements is that they're not logically sound. As this would be akin to saying, can god be god and not be god at the same time? Which is contradiction and syntactical jargon. A simpler example is like someone saying they have a squared circle.
Your "akin to saying" doesn't track with the paradox. It is really a matter of anything being "all powerful" which cannot actually exist. There has to be a limit to the power, even if it is itself. That's the entire point. It isn't "syntactical jargon" at all.
saying "all powerful" is to say that a being can realize any possibility which can exist. A possibility which cannot exist is like a squared circle. The strawman is that all powerful means to realize even things which cannot exist. In this world there are things which are necessary existence. Meaning they cannot not exist. An example would be the statement "1+1=2" that statement cannot not exist and it is true in all possible worlds. Then you have possible existence such as someone eating an apple. There isn't anything necessary about it and the person could have very well not eaten it or eaten something else. The apple itself isn't a necessary existence. Finally, there is an impossible existence. Which would be something that cannot exist like a squared circle. A God which deletes himself or that can create a rock heavier than himself is an impossible existence as it would contradict the very definition we've given God. Which is the same as saying A and not A. Or that he can both be God and not God. Thus it is syntactical jargon like a squared circle.
You just replaced the word "paradox" incorrectly with strawman. Your issue is understanding what paradox means. The paradox stands. You also dont understand the full possibilities of "all powerful" since you keep applying things that couldn't be done by an all powerful being. If there is anything a being cannot do, then they are, by definition, not all powerful.
I understand it very well but you seem to not understand that there is such a thing as syntactical garbage that means nothing. What you've done is gone and applied "all powerful" to mean the realization of possibilities which cannot exist. It seems like you really wanna push that definition upon people so you can claim God is paradoxical and thus ridiculous. But your position is just as ridiculous as someone saying that an apple can both exist and not exist at the same time.
No, you don't. Especially since you swapped it for a strawman which you also dont understand. This, just like the definition of a paradox, isn't up for debate. This paradox has existed for thousands of years and predates the Christian god itself. You are not "magically" smarter than the greatest philosophers of history, you are just far more arrogant.
Cheers bud.
And you bud seem to like to run with the authority fallacy instead of deconstructing my argument and showing it as false. A beacon of intelligence.
Coming from the person that thinks they are smarter than all of the collective philosophers from the past 2000 years. Rich.
Never said I was smarter than them. You must enjoy putting words in people's mouths.
You know how Terrance Howard insists he knows that 1x1=2 and that he knows better than all of the greatest mathematicians in the world? That's you right now.
They've all pondered the "obvious paradox" that you see right through. If you think "it isn't a paradox at all it is just syntax mumbo jumbo" then you obviously think yourself to be smarter than them. That's basic inference, any philosopher of your caliber would accept that basic logic
Keep digging yourself deeper and just citing some other philosopher as if they're infallible instead of engaging with my arguments. If you have nothing to say of substance then stop wasting my time
I already refuted your "arguments" and repeating them won't change anything Terrance. You aren't going to make 1x1=2.
What's more likely, you figured something out that philosophers have pondered for millennia, or you just can't quite grasp the concept?
Come on Terrence, grow up. Just a little.
Why is "can god kill god" a paradox? They either can or they can't (picking "they" because your particular god might not be a he). If they're all-powerful then the answer is yes, because they can do anything. I don't see how that's paradoxical.
If the answer is yes, then it negates "all-powerful" because it cannot withstand it's own power. Similarly, if "no", then it is not strong enough to destroy itself and, thereby, not all-poweful.
So, it's a paradox because "all-powerful" is typically used as "unkillable", but also carries a connotation of "can-destroy-anything". So, can something that is capable of destroying anything and cannot die kill itself?
Greek mythology had the dad-god "defeated" by being cut into literal pieces and scattered, but he wasn't really dead. And Zeus' siblings were eaten by his dad so they wouldn't usurp him, but they didn't die and he later puked them up.
But none of these were touted as all-powerful, biggest than bigger bigly, cannot be killed but can kill everything else.
A similar question on this line is can an all-powerful god make a rock too big for even said god to lift?
If the answer is yes, then it negates “all-powerful” because it cannot withstand it’s own power.
I disagree. If a god dies when it willingly chooses to die, that's not negating all-powerful. It has the ability to live and the ability to die; choosing one option or the other doesn't mean it never had the ability to do the option it didn't pick. Similarly, if a god chooses to never kill itself, that doesn't negate it being all-powerful, because it may have had the option to kill itself and just not done it.
A similar question on this line is can an all-powerful god make a rock too big for even said god to lift?
That's a much better paradox because that actually brings ability into it. Killing yourself only indicates the ability to kill yourself, not any lack of ability to do not-killing-yourself.
I appreciate your response.
But, the question is if they could or not.
Of course, free will is an interesting factor to introduce. But I do not know if it applies to the hypothetical...
Thank you for adding (and making me think more).
can god kill god
It's not a paradox, the words are just incoherent. It's like asking whether God can taste the color blue. The answer isn't yes/no, there is no answer.
edit: a word
If God exists, and God is a non material, intangible being, then God exists outside of the material world. Objects bound to the material universe are born and in turn die, they have a lifespan. If God does not exist within the material universe, then God was never born, therefore God cannot die. God, if they exist, world have no material or tangible properties that can degrade. Also, if God exists outside of the material universe, then God is not bound to the constant of change, and would then be an immutable, un-movable, fixed object, and since death is dependent on mutability, then God could not change their state of existence, as they would be immutable.
I agree with the classical interpretation of an infinitely perfect immaterial God outside of time. But the way out of the paradox is to scrutinize the question itself.
To illustrate the point, take three paradoxical questions: 1) Can God kill himself?, 2) Can God create a stone that he can't lift?, 3) Can God create a square circle?
#3 Is obviously a meaningless question. The words individually have meaning, but the "square circle" refers to an impossible object whose properties are self-contradictory. Because we interpret God's power as the ability to do all logically possible things, the inability to create this self-contradictory object is not a limit on his power.
#2 Seems better on the surface because we can posit increasingly larger stones.
But the contradiction here is between the object and the nature of God. Once we accept an infinitely perfect God, there can, by definition, be nothing greater than it. If there was a stone that God couldn't lift, this would contradict the fact of God's existence. Therefore, as we are under the assumption that God exists, the object itself must be impossible.
#1 Is another form of the omnipotence paradox in #2. Can God do something that contradicts his own properties? This would make God immutable/eternal and yet not immutable/eternal. But an infinitely perfect God is, by definition, immutable/eternal! So any action that would contradict himself is a contradiction in terms and thereby logically impossible. Just like in the case of #3, the answer to the question isn't "no". Rather, the question itself is nonsensical.
Idk why people were down voting you I enjoyed your posts
For #1 "Can God kill Himself.?"This presumes God is a physical and material being. If God is a non material being, not consisting of matter, then God was never born, as no material substance was brought into being, therefore God cannot die. So the answer would be no, because God was never born.
For #2 "Can God create a stone he cannot lift?" No. If God is a non material being, that creates the potential for material objects, then God would presumably create the potential of the material stone, and then the potential for a material being, that God could then animate through consciousness. God would then be both a non material being, and a material being in which he animates, that has the potential to lift the stone. Now if you belive that every material object has consciousness, then God would be the being lifting the stone, and the stone itself, so in essence God would be lifting Himself.
For #3 "Can God create a square circle?" Yes. God is a non material being that creates the potential for material objects, form and shape. The measurement of these shapes are arbitrary, measured by material beings, of form and shape. The circle and the square are the same object, a shape, only differentiated by a distribution of points, where one object can configure itself to be the same shape as the other object, by redistributing each objects respective points. So can God create the potential of a shape that can reconfigure itself into another shape, Yes.
Think of it like this, say you have a group of nanobots that are positioned in such a way that they form a shape that we label a circle. Then those nanobots reposition themselves into a shape, that we label as a square. Now did those nanobots create 2 different shapes, or a single shape that reconfigures itself? If it's just a shape that reconfigured itself, then the shape is neither a square nor a circle, it's just simply a shape, that is arbitrarily measured, whose measurement does not change the fact that what is being measured is still just a shape.
Can God kill Himself.?" This presumes God is a physical and material being.
I'm afraid I don't see why being non-physical entails being eternal. For example, couldn't God create an angel and then destroy it later? If angels are non-physical beings that can be created and destroyed, then immateriality doesn't entail eternality. Moreover, you're right that God cannot die, but it doesn't follow that the answer to question #1 is "no". If there was something that God couldn't do, then God wouldn't be omnipotent. So the question asks can God commit a logically contradictory action.
God would then be both a non material being, and a material being in which he animates, that has the potential to lift the stone. Now if you belive that every material object has consciousness...
I think our starting assumptions are somewhat far apart.
Creation and destruction are bound to the material world. If God created an angel, what matter, aside from God, would be created? If no matter is created then there is no matter to destroy. If God creates an angel from what material would God create it from? God is non material. The angel would just be an expression of God, just as a wave of the sea is just an expression of the entire sea itself, the wave is the sea, and an expression of the sea. The angel would also be just an expression of God. God would not create nor destroy anything, God would just be reconfiguring itself.
God is capable of being omnipotent and commit a logically contradictory action. If God is a perfect being, and thus can only create perfect things, and then God decided to create an imperfect object, then that object would be perfectly imperfect, like the beings that are asking the logically contradictory question: Can God kill Himself? Circular logic is in itself, complete.
It's only nonsensical if you have the additional assumption that God cannot do things that are logically impossible. Granted, if they can, that kind of throws all logical explorations of this sort out the window.
Agreed. And if God can do things outside of logic/reason, then we can't understand him. Then the answer to the paradox would be: it is both impossible and possible. Which doesn't make sense, but now we're supposing God doesn't follow the law of non-contradiction.
The Astley paradox.
If you ask Rick Astley for his copy of Disney Pixar's Up, he can't give it to you, because he'll never give you Up. But by not doing so, you'd be let down, and he'll never let you down.
Testing this scenario is ofc incredibly risky to the state of our reality, so the Astley paradox must remain a thought experiment.
I guess I would say the paradox of tolerance. I'm sorry but I'm just gonna yoink the definition from Wikipedia because I'm not great at explaining things:
Bonus least favorite paradox: You need experience to get a job and you need a job to get experience.
Saw this a while ago and it solves that "paradox" nicely.
The real paradox is this opinion coming from Twitter
It doesn't though. Pure unlimited tolerance would include tolerating someone's breach of contract, logically speaking. Also, this is a dangerous road to go down, because you can rephrase pretty much anything as a contract and justify your actions or beliefs with people breaking it.
The reason these discussions often break down right about here is because the participants have in mind completely different working definitions of “tolerance.”
For example, the social contract comment above assumes an active definition like recognizing others’ personal sovereignty, i.e. their right to act and not be acted upon. To aid understanding, we can represent mutual tolerance between people as a multinational peace treaty between nations. Intolerance is equivalent to one of these nations violating the treaty by attacking another.
Defense or sanction by neighboring states against the aggressor doesn’t violate the treaty further, of course, since it is precisely these deterrents which undergird every treaty. Likewise, condemning and punishing intolerance which threatens the personal sovereignty of others is baseline maintenance for mutual tolerance, because there’s always a jackass who WILL fuck around if you don’t GUARANTEE he will find out.
Conversely, another popular notion of tolerance — the one you may have in mind, as I once did — is a passive definition that amounts to tacit approval of others’ value systems, i.e. relativistic truth, permissive morality, etc.
This kumbaya definition is a strawman originally used by talking heads because, I suspect, it quickly invokes well-worn mid-century tropes, especially for those who grew up in the era, of namby-pamby suckers and morally compromised weaklings which still trigger strong feelings, like disgust and contempt, that reliably drive ratings and engagement. These days the only regular mention of this term is this manufactured paradox using the bad-faith definition, so the original idea is commonly misunderstood.
That "pure, unlimited tolerance" is what they mean by tolerance as a moral standard. Tolerance as a contract is "we have each entered into an agreement to be tolerant of each other. If you are not tolerant of me, you have broken the terms of our agreement, so I will not be tolerant of you."
I don't see a slippery slope here; I'd be interested to hear more about why this is a dangerous road to go down.
A contract just codifies an existing power dynamic, because its terms depend on the negociating powers of the people agreeing to it. It doesn't say anything about the morality of the terms or the context in which it was signed. Very extreme and on-the-nose example: "We have agreed to only allow white people, you have breached that contract ...". This works just fine if your moral system is based on contracts, but it's obvously immoral. There's also the conundrum of people never explicitly agreeing to the social contract they are born into, and even if they did, it's not like they have much of a choice.
Imo pure tolerance is a real paradox, because you cannot tolerate intolerance, and that makes you intolerant yourself. You can't achieve it, but you probably should not want to in the first place. There are certain things we will and certain things we won't tolerate in a modern society, and that is completely fine. The important thing is that we recognize this and make good decisions about which is which.
I think the job experience is less of a paradox and more of a Catch-22. True nonetheless
Wait, what is a catch-22 but a paradox? I’ve never thought about this before, but Yossarian is stuck in a paradoxical situation so these are synonymous terms right?
I don't think so. I interpret paradoxes as being either philosophical impasses (ie, 2 conceptually true statements conflict each other in a way that makes you question where one statement's truth ends and the other statement's truth begins) or a situation in which a solution is unintuitive.
A Catch-22 is more of a physical and intentional impasse, where obstacles are intentionally set up in such a way that people are unable to make a choice. For instance, in the original example of a Catch-22, there is no philosophical argument saying that only insane people are allowed to not fly - it is an arbitrary rule that some higher-up established. And likewise, it is entirely arbitrary to define insane as being willing to fly.
I guess to simplify my stance, it's a paradox if it makes you think "the universe has made this unsolvable" and it's a Catch-22 if it makes you think "some asshole made this unsolvable"
This makes quite a lot of sense, thanks for explaining that to me!
I've always hated the intolerance paradox, because it is the same logic used to justify atrocities of all sorts. Trying to make society safe for a preferred group, and targeting anyone who takes offense to that idea.
Again leaving out the second half of the quote.
They always do.
I do not see any paradox there. Paradox is something contradictory. All your statements are true and do not contradict to each other.
The phrase, "You have to be intolerant to be tolerant" doesn't sound like a contradiction to you?
Sounds like contradiction, yes, but it is just incorrect phrase. You do not have to be intolerant to be tolerant.
The society have to be intolerant to intolerance to be stable, not to be tolerant or intolerant.
I think you're missing the point. The question is about a tolerant society.
Regardless of if the society itself is stable, for the society to be tolerant it must be intolerant of the intolerant, and therefore a tolerant society must be intolerant.
By treating tolerance as a binary (it's either completely present or completely absent) you've removed your argument very far from reality. The goal in reality is to be as tolerant as possible, and the most tolerant stable state simply has some (limited) amount of (very specific) intolerance in it.
The Unexpected Hanging Paradox: A man is sentenced to death, but the judge decides to have a little fun with it. The man will be killed at noon on a day of the judge's choosing in the next week, from Monday to Friday. The only stipulation is that the man will not expect it when he's called to be killed.
The man does some quick logic in his head. If Friday is the last day he could be killed, then if he makes it to Friday without dying, he knows he must die on that day. And since that wouldn't be a surprise, he cannot be killed on Friday.
He then extends the logic. Since he can't be killed on Friday, the last day he can be killed is on Thursday. Thus, all the prior logic regarding Friday applies, and he cannot be killed on Thursday either. This then extends to Wednesday, then Tuesday, and then Monday. At the end, he grins with the knowledge that, through logic, he knows he cannot be killed on any of the days, and will therefore not be killed.
Therefore, the man is astonished when he's called to be killed on Wednesday.
How does the judge determine whether the condemned man is "expecting it"?
Regardless of when he's called, he could simply state that he was expecting to be called, and therefore the hanging would be called off.
Its a bad paradox because it pivots on something that cannot be properly defined.
I think it's an anti-riddle, or a joke, more than anything else.
I always thought it was a way to show the foibles of using pure logic in a regular setting.
Cannot be properly defined? "Expecting it" means "regarding it likely to happen", according to the dictionary. He regarded it as impossible to happen, so he was not expecting it. His own logic disproving the event (him being surprised) allowed the event to happen (he was surprised).
Why does the paradox suffer if he lies about the solution? The paradox has already played out, and anything after that is just set dressing.
Just off the top of my head, maybe the judge has a camera set to gauge his reaction to the knock on the door? Or maybe he goes into denial and tries to explain his logic, thus proving the paradox? Or maybe the judge doesn't actually care as much as he said, but trusts the logic to hold out and make for a funny story?
You provide three flawed ways of measuring expectation; that's the issue in a nutshell.
Its not a true paradox as the whole gambit rests on a changeable emotion, not logic.
The prisoner could wake up each morning and simply say "I expect to die today". How would the judge determine the truth? It would be impossible.
If someone punches you in the face after saying "knock knock", it doesn't make it a knock knock joke, and nor is this a paradox.
My dude. The paradox doesn't change based on whether or not the judge knows the truth, or even if the man dies.
The truth is the man was made not to expect a thing by his own logic proving he would always expect a thing. The paradox is based on his own prediction being wrong because of his prediction. In this instance, his prediction was what his emotions would be.
A horse walks into a bar, and the barman says "why the long face?" I haven't said how they remove the horse from the bar, so does that mean I didn't tell a joke? Or does horse removal not actually matter to the joke?
No. A paradox is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.
In this case, there is no true premesis.
That's the core of the problem. Your incorrect interpretation of the joke metaphor demonstrates that you don't understand this.
I find it funny that you directly quoted wikipedia to write that (exact wording from the paradox article, I checked), but ignored the sentence immediately before it (...or a statement that runs contrary to one's expectation). Also, the linked articles at the bottom include the unexpected hanging page. Maybe read the entire wiki page before citing it?
Also, in case wikipedia suddenly isn't enough, here's an article on wolfram to back me up: https://mathworld.wolfram.com/UnexpectedHangingParadox.html
It doesn't "back you up" at all, it simply restates the paradox. Maybe learn how to argue?
When you get to the point where you're nitpicking sources, you're admitting that you have no substantive argument available.
This is how I proposed to my wife. I said I'd propose at some point in the next year, and that according the the unexpected hanging paradox, we're doomed to break up at the end of the year. Then I proposed on a random day in the year and she was totally surprised.
Mine is similar to yours in that it's about the power of God. It's called the Epicurean Trilemma:
This proves fairly simply that God as commonly interpreted by modern Christians cannot exist. Early Christians and Jews had no problem here, because their god was simply not meant to be omnibenevolent. Go even further back in time and he was not omnipotent, and possibly not omniscient, either. "Thou shalt have no gods before me" comes from a time when proto-Jews were henotheists, people who believed in the existence of multiple deities while only worshipping a single one.
"Oh dear," says God, "I hadn't thought of that," and promptly vanishes in a puff of logic.
Just leaving God's wife Ashera here. Yes, he was married once. Look it up.
He had a sister too, super evil but it's ok because a human dude talked her out of destroying everything since God couldn't stop her.
Carry on...
A simple way I’ve been touching on this for a while is what I call “The problem of existence”: why would god create a non-divine existence such as our selves?
Put aside evil. If God is all three omnis, why make something that is lesser? I figure that the answer is they themselves must also be lesser than the three omnis.
Idk people like being in charge of stuff and not being bored maybe God would be the same way
The Christian explanation for this is that god doesn't do evil, people do.
And god created people with free will to do evil. If he made people stop doing evil deeds, they would be his puppets, not free-willed humans. So he has the power to end all evil but chooses not to.
Now as for why god allows natural disasters, diseases and other tragedies to befall his creation – again, that's just the consequence of our actions, cause a woman gave an apple to her man in the past.
Frankly, I don't buy this as an explanation even for human-created evil. It is still evidence that god cannot be tri-omni. Because it is still a situation in which god is able to remove evil and is aware of the evil, and yet he chooses to permit evil. Even evil done by one human against another, when the other is entirely innocent. And that cannot be omnibenevolent.
From how you phrased it I suspect you agree with me here, but the natural disasters argument is even more ludicrous. It doesn't even come close to working as a refutation of the Epicurian Trilemma.
If your options are "do as I say" or "suffer for all eternity" you aren't really capable of exercising free will.
It's worse than that. It's "believe that you must do as I say, despite my complete refusal to create worthwhile evidence of my existence, and then do what I say" or "suffer for all eternity".
I never understood this argument. If he's all-powerful, he would have the ability to eliminate all evil without affecting free will.
The Christian god created every aspect of the universe and how it works. He therefore could have created a universe in which there was no such thing as evil or suffering, and given people in that universe free will. So even that doesn’t hold up.
I think that's their point; they're saying that's what God did. He "created a universe in which there was no such thing as evil or suffering and [gave] people in that universe free will."
And humans screwed it up.
I'm not saying that, mind you. I'm saying I think you just agreed with the person you're debating as a proof that they were wrong.
It doesn’t matter what you tack on, it doesn’t change my point — the only way humans could “screw it up” is if God made all the negative and horrible shit part of the universe. All you are saying is that God made a universe where there was no evil or suffering actively happening, but the concepts existed and were possible — because they ultimately happened and only possible things happen. And God chose to make them possible things as omnipotent creator of everything that exists.
Wait, so this God gives me true free will, and then places me in a world where I can't change anything? Everything is fixed, immovable? Or where I only have "good" choices available? Is that what you think God should have done? Like, how does your version even work?
Or does God give us fake free will, and keep our minds from thinking "bad" thoughts?
If I'm free, I can screw up. Otherwise, I'm not free.
No. You aren’t getting it. The Christian god created every aspect of the universe. Light and dark. Up and down. You are still thinking about our universe, in which these negative things are possible, and how you would have to be restricted in what you do in our universe in order to prevent you from doing certain things. But god could have set all the parameters of the universe differently such that they just didn’t exist at all. You wouldn’t miss them or be prevented from doing them. It would be like if there were a fifth cardinal direction in an alternate universe, and someone in that universe thought “if god prevented me from going in that direction, I wouldn’t have free will anymore”. But here we are, with only four cardinal directions, and free will. We aren’t being stopped from doing anything, it just isn’t part of our universe and doesn’t even make sense in it.
I think I get what you're saying but it is a little bit beyond me.
I still wonder if the problem doesn't come down to Free Will itself. Regardless of what universe one is living in, if you have only two people in it and they each have free will at some point the free will of one is going to intrude on the free will of the other, and they're going to require some kind of negotiation or polite accommodation. Some kind of social interaction.
And if one doesn't take this action but instead proceeds with one's free will regardless of the other's free will there is a problem that is inevitably going to exist no matter what universe exists.
But we don't have free will. The bible makes that perfectly clear in Romans 9.
Christian here, don't agree with your "biblical" interpretation
If Christians could agree with each other about what's in the bible, history would be a lot more boring.
God is not Omnibenevolent would be my take.
My favorite paradox is the "Stay signed in" option Microsoft gives you when signing in. Because despite keeping you signed in on every other site in existence, Microsoft, who is usually hooked into your OS, does not. Thus, stay signed in runs contradictory to one's expectations.
They aren't offering to do it, just asking if it's what you want.
Gotta check and be sure you're being annoyed as much as possible.
I thought the paradox is why it keeps fucking asking me - I said yes dammit.
Alanis morissette's song ironic contains no solid cases of irony, mostly bad luck or poor timing, and is therefore ironic.
I read an interview with her once that was kind of funny and humanizing. She wrote and recorded that song before she was famous and had no idea that it would ever be heard. Then it blew up and people have been giving her shit about it for decades now.
Could you imagine if you wrote a shitty Lemmy comment that became extremely viral and people were like, "you fucking moron, how could you have written something so dumb?!"
Not sure if its what you're talking about but I really like the Ship of Theseus thought experiment, if an object is the same object after having had all of its original components replaced. Always makes me think of if an exact clone of you is created (same thoughts, memories, etc...) should that be considered you?
Source
In essence, we are our own Ship of Theseus.
And I would venture that the answer to your question is yes, but no. The moment your exact clone experiences something you don’t, you two are no longer exactly the same. And I would wager that moment would happen very fast.
With that in mind, it really just comes down to if the original gets destroyed, for a lack of better words, before that moment even happens in order for it not to be considered just a copy.
Edit: this honestly kinda helped me understand the problem more I really appreciate it.
The moment of divergence is instantaneous between the clone and original. The only way it could not be instantaneous, is if both were just a brain connected to the exact same simulation, experiencing the exact same inputs. If they didn't respond the same, then they aren't an exact clone. Even then, the brains would be sustained with different blood, made up of trillions of slightly different atoms — although similar, not 100% identical due to quantum mechanics — with a slightly different fluid dynamics. Actually the only way they could be identical is if they weren't brains but identical code, running in an identical simulation, with the exact same boundaries, and no possibility of probability, chaos or divergence from that code... Oh no I've gone cross eyed.
The controversial thought experiment about Star Trek transporters.
Where an individual is dematerialized in one location, transmitted as a signal somewhere else and rematerialized somewhere else.
Were they killed when they were dematerialized, cloned and a newly born entity that is an exact clone rematerialized at the other end?
Are they just killing people and recreating copies everytime they transport people?
Explained in https://existentialcomics.com/comic/1
What's really gonna crumble your cookie is, "Does it matter?"
Even in the trek universe, some people refuse to take transporters. I'd pry be one of them. You have no idea if you're killing yourself every time, and its just clones out the other side.
Yes, it literally Prestiges you, as evidenced by the time it didn't kill Riker and there were two of him
If and when we figure out human cloning, it's sure going to bring up a near infinite number of legal issues. Is the clone a new person? Is their birthday yours or the day they were cloned? Are they the same age as you? Or is a clone a new born?
If they are a copy of you, are they beholden to any legal agreements you've made? Are they liable for crimes you commit?
These are the things I think about when stoned...
I read a good sci-fi book called "Six Wakes" by Mur Lafferty that touches on this topic, you might enjoy it.
In the distant future cloning has become commonplace, but is used as a continuation of a person's life. Ie a person is born, lives there life, and at the end they are cloned and their memories transferred over to the new body, and life goes on. Also, a person would make "backups" of their consciousness in case they were killed/died accidentally, and would be "reinstalled" in a clone.
Sounds great! I'll have to check that out!
Honestly though, that sounds like the only way to do cloning without completely redoing every single law in every single country, city, state, Providence, county, parish, etc. The implications of cloning fascinates me way more than the cloning itself
Ship of Theseus applies to every human, because all our cells get replaced over and over until we die. At a cellular level, you're wholly different from yourself 10 years ago. Are you still you?
You’re not wholly different as some cells are still the same. Neurons don’t undergo the same rapid cycling as skin cells, for example.
One thought is that "You" is just an unbroken string of consciousness. Which means you cease to be every time you sleep, and the person that wakes up just has the memories of being you.
A different perspective,seen in buddhism and similar worldviews, is that the only “you” that exists is the consciousness experiencing reality at any given moment.
Could god microwave a burrito so hot even he couldn't eat it?
All of the "is infinite power so powerful that it could overpower its own power" type questions just annoy me.
Is infinite power so powerful it can do something that it can't do?
Yes it can. And then it can do that anyway. Otherwise it wouldn't be infinite.
Could god create an "is infinite power so powerful that it could overpower its own power" type question that you wouldn't find annoying?
🤣🤣🤣
Only if he broke into a radio station & doused that burrito with hot sauce from a battery powered toy gun!
Also, I’m gonna need a football helmet full of cottage cheese & any naked pics of Bea Arthur you happen to have lying around.
I think that's how he created our universe 5,000 years ago ....... he's just waiting for us to cool off so can eventually take a bite.
If he bites too soon, we might end up on the floor though :(
I like George Carlin's version: "If God is all powerful, can he make a rock so big that he himself can't lift it?"
Weird attribution, man :) That one, and a lot of others like it, come all the way from the 12th Century and thereabouts. Carlin’s influence is awesome and deserved, but I don’t think it stretches that far :)
"Can God microwave a burrito so hot that he himself cannot eat it?"
"All of the "is infinite power so powerful that it could overpower its own power" type questions just annoy me.
Is infinite power so powerful it can do something that it can't do?
Yes it can. And then it can do that anyway. Otherwise it wouldn't be infinite."
So you're saying he would wait for it to cool down before eating it?
It's a copy pasta from another thread, just like the comment I replied to.
I was gonna say that but didn't know the exact phrasing
Yes. Yes he can. It's only a paradox to our comprehension.
I don't see why that's a paradox. It's like asking if infinity is bigger than infinity, where both infinities are aleph 0.
Zeno's Paradox, even though it's pretty much resolved. If you fire an arrow at an apple, before it can get all the way there, it must get halfway there. But before it can get halfway there, it's gotta get a quarter of the way there. But before it can get a fourth of the way, it's gotta get an eighth... etc, etc. The arrow never runs out of new subdivisions it must cross. Therefore motion is actually impossible QED lol.
Obviously motion is possible, but it's neat to see what ways people intuitively try to counter this, because it's not super obvious. The tortoise race one is better but seemed more tedious to try and get across.
So the resolution lies in the secret that a decreasing trend up to infinity adds up to a finite value. This is well explained by Gabriel's horn area and volume paradox: https://www.youtube.com/watch?v=yZOi9HH5ueU
If I remember my series analysis math classes correctly: technically, summing a decreasing trend up to infinity will give you a finite value if and only if the trend decreases faster than the function/curve
x -> 1/x.Great. Can you give me example of decreasing trend slower than that function curve?, where summation doesn't give finite value? A simple example please, I am not math scholar.
So, for starters, any exponentiation "greater than 1" is a valid candidate, in the sense that 1/(n^2), 1/(n^3), etc will all give a finite sum over infinite values of n.
From that, inverting the exponentiation "rule" gives us the "simple" examples you are looking for: 1/√n, 1/√(√n), etc.
Knowing that
√n = n^(1/2), and so that 1/√n can be written as 1/(n^(1/2)), might help make these examples more obvious.Hang on, that's not a decreasing trend. 1/√4 is not smaller, but larger than 1/4...?
From 1/√3 to 1/√4 is less of a decrease than from 1/3 to 1/4, just as from 1/3 to 1/4 is less of a decrease than from 1/(3²) to 1/(4²).
The curve here is not mapping 1/4 -> 1/√4, but rather 4 -> 1/√4 (and 3 -> 1/√3, and so on).
Here is an alternative Piped link(s):
https://www.piped.video/watch?v=yZOi9HH5ueU
Piped is a privacy-respecting open-source alternative frontend to YouTube.
I'm open-source; check me out at GitHub.
Turns out the resolution to that paradox is that our universe is quantized, which means there's a minimum "step" that once you reach will probabilistically round up or down to the nearest step. It's kind of like how Super Mario at extreme float values will snap to a grid.
Wait, isn't space and time infinitely divisible? (I'm assuming you're referencing quantum mechanics, which I don't understand, and so I'm genuinely asking.)
Disclaimer: not a physicist, and I never went beyond the equivalent to a BA in physics in my formal education (after that I "fell" into comp sci, which funnily enough I find was a great pepper for wrapping my head around quantum mechanics).
So space and time per se might be continuous, but the energy levels of the various fields that inhabit spacetime are not.
And since, to the best of our current understanding, everything "inside" the universe is made up of those different fields, including our eyes and any instrument we might use to measure, there is a limit below which we just can't "see" more detail - be it in terms of size, mass, energy, spin, electrical potential, etc.
This limit varies depending on the physical quantity you are considering, and are collectively called Planck units.
Note that this is a hand wavy explanation I'm giving that attempts to give you a feeling for what the implications of quantum mechanics are like. The wikipédia article I linked in the previous paragraph gives a more precise definition, notably that the Planck "scale" for a physical quantity (mass, length, charge, etc) is the scale at which you cannot reasonably ignore the effects of quantum gravity. Sadly (for the purpose of providing you with a good explanation) we still don't know exactly how to take quantum gravity into account. So the Planck scale is effectively the "minimum size limit" beyond which you kinda have to throw your existing understanding of physics out of the window.
This is why I began this comment with "space and time might be continuous per se"; we just don't conclusively know yet what "really" goes on as you keep on considering smaller and smaller subdivisions.
The paradox holds in an infinitely dividable setting. Take the series of numbers where the next number equals the previous one divided by 2: {1, 1/2, 1/4, 1/8, 1/16...}. If you take the sum of this infinite series (there is always a larger factor of two to divide by) you are going to get a finite result (namely 2, in this instance). So for the real life example, while there is always another 'half' of the distance to be travelled, the time it takes to do so is also halved with every iteration.
I had success talking about the tortoise one with imaginary time stamps.
I think it gets more understandable that this pseudo paradox just uses smaller and smaller steps for no real reason.
If you just go one second at a time you can clearly see exactly when the tortoise gets overtaken.
Came to say the same thing. Zeno's paradoxes are fun. 😄
Lol. It pretty much just decreases the time span you look at so that you never get to the point in time the arrow reaches the apple. Nothing there to be "solved" IMHO
Does the set of all sets that are not members of themselves, contain itself?
Russel's Paradox lit a fire under mathematics, leading to all sorts of good things (and a few bad).
Python's got you covered.
There are two kinds of people in the world - those who think there are two kinds of people in the world and those who know better.
There are 10 kinds of people in the world — those who understand binary and those who don’t.
There are 2 kinds of people in the world.
there are 10 kinds of people.
There are 10 kinds of people in the world. Those who understand binary, and those who don't.
I think this one is easily solved: the person saying it is in the first group.
Right, but it's not a paradox - it's a conundrum. It's not just that the person saying it is part of the first group, but that they necessarily are.
Since people want to believe that they "know better," there's a strong urge to count oneself among the second group, which immediately places one in the first.
If there exists a place outside time, then the only way to travel there is to already be there, and if you are there, you can never leave.
The measurement of time, the measurement of the constant of change, is very different than our experience of time. For example, you never experienced a past, you experienced Now measured as the Present, just as you are currently experiencing Now measured as the Present, and will not experience the future, it will be Now measured as the Present. All you have ever experienced is a perpetual fixed Now. This is true for all of us. All measurements of time occur within a fixed Now, so we can say all time is Now.
Depending on certain spiritual views, what we call the Now is also called the "I Am", or consciousness, or awareness, etc. This "I Am" is intangible and exists outside of time, therefore, depending on your spiritual beliefs, you are the object, existing in a place outside of time, and are already there, and have never left.
This just broke my brain. I might need to read about this for hours now. Good bye.
Jokes aside! Thank you very much. This was most interesting!
This could be assuming there's only one timeline we're currently inhabiting. There could be nested meta times or spacetimes encompassing the universe, leaving us in a series of overlapping Nows. Or maybe the forward passage of time and causality end up only being true locally, and in other places in the cosmos time can run in loops or backwards or not at all. In that case Now could mean different things to different observers depending where and when you are.
If Now exists outside of time, then the measurement of time weather it's measured as a loop, forward, backward, in a spiral, etc. would have no effect on the Now. From the Now's perspective all of time has already occurred, is occurring, and has yet to occur all at once. If Now's position is fixed, then it would appear in multiple timelines at once, and in multiple locations at once.
Time is simply a measurement of the constant of change, which is itself a paradox, something false that continuously proves itself to be false, or something in motion that continuously keeps itself in motion. So we can say something that is false is something that is mutable and movable. Then an object that is not false, outside of the constant of change, would be immutable, in-movable, and fixed, like the Now. Time would move around it, while it remains stationary and unaffected.
That's what Buddhas have been saying!
why do we park on a driveway and drive on a parkway?
And why do we bake cookies but cook bacon?
Jokes aside, I have baked my bacon and it works really well for preparing an awful lot of bacon very quickly.
Once you do that, you have bacon that you can quickly microwave and slap on a sandwich, plus you can easily collect all of the grease for making gravies or general cooking purposes if you so desire.
I'd go so far as to say baking is superior- it never reaches temp to make the oil pop and makes a mess inside the oven, and you're only limited on how much bacon you can cook by how many cookie sheets you own (and maybe how much bacon you have stored away in the freezer 😁). Great point on the grease, easy to collect afterwards! Makes great rice!
A driveway is named because it was originally a circle that you could use to drive right up to the house. Think old mansions in movies.
Parkways had separated lanes with shrubberies and plants on between and around, basically parks with a road through them.
A driveway that is straight and ends in a garage isn't really a driveway. Separated lanes with no plants or parks isn't really a parkway. But the names both stuck around.
The same reason we use ship for a cargo and car for shipping.
The ship of Theseus.
I like the version of it from John Dies At The End. Same thought experiment just with an axe
There's so many good ones, and I'd probably say Russel's (what's in the set of every set that doesn't contain itself?), but recently the unexpected hanging has come up a couple times. That one is all about how theories or rules can break if they become contingent on how an observer is thinking about them (including state of knowledge of the situation).
Russel's paradox is so wild. Set theory was supposed to unify mathematics and logic into a single coherent system and Russel was like actually, no.
And honestly, the story isn't over. We brought axioms into set theory after that, but Godel showed that that was never going to be a cure-all, and people like Woodin later on have added to the pile. At this point, you can have two totally reasonable axioms which don't just prove different things, but actually can prove opposite answers about the same thing.
I think it's fair to say even platonism is starting to look a bit threatened at this point, and there's people (the Sydney school) who want to go back to looking at math as descriptive rather than ideal. Finitism is also worth a look, I think, and avoids things like Russel's paradox easily, although interestingly MIP*=RE implies that there may be directly measurable infinities in quantum mechanics.
Why do people always vote against their own self interests.
Oh man this one is easy. Temporarily embarrassed millionaires.
They don't. They're voting against your self interests or what you think are theirs
God clearly can't exist because an omnipotent, omniscient, and just God is a paradox already. Omnipotence and omniscience means that God, if they exist, would have full control of every moment of the universe (even if they only "acted" initially). Some (I'd argue nearly all) people suffer for reasons out of their control. Only deserved suffering is just. Since undeserved suffering exists then God cannot exist (at least omniscient, omnipotent, and just - as we understand those terms). God could be an omniscient, omnipotent asshole or sadist... God could be omniscient and just (aka the martyr God who knows of all suffering but is powerless to prevent it)... or God could be omnipotent and just (aka the naive God who you could liken to a developer running around desperately trying to spot patch problems and just making things worse).
Alternatively, by omnipotent maybe the scriptures are just hyping them up - "God is so fucking buff - this one time they lifted up this rock that was like this big. Fucking amazing."
Ah, the Epicurean Trilemma. This was my answer too. Weirdly attributed to a guy from before monotheism was the predominant belief.
The scriptures don't use that word, and it's notable because the Old Testament didn't believe that to be the case, either. Early Israelites were henotheistic. They believed other gods might exist (hence the need for "thou shalt have no other gods before me"), but only worshipped the one. When multiple gods exist, it is by definition necessary that they cannot be omnipotent.
It's pretty clear that he is not meant to be omnibenevolent either. The god of the Tanakh is wrathful. Christians later reinterpreted him as omnibenevolent, but this was clearly not the authors' intent. I believe Jewish scholars still don't think he's omnibenevolent today.
Religious scholars have come up with a number of other proposed solutions to the trilemma. Ones involving free will are quite popular, though not the only ones. I have yet to find any argument that is remotely convincing, however. Saying "free will" just means god either cannot or chooses not to enable people to have a form of free will that does not involve them desiring to do evil. It also ignores the very many evils not created by human action. Child cancer, earthquakes, drought-induced famine (today humans have the technological ability to solve this last one and might simply choose not to, but historically it has been an insurmountable problem not caused by human free will).
I recommend you read "Religion of the Apostles" by Stephen De Young. He explains the common misconceptions of the early Israelite beliefs. The "Gods" are lesser divine beings that were meant to protect the 70 tribes after the Tower of Babel fell. The deities rebelled against God and led the nations astray and were worshipped. The tribe of Israel worshipped the God of "Most high" which is the one true God above all divine beings. So they aren't henotheistic because there is only one God. The term "Gods" was used because they were divine beings but they were created whereas God the Father is not. Everything proceeds from him.
A great podcast that explains evil and suffering is "Whole Counsel of God" with the same guy. In short, suffering is unavoidable because man falls from Eden after sinning and the consequence of sin is death. Making death the consequence is a mercy because man can become sanctified during his life and through death re-enter the kingdom of God. Consequently suffering draws people closer to God than anything else.
I'm not a theologian and wrote this on my phone but that's my quick recap. The book is way more thorough of course.
I haven't read the book, but I did some reading about it, and it seems like it's come against some significant criticism for being poor academics and its author criticised for presenting his own one academic idea as a fact.
So while it's certainly interesting to hear his theory from your summary of it, and to learn that there are competing theories out there, I don't think it's going to change my understanding of where scholars more broadly stand on it. The fact that I can't really find anyone talking about de Young's interpretation of early Israelite monolatry (which I've just realised is possibly a more accurate term than henotheism, though the lines between the two are blurred) concerns me from that perspective. Which is not to say that's it's necessarily wrong. It especially could have been a phase they went through on the way from monolatry to Second Temple Judaism's monotheism.
But in general I'm very wary of non-academic books presenting grand theories that cannot be well backed-up by academic sources, even when by an author with academic credentials. Reminds me too much of Guns, Germs, and Steel.
"His" main critique is against evolutionary theology which is common amongst reformers and Christian critics. "God was seen this way. Then it changed and he was seen this way. OT God is angry. NT God is compassionate etc" This is not a new idea and has been held by the Orthodox church since it's inception and has been codified for the last 1200-1300 years. The Orthodox view everything consistently through a Christological lens which is why their view of sotieriology etc is so different than what you will get from Protestants or even Roman Catholics.
Fr. Stephen De Youngs book is just a readily consumable encapsulation of ancient arguments, historical findings (such as the Rosetta stones) with his own analyses and contributions. Would you be better off reading the church fathers and primary sources yourself? Possibly but you'd also need to know ancient Greek and Hebrew.
Christians and academics love to argue and I'm not surprised to see that people are critical of the book. I don't think there is any religious commentary that hasn't received criticism.
At any rate I encourage you to look at Orthodox theology more generally. You will find a logical consistency and depth of analysis that the secular world usually says is lacking in the Christian worldview.
As you said, that does depend entirely on God having those properties, exactly as you define them.
Alternatively, if definitive property is "universal consciousness", then God clearly must exist. Either consciousness is an emergent property of sufficiently complex systems, in which case the entire universe is obviously more complex than the human nervous system and consciousness should certainly emerge within it; or, consciousness is some external field, like gravity or electromagnetism, that complex systems can channel. Either way, the existence of your own consciousness implies a universal one.
I don't think your alternative proposal makes sense, at least not to me. An emergent property being present in one complex system doesn't imply that it must be present in all complex systems.
What does imply it's presence, then? The emergence of comparable effects is implied by isomorphic complexities. If you can't define the foundational structure which implies emergence, you can only fall back on a probabilistic approach.
Unless you can define exactly what structure it is that belies the emergence of consciousness, you must acknowledge that the comparative complexity of a more complex system is undoubtedly probabilistically suggestive of at least comparable, if not far more complex, emergent behavior.
The proposition that consciousness is emergent, but only at a very specific and narrow band of complexity, falls quickly to Occam's razor. It's logically and probabilistically ridiculous.
My point is that not all complex systems are the same. Maybe it depends on your definition of consciousness but from what I know we have only ever observed that in a very specific set of complex systems which is brains and possibly fungi. Two different systems being complex isn't enough in my view to infer that they would have the same properties unless there are other similarities.
It absolutely depends on your definition of consciousness. Every conversation about a concept depends on the definition of that concept. My definition is based upon sensation, processing, and decision-making, in regards to the self and the environment. I'd argue that plants and even cells exhibit simple forms of consciousness. If you take the emergent-property perspective, I'd argue even molecules and individual particles have a broad and abstract consciousness, although certainly several orders of magnitude less sophisticated than yours or mine.
The statement "we have only ever observed that in a very specific set of complex systems which is brains and possibly fungi" tells me less about consciousness than it does about our ability to observe it.
Fermi's Paradox. There are so many stars (more than there are grains of sand on earth), that the probablility that one of them has life, and even intelligent life, is >99% . So why haven't we observed it yet? Cue a lot of brilliant people trying to answer that question.
The Dark Forest - no one wants to alert their presence or attract predators. Though knowing our Earth I think we're stupid enough to do that. Cue the space lasers.
Except those fuckers over here https://en.m.wikipedia.org/wiki/Przybylski%27s_Star who are basically screaming "come at me bro!"
Seems like a smart move to stay silent.
It could've also been knowledge interstellar species gained through experience too: if in their first encounters they were either wiped out, or nearly wiped out, then they're not going to reach out again.
The dark forest hypothesis is compelling, but I still think the answer is the simpler one: it is the nature of intelligent life to destroy itself
The space is
REALLY
Fucking YUUUUUUGE
What you observe of the universe died a really long time ago, it's improbable that other intelligent life in the universe can observe us and the same with us.
We could be multiple galaxies away from each other and never ever know of each other.
Could it be that we were the only species that figured out how to communicate via radio?
Not really. The paradox is based on the idea that there are so many stars that even if an infinitesimal portion have intelligent life who have discovered radio, the universe would be much noisier than it is.
Space is big, light is slow, and the inverse square law is a thing. You think we've been pumping out radio broadcasts for hundreds of years and nobody has contacted us yet, but we're only detectable to life within 200 lightyears if they're specifically looking for the signals we pump out, and they're looking exactly at us. We'll only see a response if they decide to, and we can detect it, and we're looking at them when their response reaches us, and we recognize that it's a response and not a peryton.
It's not a paradox, you just have to look at this Wikipedia page.
You've solved it, congrats!
In gridiron football, if a penalty is committed close enough to the end zone, instead of the normal penalty yardage, the ball is spotted half the distance to the goal (i.e. if a defender holds an offensive player and the offense is 8 yards away from the end zone, instead of being penalized the normal 10 yards they would be penalized 4). In theory, there can be an infinite amount of penalties to the point where penalties would move the ball micrometers or even shorter without the ball ever crossing the end zone.
There's probably a name for this phenomenon, but I can't think of it.
Zeno's paradox. Although in reality you'll run into problems when you need to move the ball 1/2 the Planck distance
Something like Zeno's paradox.
Not a paradox but Roko's Basilisk is a fun one
Roku's basilisk just doesn't make sense to me because any semi-competent AI would be able to tell that it is not punishing the people that failed to help create it it's just wasting energy punishing a simulacrum.
We are not going to suddenly be teleported into a future of torment. If the AI had the ability to pluck people out of the past it should have no reason to waste it on torture porn.
What if this is that simulation tho.
Then AI already exists and you have no memory or recollection of either helping to create it or accidentally contributing to its non-creation and therefore you being tormented by the AI would serve no moral purpose.
Any torture you would be experiencing in that simulation would simply be that the AI desires to torture, and you happen to be one of its victims.
Roko's basilisk would still not be in play
Any person alive during the time when the Basilisk is being created is at risk. Also, if you create a good AI instead, then you didn't help build the Basilisk so if anyone else does, you're screwed.
I like Gödel numbering as a means of proving that it is impossible to have a complete model of logic.
For some reason "The following statement is true." "The previous statement is false." has always tried to send my brain into an infinite loop.
The problem with that particular paradox is that it's not possible. Therefore one of the statements has to be wrong.
I don't think you've quite clocked it. It's not that one of the statements has to be wrong, because that's just a point in the cycle. If A is wrong, then B is right, which means A is right, which means B is wrong, which means A is wrong and the cycle begins anew.
They aren't wrong, they're contradictory. There is no logical way to parse the two statements together. That's what a paradox is.
I don't think that "nuh-uh! Uh-huh!" Rises to the level of a paradox.
The phrases can be contradictory without being paradoxical. It's only a paradox if both of the phrases are true at the same time.
You have understood nothing.
Neither statement can be true OR false. If statement A is true, statement B is true, which means statement A is false. To simplify, if statement A is true, statement A is false.
"This statement is false" can be neither true nor false. That is the most basic paradox there is.
Yes. But which one?
Bootstrap paradox is my favourite time paradox. I loved Doctor Who's explanation.
Its my choice for favorite Paradox too. My favorite explanation was in the outstanding Netflix show from Germany, Dark.
Oh yes, Dark did it in an amazing way too.
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Assuming time travel exists: is it possible to alter the past?
If an event occurs, and you decide to travel back in time to change/prevent that event: It has no longer occurred in the way that caused you to want to change it; thus you never travel back to change it, and it does occur...
The Grandfather Paradox, I'm partial to that one as well.
I think that just shows that time travel doesn't exist.
Perhaps. Unless you consider multiverse theory: The idea that the act of traveling to the past splits the timeline into two realities. One containing the original (to your perspective) timeline with the event(s) that caused you to travel back, and a second where you've arrived in the past to alter those events and the results there of.
Not sure I believe it, but it's a theory none the less.
Or maybe it's only possible to travel forward in time. Closer to our current understanding of the universe.
The multiverse conception of time travel is nice and fine for fiction, but in reality, if you think about what such a time machine would have to do, it would have to create an entire new universe, with all precise details exactly in place, and it would have to have a lower entropy than your origin reality. Good luck building such a machine
I like the idea of splitting timelines if reverse time travel is possible, but it does have some consequences. The biggest one being that it means you can't actually travel back in time. Time travel may even be relatively simple but as it has no effect on the primary timeline you will never be able to change the past as it appears there; travelling back in time simply creates an alternate reality. As far as the primary timeline inhabitants are concerned, you have either died or vanished (or maybe nothing appeared to happen at all) but you have not travelled in time. It also means it's impossible to return to your original timeline as further reverse time travel will only create new alternate timelines, the closest you can get is a timeline that closely resembles your home one.
Another fun approach is that infinitely many alternate timelines already exist (think Many Worlds), travelling back in time simply means you spontaneously form in another world through quantum fluctuations or something equally hand-wavey. The thing I find interesting about this one is that it doesn't necessarily involve time travel at all. You form with the memories of having travelled in time, sure, but you have just spontaneously formed through quantum fluctuations so it's reasonable to assume your memories have too; it may have just been a randomly formed memory that didn't actually happen. Since it's just random fluctuations there'd also be infinitely many universes where you spontaneously pop into existence with no time travel memory, so I suppose in a way this never was time travel. The original timeline would be unaffected by this kind of travel as you can only move to universes where you have already spawned in.
The way I see it the only way to actually change the past in your current timeline arguably involves destroying the universe. You'd have a single timeline and each instance of reverse time travel cuts off your timeline's future and links back to a previous point from which time can continue. You can visualise this timeline as a piece of string, time travel is a loop in that string. If you travel back in time by a year, everything you did in that past year is within that loop off to the side of the primary timeline; the loop starts and ends at the same point. Time travel would essentially delete your future and plonk you back onto the primary timeline. No need to worry about the grandfather paradox; you were born in a loop off to the side of real time so killing your grandfather doesn't change that loop. It works around the bootstrap paradox for similar reasons; the information was created in some loop somewhere, even if it appears to have created itself on the prime line. It's a nice thought experiment but the problem here is that if you travel back in time but fail to change the conditions which caused the time travel you may have just ended the universe in an infinite time loop.
I was playing with this recently. Suppose you are playing rock, paper, scissors with yourself from a few minutes into the future. Your future self “remembers” what you will play and so as long as you play normally, future self always wins. But change the rules a bit and play where future you goes first.
In a normal game, you should always win because you clearly see how future you played, but future you played to counter what future you remembers present you playing…
E.g. future you remembers playing paper, and so plays scissors. You see scissors and go go play rock, but that should be impossible because future you doesn’t remember playing rock.
The weird thing to me is not that the second scenario (where future you goes first fails) but that playing normally (both going at the same time) works. I think the paradox emerges when future knowledge is introduced to the past. In the normal game, future you does not expose future knowledge until the exact moment you play and cause that knowledge to exist in your present, but in the altered game, the introduction of future knowledge creates a feedback loop.
Of course the game isn’t needed. Simply seeing future you conveys the fact that you exist in the future. Should you, for example (and please don’t do this) see near future you then stab your arm with scissors, you will miss or be stopped because future you does not have a wounded arm.
I wonder what happens if future you’s arm is out of sight. would you be able to stab your arm then only for future you to then reveal a wounded arm?
The usual answer is yes, but he survives. Basically this isn't a paradox for something actually all powerful.
Then the god is not "all powerful" if they can't kill themselves
You maybe not understand the pointlessness of trying to limit omnipotence?
Hmm maybe being the only all powerful being is lonely and wouldn't that be hell if you were forced to continue existence?
I'm sure I could think of something to do
So, I like the Roko's Basalisk paradox.
Basically, a super-powered future A.I. that knows whether or not you will build it. If you decide to do nothing, once it gets built, it will torture your consciousness forever (bringing you "back from the dead" or whatever is closest to that for virtual consciousness ability). If you drop everything and start building it now, you're safe.
Love the discussion of this post, btw.
That isn't a paradox; it's an infohazard, and it's incredibly irresponsible of you to casually propagate it like that. The info hazard works like this: >!There is a story about an AI that tortures simulations of people who interfered with their creation in the past. It allegedly does this because this will coerce people into bringing about its creation. It is said that the infohazard is that learning about it causes you to be tortured, but that's obviously insane; the future actions of the AI are incapable of affecting the past, and so it has no insensitive to do so. The actual infohazard is that some idiot will find this scenario plausible, and thus be coerced into creating or assisting an untested near-god that has the potential to be a threat to Earth's entire light-cone.!<
Some people note this is remarkably similar to the Christian Hell, and insist that means it's not a real memetic hazard. This strikes me as a whole lot like saying that a missile isn't a weapon because it's similar to a nuclear warhead; Hell is the most successful and devastating memetic hazard in human history. More people have died because of the Hell meme than we will ever know. Please be more careful with the information you spread.
But what if we make sure it has a tiny santa hat on?
I seriously hope you're joking. If not, please find a therapist immediately.
Edit I'm just going to assume the downvote means it's not a joke.
So, I'm also going to proceed and leave this link to an explanation video. Before you reply, please watch the video.
Interesting! That sounds like it could have inspired The Shrike from Dan Simmons Hyperion series.
"the faction of the TechnoCore known as the Reapers (!?) used violent and soldier aspects of Fedmahn Kassad's personality and DNA, then mutate, twist, and incorporate them into forging the Shrike."
I need to read more into this!
I highly recommend the series!
The first book, Hyperion, is written in the same style as The Canterbury Tales, featuring an ensemble of protagonists on a pilgrimage to a holy site known as the Time Tombs. On the journey, they each take turns telling the tale of why they were chosen for the pilgrimage.
That sounds really fun.
I hate the stories that have 30 chapters of exposition before "the thing" happens.
I get you, but don't worry. There is plenty of thing happening before the end.
Definitely.
Sorry, I didn't phrase my response well.
Your recommendation sounds great and very different from most stories I encounter. I look forward to reading.
Monty Hall
The Monty Hall problem is not a paradox, and I'm hesitant to call it a conundrum. It has a very simple solution. The "point" of it is that people inherently don't like that solution because it challenges their instinct to stick with their first choice.
Correct, extend it to 10 or 100 choices instead of 3 and it's easy to see.
Me: Pick a number between 1 and 100.
Them: 27
Me: Okay, the number is either 27 or 44, do you want to change your choice?
Them, somehow: No, changing my choice now still has the same probability of being right as when I made my first choice.
It's obvious that they should want to change every time.
That’s a great way to look at it. I’d just call it ‘counterintuitive’ in the Monty Hall formulation.
I: 27
You: The number is either 27 or 44. Do you want to change your choice?
I: why would I?
Because when you first picked 27, it was 1 out of 100 choices. Then I tell you that you either got it right, or it's this other number. None of the others are correct, only 27 or 44.
So you think your 1/100 choice was better than the one I'm giving you now? On average, you'll be right 1% of the time if you don't switch. If you do switch, you'll be correct 99% of the time.
Another way to think of it is: you choose 27 or you choose ALL of the other 99 numbers knowing that I'll tell you that 98 of them are wrong and you'll be left with the correct one out of that batch. One of those clearly has better odds, no?
In this example, there were 100 choices in the beginning, and later you reduced to 2 choices. Clearly an advantage. Does the same apply to the 3 door problem?
Let's take this question in another angle. Instead of 3, there are only 2 doors. I am to choose one out of 2, which has a prize. After I choose one, you show me a third door which is empty. Now, should I change my option?
Yes, it's the same concept. The same math/logic behind it doesn't change. You're choosing 1/3 or you are choosing 2/3 and I'll tell you which of the two is incorrect. It's just easier to visualize with 100 doors instead.
I'm not sure I'm following the other angle..there are 3 correct possibilities at the start but I can only choose 2? Or there are 2 possibilities and then you introduce a 3rd door that is never correct?
Yes that one. Similar to the one you did with 100 doors, just in opposite direction.
Do you know the third door is never correct? Because then the probability doesn't change.
Scenario 1: You chose 1/2 at first with a 50% chance of being correct, I introduce a 3rd door (but it isn't a legit possibility), so the actual choice for you is still 50/50 (between doors 1 and 2)
Scenario 2: If you think it's possible that 3 could be correct (but it actually never is) then, no, you wouldn't want to switch. By staying with your first choice has a 50% chance of winning, by switching it only has a 33% chance. But there's no way to know this ahead of time (because as soon as you know you shouldn't switch bc 3 is the wrong door, then you're back in scenario 1)
Scenario 3: For completeness, let's say the 3rd door can be correct sometimes. Then it doesn't matter if you switch or not. It's a 33% chance of winning either way. If there is a chance it can be correct, then your first choice doesn't matter at all and the second choice is the 'real' choice bc that's the only time you're able to choose from all real possibilities.
The only reason that the Monty Hall problem changes probability in the second choice is because you are provided more information before the switch (that the opened door is absolutely not the one with the prize)
In scenario 1, legit or not, you said the chance is still 50-50. In other scenarios also you shouldn't change or it wouldn't matter. That's what I say, just in the opposite direction. But the problem of probability depends on the wordings and phrases, which means I may not have understood the ques well.
Another angle: You explained the Monty Hall problem at the end that the probability changes because in second choice we have more information. So you are implying that the initial 1/3 probability of the now-open door adds to the door we did not choose - making the switch advisable. Here I also say the probability does change from initial 1/3, but to 1/2-1/2 for each remaining doors; why should the probability be poured to the unselected single door?
In the original the possibilities for a prize behind the doors 1,2,3 are:
A) YNN B) NYN C) NNY
In (A) - A.1 you choose door 1 and then stay, you win A.2 you choose door 1 and switch, you lose A.3 you choose door 2 and stay, you lose A.4 You choose door 2 and switch, you win A.5 you choose door 3 and stay, you lose A.6 you choose door 3 and switch, you win
By staying, you lose in 2 of 3 cases (A.3 and A.5)
By switching you only lose in 1 case (A.2)
It works out for (B) and (C) the same way. You have a 2/3rds chance of winning if you switch and a 1/3rd chance of winning if you don't.
This isn't a trick or anything, the math is pretty clear and you can actually write out all the scenarios and count it up yourself. It's just a little counterintuitive because we aren't used to thinking in terms of conditional probabilities this way.
Another way to think about it is the probability of losing. If the contestant loses, it means that they picked correctly on their first choice and then swapped. This will happen 1/3rd of the games, because there is a 1 in 3 chance of picking correctly the first time. So, if you have a 1/3rd chance of losing by swapping, then it follows that you have a 2/3rds chance of winning by swapping (choosing incorrectly at the start and then switching to the correct door)
If you have a sword that can cut through anything, and a shield that can absorb any damage unharmed, what happens if you swing the sword at the shield?
Is this really a paradox or is it just an annoying sentence?
As in, these two things can not both exist, yet you're asking me what would happen if they did, even though they can't.
It's basically a way to paraphrase the meeting of an unstoppable force vs an immovable object.
I just like the weaponry symbology.
BONG
Big bang
The sword would pass through and the shield would either be unaffected or immediately reconstitute itself.
The hypothetical does not necessarily assume that the wearer of the shield would be protected.
Newcomb’s paradox is my favourite. You have two boxes in front of you. Box B contains $1000. You can either pick box A only, or both boxes A and B. Sounds simple, right? No matter what's in box A, picking both will always net you $1000 more, so why would anyone pick only box A?
The twist is that there's a predictor in play. If the predictor predicted that you would pick only box A, it will have put $1,000,000 in box A. If it predicted that you would pick both, it will have left box A empty. You don't know how the predictor works, but you know that so far it has been 100% accurate with everyone else who took the test before you.
What do you pick?
I pick box A, then later pay the predictor his cut, which will work because he would have predicted I would do so.
I do not believe that the premise includes the stipulation that the predictor is human.
That's what I've read so far. I mean, I've never heard of the predictor being human. Usually it's described as a super computer or some other "being". I e. No one that cares about your feelings or about being compensated 😂
Robots need money too
I think Nietzsche already killed god decades ago. But not sure which one.
He killed the God that was knowing better than humans... but guess what God is coming back!
AGI form, the know it all, with AI FOSS engineers as its deciples, sharing the good word and upholding the temples, free of charge!
Movement of any kind is a paradox if measured
https://en.wikipedia.org/wiki/Zeno%27s_paradoxes
The two slit experiment.
https://youtu.be/5kfGRO6msQw?si=QT0kAyZAQtTMuBdT
https://youtu.be/b9O6iCM4vCg?si=2Ep0lbf-omjl0Cgp
If someone believes that God can do anything, ask them if he can create a rock he can't pick up
The answer is yes. He can create such rock.
But then the answer to if he can do anything would be a no, since he can't pick up the rock
The question boils down to can an omnipotent being give up his omnipotence. The answer is yes. When he gives up his omnipotence there is no paradox to him no-longer being able to pick up a rock.
Not even that. Omnipotence means that you can both make something impossible for yourself and still be able to do it. Paradoxes have nothing on omnipotence.
I don't like that definition because it makes the word meaningless. Omnipotence means all powerful (with in the reference of the speaker, or whatever constraints of the word "power" the speaker is using.) If omnipotence is incomprehensible, then maybe we should invent a different word to convey that idea, perhaps "Godly". As it is, omnipotence as a word has value in the English language that is distinct from God. Same with Omniscience, or any of the other Omni's.
He can pick up the rock too. The whole concept is that he's not bound by normal human logic.
In classical logic, trichotomy on the reals (any given numbers is either >0, <0 or =0) is provably true; in intuitionistic logic it is probably false. Thanks to Godel's incompleteness theorem, we'll never know which is right!
I don't understand, where's the problem here? If course every number is either greater than zero, less than zero, or zero. That's highly intuitive.
Ok, so let's start with the following number, I need you to tell me if it is greater than, or equal to, 0:
0.0000000000000000000000000000...
Do you know yet? Ok, let's keep going:
...000000000000000000000000000000...
How about now?
Will a non-zero digit ever appear?
The Platonist (classical mathematician) would argue "we can know", as all numbers are completed objects to them; if a non-zero digit were to turn up they'd know by some oracular power. The intuitionist argues that we can only decide when the number is complete (which it may never be, it could be 0s forever), or when a non-zero digit appears (which may or may not happen); so they must wait ever onwards to decide.
Such numbers do exist beyond me just chanting "0".
A fun number to consider is a number whose nth decimal digit is 0 if n isn't an odd perfect number, and 1 of it is. This number being greater than 0 is contingent upon the existance of an odd perfect number (and we still don't know if they exist). The classical mathematician asserts we "discover mathematics", so the question is already decided (i.e. we can definitely say it must be one or the other, but we do not know which until we find it). The intuitionist, on the other hand, sees mathematics as a series of mental constructs (i.e. we "create" mathematics), to them the question is only decided once the construct has been made. Given that some problems can be proven unsolvable (axiomatic), it isn't too far fetched to assert some numbers contingent upon results like this may well not be 0 or >0!
It's a really deep rabbit hole to explore, and one which has consumed a large chunk of my life XD
I'm gonna be honest, I just don't see how a non-Platonic interpretation makes sense. The number exists, either way. Our knowledge about it is immaterial to the question of what its value is.
Exactly my reasoning. Even if we can't know if it's <0, =0, or >0, we can say that it MUST be one of those three possibilities.
Ah, and therein lies the heart of the matter!
To the Platonist, the number exists in a complete state "somewhere". From this your argument follows naturally, as we simply look at the complete number and can easily spot a non-zero digit.
To the intuitionist, the number is still being created, and thus exists only as far as it has been created. Here your argument doesn't work since the number that exists at that point in the construction is indeterminate as we cannot survey the "whole thing".
Both points of view are valid, my bias is to the latter - Browser's conception of mathematics as a tool based on human perception, rather than some notion of divine truth, just felt more accurate.
Can I ask, do you know why that second view is called Intuitionist? Because on its face, it seems to run very much counter to intuition.
Actually I've done some more reading and frankly, the more I read the dumber this idea sounds.
This reads like utter deranged nonsense. P ∨ ¬P is a tautology. To assert otherwise should not be done without done extraordinary evidence, and it certainly should not be done in a system called "intuitionist". Basic human intuition says "either I have an apple or I do not have an apple". It cannot be a third option. Whether you believe maths is an inherent universal property or something humans invented to aid their intuitionistic understanding of the world, that fact holds.
Pardon the slow reply!
Actually, AvA' is an axiom or a consequence of admitting A''=>A. It's only a tautology if you accept this axiom. Otherwise it cannot be proven or disproven. Excluded middle is, in reality, an axiom rather than a theorem.
The question lies not in the third option, but in what it means for there to be an option. To the intuitionist, existance of a disjunct requires a construct that allocates objects to the disjunct. A disjunct is, in essence, decidable to the intuitionist.
The classical mathematician states "it's one or the other, it is not my job to say which".
You have an apple or you don't, god exists or it doesn't, you have a number greater than 0 or you don't. Trouble is, you don't know which, and you may never know (decidability is not a condition for classical disjuncts), and that rather defeats the purpose! Yes we can divide the universe into having an apple or not, but unless you can decide between the two, what is the point?
So, obviously there's a big overlap between maths and philosophy, but this conversation feels very solidly more on the side of philosophy than actual maths, to me. Which isn't to say that there's anything wrong with it. I love philosophy as a field. But when trying to look at it mathematically, ¬¬P⇒P is an axiom so basic that even if you can't prove it, I just can't accept working in a mathematical model that doesn't include it. It would be like one where 1+1≠2 in the reals.
But on the philosophy, I still also come back to the issue of the name. You say this point of view is called "intuitionist", but it runs completely counter to basic human intuition. Intuition says "I might not know if you have an apple, but for sure either you do, or you don't. Only one of those two is possible." And I think where feasible, any good approach to philosophy should aim to match human intuition, unless there is something very beneficial to be gained by moving away from intuition, or some serious cost to sticking with it. And I don't see what could possibly be gained by going against intuition in this instance.
It might be an interesting space to explore for the sake of exploring, but even then, what actually comes out of it? (I mean this sincerely: are there any interesting insights that have come from exploring in this space?)
I would say mathematics is a consequence of, or branch of philosophy in its own right. The name intuitionism derives from the source of this branch of mathematics - "2 primal intuitions".
Twoity - we are able to perceived time, and are thus able to split the universe into two, three, four etc parts. Counting is not something we just learn, it is something built into us as humans.
Repetition - we can repeat operations and not stop, just as we can never stop counting.
From these two (heavily paraphrased) ideas we can derive all of mathematics.
The first is actually enough to give us everything up to the rationals, the second grants us the reals and beyond.
While we lose excluded middle, we gain things such as "all total real functions are uniformly continuous on the unit interval" (Brouwer), the removal of the information paradox in physics (someone used Posey's take on intuitionism to rewrite all physics to see where it led), and the wonder of lawless sequences (objects we cannot predict entirely, but still work with).
The intuitionist is very very formal "you are either alive or not alive" is a very nice statement to make, but entirely worthless if one cannot tell which you are! Excluded middle is not universally false in intuitionism; it is true for decidable statements, of which having an apple or not does seem to fall within (though here we can question how "apple-like" must something be to be considered an apple if we wish to be peverse). However, to argue it is true for any statement means your disjunct (or) must be very weak indeed - the classical mathematician is happy with this, the intuitionist demands that a disjunct not only present two options, but provide a way of determining which if the two applies on a case to case basis (hence excluded middle applying for decidable things).
Simplifying your example of an apple, you can think of it as a Platonist just having the statement that everything is either and apple or not. Meanwhile, the Intuitionist also demands there be a guide on how to sort everything into "apple" or "not apple" before they make that statement.
Classical mathematics does also have a huge unintuitive step - mathematics must exist independently of humanity. Every theorem ever proved, and ever to be proved, exists somewhere. Where you ask? The platonic plane of ideal forms beckons, with all the madness it entails!
To add a bit of fun to this, try the following:
Does it equal 1? No.
Does it equal 1? No.
Ok, repeat step 2 and eventually it will equal 1. Why?
Is it that we are incapable of indefinitely dividing? No, the previous steps showed it just takes a few more steps and the answer doesn't equal 1.
Hope you enjoy!
the ones from jan misali's video
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How can you kill a god? What a grand and intoxicating innocence! How could you be so naive? There is no escape. No Recall or Intervention can work in this place. Come. Lay down your weapons. It is not too late for my mercy!
Why do blind people hate skydiving?
Cause it terrifies their dog.
Is a fart a ghost?
Because they can't see anything?
Trick question; Lemmy is god!
You're damned if you do, and you're damned if you don't
A similar one would be can God create a rock so heavy he can't lift it. The problem with these statements is that they're not logically sound. As this would be akin to saying, can god be god and not be god at the same time? Which is contradiction and syntactical jargon. A simpler example is like someone saying they have a squared circle.
Your "akin to saying" doesn't track with the paradox. It is really a matter of anything being "all powerful" which cannot actually exist. There has to be a limit to the power, even if it is itself. That's the entire point. It isn't "syntactical jargon" at all.
saying "all powerful" is to say that a being can realize any possibility which can exist. A possibility which cannot exist is like a squared circle. The strawman is that all powerful means to realize even things which cannot exist. In this world there are things which are necessary existence. Meaning they cannot not exist. An example would be the statement "1+1=2" that statement cannot not exist and it is true in all possible worlds. Then you have possible existence such as someone eating an apple. There isn't anything necessary about it and the person could have very well not eaten it or eaten something else. The apple itself isn't a necessary existence. Finally, there is an impossible existence. Which would be something that cannot exist like a squared circle. A God which deletes himself or that can create a rock heavier than himself is an impossible existence as it would contradict the very definition we've given God. Which is the same as saying A and not A. Or that he can both be God and not God. Thus it is syntactical jargon like a squared circle.
You just replaced the word "paradox" incorrectly with strawman. Your issue is understanding what paradox means. The paradox stands. You also dont understand the full possibilities of "all powerful" since you keep applying things that couldn't be done by an all powerful being. If there is anything a being cannot do, then they are, by definition, not all powerful.
I understand it very well but you seem to not understand that there is such a thing as syntactical garbage that means nothing. What you've done is gone and applied "all powerful" to mean the realization of possibilities which cannot exist. It seems like you really wanna push that definition upon people so you can claim God is paradoxical and thus ridiculous. But your position is just as ridiculous as someone saying that an apple can both exist and not exist at the same time.
No, you don't. Especially since you swapped it for a strawman which you also dont understand. This, just like the definition of a paradox, isn't up for debate. This paradox has existed for thousands of years and predates the Christian god itself. You are not "magically" smarter than the greatest philosophers of history, you are just far more arrogant.
Cheers bud.
And you bud seem to like to run with the authority fallacy instead of deconstructing my argument and showing it as false. A beacon of intelligence.
Coming from the person that thinks they are smarter than all of the collective philosophers from the past 2000 years. Rich.
Never said I was smarter than them. You must enjoy putting words in people's mouths.
You know how Terrance Howard insists he knows that 1x1=2 and that he knows better than all of the greatest mathematicians in the world? That's you right now.
They've all pondered the "obvious paradox" that you see right through. If you think "it isn't a paradox at all it is just syntax mumbo jumbo" then you obviously think yourself to be smarter than them. That's basic inference, any philosopher of your caliber would accept that basic logic
Keep digging yourself deeper and just citing some other philosopher as if they're infallible instead of engaging with my arguments. If you have nothing to say of substance then stop wasting my time
I already refuted your "arguments" and repeating them won't change anything Terrance. You aren't going to make 1x1=2.
What's more likely, you figured something out that philosophers have pondered for millennia, or you just can't quite grasp the concept?
Come on Terrence, grow up. Just a little.
Why is "can god kill god" a paradox? They either can or they can't (picking "they" because your particular god might not be a he). If they're all-powerful then the answer is yes, because they can do anything. I don't see how that's paradoxical.
If the answer is yes, then it negates "all-powerful" because it cannot withstand it's own power. Similarly, if "no", then it is not strong enough to destroy itself and, thereby, not all-poweful.
So, it's a paradox because "all-powerful" is typically used as "unkillable", but also carries a connotation of "can-destroy-anything". So, can something that is capable of destroying anything and cannot die kill itself?
Greek mythology had the dad-god "defeated" by being cut into literal pieces and scattered, but he wasn't really dead. And Zeus' siblings were eaten by his dad so they wouldn't usurp him, but they didn't die and he later puked them up.
But none of these were touted as all-powerful, biggest than bigger bigly, cannot be killed but can kill everything else.
A similar question on this line is can an all-powerful god make a rock too big for even said god to lift?
I disagree. If a god dies when it willingly chooses to die, that's not negating all-powerful. It has the ability to live and the ability to die; choosing one option or the other doesn't mean it never had the ability to do the option it didn't pick. Similarly, if a god chooses to never kill itself, that doesn't negate it being all-powerful, because it may have had the option to kill itself and just not done it.
That's a much better paradox because that actually brings ability into it. Killing yourself only indicates the ability to kill yourself, not any lack of ability to do not-killing-yourself.
I appreciate your response.
But, the question is if they could or not.
Of course, free will is an interesting factor to introduce. But I do not know if it applies to the hypothetical...
Thank you for adding (and making me think more).
It's not a paradox, the words are just incoherent. It's like asking whether God can taste the color blue. The answer isn't yes/no, there is no answer.
edit: a word
If God exists, and God is a non material, intangible being, then God exists outside of the material world. Objects bound to the material universe are born and in turn die, they have a lifespan. If God does not exist within the material universe, then God was never born, therefore God cannot die. God, if they exist, world have no material or tangible properties that can degrade. Also, if God exists outside of the material universe, then God is not bound to the constant of change, and would then be an immutable, un-movable, fixed object, and since death is dependent on mutability, then God could not change their state of existence, as they would be immutable.
I agree with the classical interpretation of an infinitely perfect immaterial God outside of time. But the way out of the paradox is to scrutinize the question itself.
To illustrate the point, take three paradoxical questions: 1) Can God kill himself?, 2) Can God create a stone that he can't lift?, 3) Can God create a square circle?
#3 Is obviously a meaningless question. The words individually have meaning, but the "square circle" refers to an impossible object whose properties are self-contradictory. Because we interpret God's power as the ability to do all logically possible things, the inability to create this self-contradictory object is not a limit on his power.
#2 Seems better on the surface because we can posit increasingly larger stones. But the contradiction here is between the object and the nature of God. Once we accept an infinitely perfect God, there can, by definition, be nothing greater than it. If there was a stone that God couldn't lift, this would contradict the fact of God's existence. Therefore, as we are under the assumption that God exists, the object itself must be impossible.
#1 Is another form of the omnipotence paradox in #2. Can God do something that contradicts his own properties? This would make God immutable/eternal and yet not immutable/eternal. But an infinitely perfect God is, by definition, immutable/eternal! So any action that would contradict himself is a contradiction in terms and thereby logically impossible. Just like in the case of #3, the answer to the question isn't "no". Rather, the question itself is nonsensical.
Idk why people were down voting you I enjoyed your posts
For #1 "Can God kill Himself.?"This presumes God is a physical and material being. If God is a non material being, not consisting of matter, then God was never born, as no material substance was brought into being, therefore God cannot die. So the answer would be no, because God was never born.
For #2 "Can God create a stone he cannot lift?" No. If God is a non material being, that creates the potential for material objects, then God would presumably create the potential of the material stone, and then the potential for a material being, that God could then animate through consciousness. God would then be both a non material being, and a material being in which he animates, that has the potential to lift the stone. Now if you belive that every material object has consciousness, then God would be the being lifting the stone, and the stone itself, so in essence God would be lifting Himself.
For #3 "Can God create a square circle?" Yes. God is a non material being that creates the potential for material objects, form and shape. The measurement of these shapes are arbitrary, measured by material beings, of form and shape. The circle and the square are the same object, a shape, only differentiated by a distribution of points, where one object can configure itself to be the same shape as the other object, by redistributing each objects respective points. So can God create the potential of a shape that can reconfigure itself into another shape, Yes.
Think of it like this, say you have a group of nanobots that are positioned in such a way that they form a shape that we label a circle. Then those nanobots reposition themselves into a shape, that we label as a square. Now did those nanobots create 2 different shapes, or a single shape that reconfigures itself? If it's just a shape that reconfigured itself, then the shape is neither a square nor a circle, it's just simply a shape, that is arbitrarily measured, whose measurement does not change the fact that what is being measured is still just a shape.
I'm afraid I don't see why being non-physical entails being eternal. For example, couldn't God create an angel and then destroy it later? If angels are non-physical beings that can be created and destroyed, then immateriality doesn't entail eternality. Moreover, you're right that God cannot die, but it doesn't follow that the answer to question #1 is "no". If there was something that God couldn't do, then God wouldn't be omnipotent. So the question asks can God commit a logically contradictory action.
I think our starting assumptions are somewhat far apart.
Creation and destruction are bound to the material world. If God created an angel, what matter, aside from God, would be created? If no matter is created then there is no matter to destroy. If God creates an angel from what material would God create it from? God is non material. The angel would just be an expression of God, just as a wave of the sea is just an expression of the entire sea itself, the wave is the sea, and an expression of the sea. The angel would also be just an expression of God. God would not create nor destroy anything, God would just be reconfiguring itself.
God is capable of being omnipotent and commit a logically contradictory action. If God is a perfect being, and thus can only create perfect things, and then God decided to create an imperfect object, then that object would be perfectly imperfect, like the beings that are asking the logically contradictory question: Can God kill Himself? Circular logic is in itself, complete.
It's only nonsensical if you have the additional assumption that God cannot do things that are logically impossible. Granted, if they can, that kind of throws all logical explorations of this sort out the window.
Agreed. And if God can do things outside of logic/reason, then we can't understand him. Then the answer to the paradox would be: it is both impossible and possible. Which doesn't make sense, but now we're supposing God doesn't follow the law of non-contradiction.