The monotheistic all powerful one.
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.
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.
I guess I’m the ladder 🪜
There are 10 kinds of people in the world. Those who understand binary, and those who don’t.
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
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).
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.
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.
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?)
Trick question; Lemmy is god!
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!
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.
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
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.
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: https://www.youtube.com/watch?v=yZOi9HH5ueU
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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…?
can god kill god
It’s not a paradox, the words are just incoherent. It’s like asking whether God taste the color blue. The answer isn’t yes/no, there is no answer.
An all powerful god couldn’t taste the color blue? First, synesthesia exists. Second, the judeo/christain god “smells prayers.”
Also, god died… in the Bible. Anyway w/e. You don’t strike me as someone I want to interact with.
The specific example doesn’t matter much. Google “category error” or read the comment below where I explain the response in more detail.
You don’t strike me as someone I want to interact with.
It’s not like I’m trolling. This stuff is philosophy of religion 101. But, you are, of course, always free to ignore information that contradicts your world view.
This stuff is not philosophy of religion 101, though it might be one seminary professor’s lesson notes in systematic theology for christianity. Specific religions will typically have mental gymnastics or say things like, “It’s just too complicated to understand with our limited capacity as mortals.”
Given a being exists outside of this reality, the laws of this reality do not apply to it. And given a being created this reality, that being can do whatever it wants, regardless of this reality and it’s laws. So the paradox still stands.
Given a being exists outside of this reality, the laws of this reality do not apply to it.
When we assume a contradiction is true (e.g., God is immutable and God is not immutable: P ^ -P), then we can derive any proposition and it’s negation from that contradiction.
- P ∧ -P
- P (1)
- -P (1)
- P ∨ X (2)
- X (3, 4)
- P ∨ -X (2)
- -X (3, 6)
If God can make a contradiction true, then every other proposition whatsoever can be proven true and false at the same time. We can infer the following: 1) All questions about God are useless because God is now beyond reason/logic and 2) Reason itself would lose all applicability as logic, necessity, mathematics, etc. can no longer be taken for granted. These seem like untenable consequences. We have, however, an alternate conception of God’s omnipotence that doesn’t force us to abandon reason/logic.
So, what you’re saying is, if it doesn’t fit our logic, we have to make up a logic so it fits our logic?
There are different logics that account for temporality, modality (e.g., necessity), degrees of true, etc. But I doubt there’s any logic we could construct that can account for the inconceivable and the impossible being possible. Human reason throws up its hands and sits in the corner.
So, we’re back to a paradox.
Thanks.
And… blocked.
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.
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.
You’re right it’s not a paradox but rather it is a statement that is self-contradictory or logically untenable, though based on a valid deduction from acceptable premises.
Movement of any kind is a paradox if measured
the ones from jan misali’s video
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).
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?
The box with $1,000,000?
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.
Also, thanks for taking me down an interesting rabbit hole. I’d never heard of that paradox before and enjoyed reading up on it.
My flaw with the two-box choice is that the predictor is - in some way or another - always described as “perfect”. Two-boxer people are contrarians!
~ Firm One-boxer
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.
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.
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…
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.
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 Grandfather Paradox, I’m partial to that one as well.
Bootstrap paradox is my favourite time paradox. I loved Doctor Who’s explanation.
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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.
