Scientist reported the other day that they have found a planet so hot that it probably rains gem stones, they cannot prove it yet but who would have thought something like that was conceivable.
There are probably millions of things that no one can even imagine but that really do exist, just don't ask for proof until they are actually discovered.

What sort of answer is this? Of course a planet so hot that it rains gemstones is conceivable, I have a mental image of it right now. And I could easily have a mental image/conception of a planet so hot that is rains gemstones any time before it was every noted by scientists.

What sort of answer is this? — maplestreet

Obviously not the one you were sitting there waiting for, less than 3 minutes to reply seems kind of fast.

Of course a planet so hot that it rains gemstones is conceivable, I have a mental image of it right now. — maplestreet

But did you conceive it before I mentioned it? that is the point I was trying to make.

And I could easily have a mental image/conception of a planet so hot that is rains gemstones any time before it was every noted by scientists. — maplestreet

But you didn't did you. Which just goes to show that anything is possible as soon as someone discovers or conceives it. No one will ever know until then whether something is actually possible.

It would seem hard to affirm this, since it seems hard to know the limits of conceivability. — maplestreet

Well what about turning it around a little? It could be that conceivability is the limit on possibility. It is basic to notions of existence that being must be intelligible. The self-contradictory is impossible to start with. It already rules itself out. So if something actually exists, it must have been possible because it had this kind of essential reasonableness of conceivability.

So it hinges on your definition of conceivable.

If you just mean are there things that we humans could never really imagine, yet they also exist, then of course this seems true for practical reasons.

We might lack access to the scales at which these things exist in a way that might give us the usual clue to get conceiving. They may simply escape our notice, rather than being actually inconceivable.

And also we might only ever get an imperfect grasp of something that can attract our notice. We can still conceive of the thing (as an explanation for some phenomenon), yet that conception might be held as extremely general, or partial. However again, that is a practical issue of either effort or access. There is some level of conception that is going on even to know that there is a phenomenon in need of explanation.

But at the deeper level of metaphysical possibility, we would have arguments that any forms of existence must depend on the kind of possibilities which are conceivable - that is, which meet rational principles like being not self-contradictory.

However then after that we get into the tricky area where possibility itself is defined in terms of self-contradiction. A potential - like say electric charge - can exist because it is the breaking of a symmetry. You can have positive because you can also have the contradictory state of being negative. And neutral is neither - in being both.

Get down to the quantum fine grain of things and the neutral vacuum seethes with matched pairs of virtual particles having temporary (measurable) existence before mutually annihilating. At least that is one useful conception that seems a good way of accounting for the phenomenology.

So the message there is that if conceivability is taken as something stronger than a "mere combination of words" approach to imagining possibilities - if it is in fact taken as a logical constraint like the principle of non-contradiction - then physics suggests that only that kind of conceivability has a strong relation to the facts of material existence.

A "hot planet raining gemstones" is a "random combination of words" type conception. It suggests an actuality but is too vague a proposition to be answered without further information.

However the proposition that "there must be a solid gold planet the size of Jupiter somewhere in an infinite universe" can be ruled out as self-contradictory from known physics. We can know from general relativity that a mass that heavy would collapse under its own gravity and turn into a black hole.

So a ball of gold the size of Jupiter becomes only possible if the Universe is other than what it is. Issues of conceivability limit the actual possibility, even if the statement itself - there is a gold ball that large - is easy to say.

The point though is that conceivability does not preclude the possibility of someone else or myself having a conception of it at any time prior to its scientific discovery. I easily could have conceived of it. Hence it is conceivable.

Alternatively, I would almost bet money that some science fiction writer in the past conceived of such a notion, but I am too lazy to look.

Edit: I suppose I should have just said that even the scientists that made this discovery thought of this exact sort of planet, so it was conceivable to them.

Definitely not in agreement with the notion of physics determining what is possible or with the notion of self-consistency determining what exists either, but you touched on a lot of classic points. To give you a better idea of what I take conceivability to mean, I interpret 'x is conceivable' to be more or less equivalent to 'x can be thought of' (even if for reasons of practicality, no one ever actually DOES think of it)

Definitely not in agreement with the notion of physics determining what is possible or with the notion of self-consistency determining what exists either — maplestreet

Well given physics is what has examined this question in the most exhaustive fashion, I'm not sure what you would be basing your reluctance on.

o give you a better idea of what I take conceivability to mean, I interpret 'x is conceivable' to be more or less equivalent to 'x can be thought of' (even if for reasons of practicality, no one ever actually DOES think of it) — maplestreet

But that is merely the trivially true "random combination of words" approach to conception. An infinite number of typing monkeys would surely generate every conceivable truth on that score - but leave the whole question of why any one conception would rate as carrying any reasonable force quite untouched.

So even if you deny it, you are still in fact going to be seeking not just conceivable in a bare propositional sense divorced from any likelihood. Surely you would want to be talking of conceptions with some kind of further motivation behind their utterance.

And then, as I say, practicality does come into it. There is always going to be a conceiver with both a purpose and a matching level of indifference. You can't simply ignore that aspect of the question and expect any sensible comment.

God

A decent candidate, but many people would claim that God can conceive of Himself

A square circle.

They exist in Godelian space.

I guess I'm unclear on a lot of things you find important or relevant here. For the sake of this question, all I care about is whether or not there is something that can't be thought of. Is it trivially true to you that everything can be thought of? Ok, that's great. That's sufficient to me.

For the record, I don't think it's necessarily true, much less trivial at that, that all the typewriter-monkey-brains would eventually think up anything possible. Just like even if you have the infinite set of even numbers you won't find an odd number among that infinite set. Or equivalently, just because we can mash together all the words in the world in any sort of combination doesn't mean that there is something possible out there that is unexpressable in any sort of string of words (something that analogously is not conceivable).

Physics is either inaccurate, or is just a few specific types of perceptions. I dislike it on a whole as an enterprise, because it is often used to conclude far more than the actual perceptions it is based off could conclude themselves.

For the record, I don't think it's necessarily true, much less trivial at that, that all the typewriter-monkey-brains would eventually think up anything possible. — maplestreet

Well I don't either. And so my point is that focusing on conception as "that which can be said" is trivial. It is clearly not sufficient.

I guess I'm unclear on a lot of things you find important or relevant here. — maplestreet

They go to the issue of what would even count as sufficiency when it comes to this apparently rather nebulous thing of "conceivable".

Or equivalently, just because we can mash together all the words in the world in any sort of combination doesn't mean that there is something possible out there that is unexpressable in any sort of string of words... — maplestreet

The missing argument there is why words couldn't be invented as fast as the need arises. Clearly, words and conceivability go together somehow. I was focusing on that how. The relation is tricky.

Physics is either inaccurate, or is just a few specific types of perceptions. I dislike it on a whole as an enterprise, because it is often used to conclude far more than the actual perceptions it is based off could conclude themselves. — maplestreet

People never like what they don't understand.

I think the universe is a good example.

We don't have a theory of everything so in a sense the existence of the universe is yet inconceivable to us, but the universe exists despite that fact.

But I don't need to conceive of every single property of the universe in order to have a conception of the universe. My mind can simply grasp the idea of the universe as "all of existence", and this means the universe would be conceivable.

1. What is a square circle, and what is Godelian space? 2. More importantly, how can you prove that one cannot have a conception of a square circle?

I suppose, but your question made me think of this quote.

I have no doubt that in reality the future will be vastly more surprising than anything I can imagine. Now my own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose.

-J. B. S. Haldane

I can accept this quote. Just because something is unimaginable to someone now, does not mean it is unimaginable in general.

That is true, but it could be that the universe is more strange than we are even able to comprehend.

Well yes, hence my original question. I am looking for a proof or serious argument that would give me a good reason to believe that "the universe is more strange than we are even able to comprehend".

Oh I don't know of any proofs that universe is incomprehensible.

Maybe this?
https://arxiv.org/abs/1502.04573

It is a proof that a problem in physics has no logical solution.

No, but you at least have a much better understanding of my problem now.

To say that something is (formally) undecidable in an axiomatic system is to say it is true in a certain system and false in another. This is a much different meaning from incomprehensibility, which has a much more cognitive aspect.

No to say something is undecidable is to say there is no axiomatic system that can be used to resolve the question in a finite amount of steps.

If something is undecidable in one system it will also be undecidable in any other system.

That is to say you can not obtain true or false about that problem.

"Possible" refers to what can obtain. (And can refer to different contexts, such as what can obtain logically, metaphysically, etc.)

"Conceivable" refers to what someone can coherently imagine.

The two are not at all the same.

The former (at least when we're talking about metaphysical possibility) is limited by facts in the world independent of persons.

The latter is limited by an individual's mental abilities.

Obviously one can't list something that one believes is possible but not conceivable, because by imagining it, one can conceive of it. It's simply asking someone to do something they are not capable of doing.

But some people can conceive things that others cannot. We do not all have the same mental abilities. So conceivability is always a matter of who we're talking about, exactly.

More importantly, how can you prove that one cannot have a conception of a square circle? — maplestreet

Asking whether it's provable that something isn't conceivable is a different (and a silly in my opinion) question. Of course that's not provable. For one, if you see it as an empirical issue, empirical claims are not provable period. But even if you simply consider whether it could be provable that something isn't conceivable on purely logical grounds somehow, all someone has to do is claim that they can conceive it, that the logical argument must therefore be flawed, and there's no way to counter that really. Proofs, after all, are always relative to particular systems of logic, and there are a lot of different systems, with some incompatible with each other.

This is an answer typical of someone who has never take a class on ZFC or basics of set theory. You are using "undecideable" in the sense of computability theory. I am using it in the traditional Godelian sense. It's quite easy to show how your statement

"If something is undecidable in one system it will also be undecidable in any other system."

is incorrect: Simply make a new system in which said statement is added as an additional axiom to this system. It is therefore (obviously) true in a very trivial manner.

Also, it's also quite clear that undecideability (in either sense of the term) is an unsuitable basis for determining conceivability, as I've already demonstated.

If it is not conceivable then it's not able to be witnessed. It would be outside of our knowledge except perhaps by indirect inference. For example, we don't really know what dark matter is, but many scientists use it as an explanation for certain phenomenon. The theologian would use God as an explanation for the causal chain. Etc.

I can think of this in one of 2 ways.

1. Yes. There does exist something (if it exists, it is possible) that hasn't been conceived of.
2. No. This implies the assertions A. that in order for something to exist, it must be conceivable, and of course.. B. We haven't conceived of it, therefore, it can't exist.

1 makes more sense to me.

It's not obvious at all to me that possibility is different than conceivability, and your comments on the matter are presently insufficient to show this.

1. Your definition of 'possibility' begs the question to say it is independent of persons. I see no reason to believe why the 'possibility' should be concerned with anything more than simply ways in which the world might exist. It also assumes a very objective sense of the term 'world'. But all I can assume is that the world is simply all of my perceptions. I have no evidence of anything independent of my perceptions. So it is possible to say that the ways in which the world might exist are simply which ways my perceptions are limited.

"The latter is limited by an individual's mental abilities."-Sure, but what if my mental abilities are equivalent to how the world can behave (akin to what I just said a moment ago)

So, it's certainly not obvious to me that they are both different.

2.

"Obviously one can't list something that one believes is possible but not conceivable, because by imagining it, one can conceive of it. It's simply asking someone to do something they are not capable of doing."

This misses the overall point. At best, if your conclusion here follows, all it shows is that one cannot generate a concrete counterexample. However, this does nothing to preclude the possibility of a proof of mere existence, that has no concrete referent. It also does nothing to preclude a proof by contradiction. However, at least you note later that " it could be provable that something isn't conceivable on purely logical grounds somehow,"

However, your justification for this is not nearly so inscrutable as you suggest. This is mainly because a mere claim of the person who disputes such a logical argument is insufficient to rebut that argument (because such a claim would require actual evidence in order to shift back the burden of proof; a claim alone won't rebut that argument). So we don't have to worry about potentially not knowing whether or not that particular person truly could "conceive of it". The keyword here is 'it', which betrays your error of supposing a logical argument would have to provide some concrete possibility, the 'it'.

1. I agree that your '1' is a legitimate possibility, with the important edit that 'hasn't been conceived' be changed to 'can't be conceived'
2. I agree that your '2a' is also a legitimate possibility, with no changes.
3. I agree that your '2b' is also a legitimate possibility, with the important edit that 'We haven't conceived of it' be changed to 'We can't conceive of it'. More importantly, I'd like you to note that 2b is the same as 2a, as it is the contrapositive of 2a. In other words, 2b is redundant.
4. Most importantly of all, I'd like you to give me some sort of justification for thinking "1 makes more sense to me."

Sure, but this still doesn't answer my overall question. It is merely the consequent of one of the possible answers to my question.

1. Your definition of 'possibility' begs the question to say it is independent of persons. I see no reason to believe why the 'possibility' should be concerned with anything more than simply ways in which the world might exist. It also assumes a very objective sense of the term 'world'. But all I can assume is that the world is simply all of my perceptions. I have no evidence of anything independent of my perceptions. So it is possible to say that the ways in which the world might exist are simply which ways my perceptions are limited. — maplestreet

Idealism is wrong. So that's your first problem. If you're not making the typical infantile conflation with respect to your perceptions and what your perceptions are of, you should have evidence of things independent of your perceptions.