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There are things that we cannot imagine because they are impossible (like a solution to Russell's set theory, since it is impossible to reach that solution because it is illogical.)

Some months ago, discussing with a user in this site, he said that although no one has reached that notion, it could be the case that someone in the future could achieve it, but he did not know the topic well enough to make any meaningful conclusion. (https://chat.stackexchange.com/transcript/73718/2018/2/28)

Maybe someone here could help me

So could we develop a notion of conceivability that would allow us to imagine all of these things? Even all things that do not exist or cannot exist or are impossible like a solution to Russell's set problem or a thing that is illogical but at the same time is logical or inventing a new logic (or illogic) system...etc? What would be needed to reach such notion of conceivability? A change in the laws of physics? Or just biological evolution in our brains?

(I need answers from a scientific perspective, preferably)

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    It is already developed, see SEP's Impossible Worlds and Nonexistent Objects. – Conifold Aug 9 '18 at 0:27
  • @Conifold In this page (home.sandiego.edu/~baber/logic/logicalpossibility.html) it said that "If something can be imagined, even though it may be physically impossible, it is logically possible" . From here I can deduce that, currently, all that we can imagine is logically possible and we cannot imagine illogical things – Forsete Aug 9 '18 at 0:53
  • This claim is doubtful, time travel is logically impossible but sci-fi authors imagine it all the time. In any case, what we can imagine is a purely psychological issue different from conceivability. And logically impossible has been conceived since ancient times in reductio arguments (like rational square roots of 2). The impossible worlds were specifically developed to conceive of things that do not exist, not in the actual and not in any possible world, so your quoted source was mistaken. – Conifold Aug 9 '18 at 2:44
  • A solution for Russell's paradox is not impossible, He was happy with the solution given by Spencer Brown and for what it's worth so am I. On the main question, I don;t believe we can conceive of phenomena that are logically contradictory but not everyone agrees. For instance, some say that Chalmer's zombies are conceivable but I would disagree and say they are merely definable. It's a subtle issue. – PeterJ Aug 9 '18 at 15:13
  • @PeterJ but the question is not about whether we have this notion now, but if we could develop it in the future or with some special conditions: maybe with a change in laws of physics or biological evolution. Also referring to Russell's set solution: All of the solutions to Russel's Set require changes to the underlying assumptions of how logic works. Which doesn't help, since that means those sets are not really Russel's Set. With impossible solution I mean a solution to Russell's set logic bomb but without changing nothing of the underlying assumptions of logic – Forsete Aug 9 '18 at 15:23
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Assuming that word means what I think it means (sorry, couldn't resist), then yes. It is absolutely possible to achieve a framework where we can conceive something we could not conceive before.

In the mathematical world, the concept of "the square root of -1" (i) would have been inconceivable at some point in time. If you go back far enough, the concept of "-1" itself was not understood.

At some point in the past, the concept of a computer would have been inconceivable. Even more so if we go back before the invention of electricity. The concept of an aeroplane, however, has likely always been conceivable, even if people thought that it would be an impossible creation. There's a significant difference between impossible and inconceivable.

In short, there are inventions/ideas/concepts that are not even thinkable without other ideas already existing. But for many things, there is a chain of connected ideas that will make that concept possible to at least think about.

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    I am tempted to follow up the Princess Bride reference... Conceivability is usually thought of as a shared human trait. If some human conceived of i, no matter how long it took, it was conceivable all along. The immovable object does not become movable because people get stronger or develop fancy technology. If that happens, it was never immovable in the first place. – jobermark Aug 12 '18 at 1:44
  • @jobermark While I agree that conceivability is a shared human trait, I don't know if I agree that it is shared across all time. If one person today can conceive of a thing, then it is not currently inconceivable. But If nobody today can conceive of a thing, it is currently inconceivable. If someone figures out the theory/thought process around the thing tomorrow, it doesn't mean it was any more conceivable by today's standards. That said, you have thrown some doubt in my mind about my theory there. I'm just not convinced you're right yet. – Ryno Aug 12 '18 at 18:42
  • The concept of "immovable object" is itself only a logical/philosophical concept - it can't really exist at all, so I'm not sure it proves this point. – Ryno Aug 12 '18 at 18:42
  • There are obviously two meanings here. And both are real in ordinary usage, but within philosophy by far the more common is the one that does not change over time. When you say something is impossible, if you don't explicitly say 'currently' or something like that, you generally mean absolutely impossible throughout all of time across all humanity, not just impossible right now or by you. (From an intuitionist POV, that is utterly stupid, but it really is what people usually mean -- that in a classical logical sense, free of time and evolution, things absolutely can or cannot be done.) – jobermark Aug 13 '18 at 21:16
  • The more I think about this, even if you're right, insisting on that definition just makes the question meaningless, rather than exploring the concept asked. So I stand by my answer as being more useful to explore the concept asked in the question, even if that definition of inconceivable is more widely used. Again, both your comment here and your answer have given me things to think about though, which is great, so thank you (even though this isn't my question!) – Ryno Aug 14 '18 at 22:36
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What is conceivable is not necessarily ultimately logically possible.

We can conceive of a moon made of Green Cheese, but since humans invented Cheese, this is not logically possible, since it seems obvious that the moon is older than we are. We didn't have any problem creating the mental image in order to analyze it, but we cannot believe in it either.

So belief is a state between conceivability and logical possibility. I would suggest there are at least two more that are actually important: (scientifically) creditable' and '(intuitively) appealing'.

(I hope what follows is not just belaboring the obvious as an excuse to describe a metaphor I find compelling.)

One way to capture the range of definitions involved would be to reify the language game of logic. Imagine that everyone who negotiates our culture's belief system made up a small number of people who could actually take turns talking, each one of them trying to get the group's approval of their thoughts, and that approval or disapproval was communicated directly via a visible emotional response. This is a simplified metaphor for what Wittgenstien describes as a cultural language-game. Logic is one such language game: one such topic this group might agree to focus on regularly under certain conditions.

One can conceive of anything that one might think could motivate a move -- that could suggest an utterance that captures an image and one might hope could contribute to a consensus it has meaning.

But something is only believable if there is not a defeating series of countermoves that reduces it to a contradiction quickly enough that the contradiction becomes apparent before the ideas consequences can be elaborated. In order to believe it, it has to set in and have meaning and effects on your other thoughts before it is dissolved by noticing its weaknesses.

And it is only 'scientifically' creditable if someone who has all the known material related to it as an expert, is still likely to find it believable. It can only gain credit as an idea in a domain of knowledge if it can be communicated around that domain without falling prey to an easy dismissal.

If there is still a contradiction, but it takes a lot of moves to prove it, and the proof is unlikely to occur to a random well-informed expert, so that the idea is actually likely to persist in most people if introduced, we might call such a thing an illusion.

If the illusion is hard to dispell, and the resulting deserved disbelief is often temporary, or has to be rehearsed in order to become acceptable, we sometimes call such a state 'counterintuitive'. This is a word you often hear describe results in mathematics related to infinities or complex structures. And we call the illusion itself 'intuitively appealing'.

But even the most intuitively appealing illusion is still not logically possible. What is logically possible is not disprovable with our most complete analysis. Disbelief in it cannot be stable over time even as something captured with difficulty.

We might develop conceivability in its raw state, but it does not seem like that would be an improvement.

Many would prefer to develop 'intuition' in the sense of being able to accept that illusions are illusions even when that is counterintuitive, and therefore to also accept counterintuitive truths -- things whose opposites are illusions that would be intuitively appealing.

This might need a broader range of concepts and therefore an ability to conceive of things and get to the point of believability, but that is not what it seems to be mostly 'made of'. We seem to be able to trust other humans enough to acquire a belief from them of which we would not ourselves readily conceive, stepping past the point of conceiving of it and 'falling backward' into that state from the arguments that led those other people into belief.

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Whether something can be conceivable and yet impossible has been discussed at length in the literature, for various senses of possibility, for example in this paper by David Chalmers.

Of course, at some level it is possible to conceive of impossible things. For example, in the Monty Hall problem, many people find it conceivable (in fact, they strongly believe) that it shouldn't matter whether you switch. But in fact that is mathematically incorrect (and thus impossible in a strong sense). Similarly, for many famous open mathematical conjectures, it is conceivable to us that they're true and conceivable to us that they're false, but in each case one of these answers is false and therefore mathematically impossible.

  • I feel like this answers a different question. Rather than "can we conceive of things that were previously inconceivable", this seems to answer "can we conceive of something impossible" – Ryno Aug 14 '18 at 22:17
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    Hmm, I thought the question actually was whether we could come up with a way of conceiving of the impossible...? – present Aug 15 '18 at 1:09

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