How do you choose a thing (or a “candidate for a thing”) without thinking about that which you are choosing to not be able to think about? If you do not think about it, then therefore your choice of “thing” is unconstrained, and the statement is vacuous.
Perhaps an example will help. I will quote Frylock and use the relevant assertion to form the example:
Is there anything I can’t think about? No–because while <candidate X> can’t be thought about, I can think about thinking about <candidate X>.
But wait, what is <candidate X>? The statement is vacuous without actually putting forward a candidate for which we may put the assertion to use by “thinking about it by considering it under the label ‘the candidate for the thing I can’t think about’”. What candidate for a thing have we put forward? If we do put forward a candidate, then the statement becomes self-contradictory because we must think about the candidate in order to nominate it as a candidate. If we do not think about it, then the statement is again vacuous because we are talking about our ability to think about something that we have not defined.
I mean, try it:
“<Cat> can’t be thought about [damn! I thought about it!]”
“<square circle> can’t be thought about [wait, what is a square circle?]”
“<X> can’t be thought about [what is X? A turkey? Ok. Damn, I thought about it!]”
This is all about semantics. I’m just pointing out that I don’t think your semantics are great. There just isn’t much information content in Frylock’s statement. It makes more sense to simply say that we can think about the possibility of things that we can’t think about. This is distinct from saying there is nothing we can’t think about, which I think is a little silly, because of course there are things we can’t think about. We know this by induction. We just can’t point to them.
Yes I supposed it. But I did not think about something I can’t think about. I just made the reasonable supposition that there are probably things I can’t think about. I did not point to some thing I can’t think about. So no, I did not think about some thing I can’t think about.
So when I think about a ball I’m not thinking about a ball in its totality. I’m not thinking about every single feature of a real ball – every atom, every vibration, every electron orbital. I’m thinking about a small collection of properties that will roughly approximate the behavior of a real ball.
What this means is that NOTHING is inconceivable. Some things will be better approximated in our thoughts than others – our understanding of some things will be less lossy. But there is always some level of crudeness of representation we can dial back to that will make thinking about a thing computationally tractable.
But you don’t have to point to a thing in order to think about it. I’m thinking about the next child concieved on the planet. I can’t point to it–indeed, it doesn’t even exist. But there I am thinking about it.
Then I suppose random numbers are inconceivable? (Being incompressible…)
Of course, they are, in a sense, since human beings can’t create true randomness. But thinking about random numbers – indeed, proving theorems about them, determining their properties and so on – poses no problem at all.
That’s one idea; I think it was a computer scientist that first came up with it (Gregory Chaitin). It’s hardly a consensus view.
Personally I think understanding as prediction works better. I have some form of understanding if I can make valid predictions or inferences about a system / entity.
Leibniz got there before him, which Chaitin readily acknowledges: he likes to cite the ‘inkblot-story’, in which Leibniz muses when a pattern of ink blots on a page can be supposed to follow a law; the answer he arrives at is that they do precisely if there is a function than generates this pattern, such that the function is ‘smaller’ than just the pattern itself. In other words, it is lawful if it is non-random, and if it is lawful, knowing that law surely constitutes understanding that pattern; but the law is precisely a compression of the set of data points, so in this sense, understanding is indeed data compression.
Since “thought” is really just the language you speak to yourself, isn’t this really a question about the formal completeness of language?
Grabbed this quote here:
I’d phrase it in terms of computational universality: the human mind is computationally universal, i.e. it can compute everything that can be computed (by some formalized notion of computability, such as furnished by Turing machines) (at least in the limit of infinite time and resources, i.e. with enough note paper), and the universe is (to all appearances), too, so anything the universe can come up with, a human mind can, too, at least in principle.
I think you might have created an unapparent tautology by using homonyms.
I’m going to give the word “conceive” two of its most common definitions. (red dictates an a priori sense, and blue an a posteriori sense):
The mind cannot conceive [imagine] a scenario it cannot conceive [understand/know].
This is untrue, as given above: I can imagine what it’s like to give childbirth, but I’ll never really know or understand the actual feelings involved, given I’m male. Females can imagine to a greater degree, but cannot ever come to full understanding and knowledge of giving birth, until she actually does.
Now, let’s reverse the definitions:
The mind cannot conceive [understand/know] a scenario it cannot conceive [imagine]
Again, this is untrue. We can understand the particulars of a hypercube, and what it would mean if we extrapolated space into 4 or more dimensions. We can even understand an infinite universe, that is eternal. Blind people can understand color, and parallax, but to really imagine it, however, is something entirely more difficult, frustrating, or downright impossible.
To keep the definition of conceive the same within the same sentence, then it goes without saying, in either case.
I was trying to think of something along those lines but then I was thinking that natural language is more like formal language than like programming language. But maybe you’re on to something with the notion that the mind is Turing equivalent to the universe. Not sure how you would prove it, though.
Could you come at the problem from this direction: What is the set of concepts that cannot be described in language? The set itself can be described, so it’s not self-referential. But it can’t have any well-ordering; otherwise, we could describe the “least element of the set of concepts that cannot be described in language”, which would be paradoxical. I think that implies that the set is either null or infinite. I don’t know how we would go about trying to prove that it’s the former rather than the latter.
Well, see, that’s sort of my point: it seems to me the OP can conceive of things, ‘in a meta way,’ that he can’t conceive of in, uh, a non-meta way – and that he’s doing so when conceiving of things (in a meta way) that he can’t conceive of.