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.
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.
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: 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.
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.
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
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.
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?
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)
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)
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!
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.
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.
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.
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!
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.
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
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.
“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.”
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 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.
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.
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.
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.
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”.
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.
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.
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?
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.
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?
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.
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
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.
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?
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.
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.
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.
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?
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?
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 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.
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.
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.
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.
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.
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.
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”
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.
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?
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.
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.
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 😂
To some people the answer is obviously box A — you get $1,000,000 because the predictor is perfect. To others, the answer is obviously to pick both, because no matter what the predictor said, it's already done and your decision can't change the past, so picking both boxes will always net you $1000 more than picking just one. Neither argument has any obvious flaw. That's the paradox.
It's only the one-boxers who describe the predictor as “perfect”, presumably interpolating from the observation that the predictor has always been right so far. Two-boxers might argue that you have no idea if the predictor is perfect or whether they've just been incredibly lucky so far, but also, they will argue that this is irrelevant because the boxes have already been set up and your choice cannot change it anymore.
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