The monotheistic all powerful one.
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.
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.
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.
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.
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 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 :)
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.
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?)
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.
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…?
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.
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.
The two slit experiment.
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.
