Of course, as far as I understand it, that's not what Gödel was arguing. I doubt that he was claiming that the process which we supposedly observe as time is an illusion any more than Einstein was claiming that the phenomena described by Newtonian physics don't exist. But then again, if he had been that skeptical about time, he couldn't have been a scientist at all, even a theoretical one.

He wasn't a scientist. Mathematician and philosopher, almost certainly, but not a scientist. Which was part of the reason why he was such a good mathematician; as he once famously said about Hilbert (re. incompleteness): "It's not that I'm a better mathematician than Hilbert. Possibly nobody could make that claim. It's that I'm a better philosopher than Hilbert."

(that's a paraphrase, but it captures the gist of what he said)

Now, Hilbert wasn't really a scientist either (as you may have noticed, I don't generally classify mathematicians as such, not least because most are Platonists), but I think you'll find that the component of Hilbert's philosophy that Gödel was criticizing was similar to what you're characterizing as the default scientific viewpoint.

I, for one, wouldn't be at all surprised if Gödel really did think time was an illusion.

For all that don't get the idea that I'm denying the possiblity of time in reality, just that it can't be imagined as an idea, and therefore can't really serve as a basis for other ideas.

At that, what things "in reality" can we imagine as an idea? Clearly any idea we have will fail to cohere, in some respects, to "reality", so what's an example of something that can be imagined as an idea?

For myself, I say that "time" clearly exists. It's a mental construct that humans invented and frames practically every aspect of our lives. Now, is this construct a faithful model of "reality" (I continue to put this word in scare quotes because it seems to be a rather undefined term), or does it diverge wildly from what an objective observer (whatever that is) might see? That, as I see it, is an entirely separate question.

Oh, and one last thing: the underlying inconceivability that you've neglected and that underlies the three that you mention is life. The other three are all essentially corollaries of this more basic idea (or un-idea, if you prefer). Or rather, given that it's almost ludicrous to even discuss life being impossible (if not inconceivable), perhaps the more apt inconceivable would be non-life.

Of course, the first step is to define terms...

He wasn't a scientist. Mathematician and philosopher, almost certainly, but not a scientist...I, for one, wouldn't be at all surprised if Gödel really did think time was an illusion.

These two statements are linked, and I'm not displeased that you've done so, because in fact you're simply re-enforcing my point. However, I think you may have misunderstood my terminology. I wasn't saying that Gödel was a scientist either by profession or disposition, simply that, when he took on concepts derived from relativity he was working with science, or at least the conceptual materials of science, and to the extent that he was working within those paramaters he was acting as a scientist. The fact that he used those materials to undermine central premises of science is why I wouldn't be surprised if one day historians consider him to have stood at the end of the true scientific age. As for whether he really thought time was an illusion, I wouldn't be surprised either, but that doesn't seem to have been what his theories claimed (correct me if I'm wrong).

As for the second part of your criticism, I'm not very pleased with your general tone. The dismissiveness might be justified if I were criticizing the correspondence principle, as you seem to think, because that is essentially a straw man that people often set up, for example, when they are trying to dismiss mathematics as totally abstract, a tendency which I criticized in an earlier post. This is an especially dubious strategy given that reality is, as you point out, a pretty vague concept, and I think we are all aware that at some level the only reality we are addressing are our own concepts (also why Kant's saving of a theoretical, unperceived outside reality is irrelevant).

That was not my point. My only concern is the internal consistency of an idea. The idea of the "present moment," the collapsing second, has none. Defined as a single moment which is neither past nor present, it is incomptible with the notion of time as a non-disjunctive process, which is itself necessary in order to imagine time as a constant property of the world. I suppose it could be claimed that there is no present, simply a constant movement from past to future, but in that case time becomes incompatible with the idea of reality, i.e. that which actually exists (actually being employed in its traditional rather than modern sense). The future is not inconceivable, simply unperceivable. That is not a judgment on my part against the possiblity of clairvoyance, simply an extrapolation of the terms, the future being that which has not come into existence and perception of reality being perception of what actually exists. But without any perceptual basis or even a notion of a mechanism by which the past could be created from it belief in the future seems pretty irrational. I note once again that I'm not basing this on an appeal to our experience of "reality," but purely on the internal definition of these concepts (well, my definition, obviously--there's no such thing as true denotation, but that's a different subject). I don't doubt that all of these concepts could be re-arranged to be brought into line, but since my point was simply one about intellectual consistency, not metaphysical reality, that doesn't really matter. Well, actually, it is somewhat relevant, since my real point was not speculation about time or lack thereof but rather the malleability of all ideas and ideologies, specifically regarding the fact that the crumbling of the traditional founding beliefs of science (or religion, for that matter) is hardly a metaphysical catastrophe, merely a change in ideas.

p.s. Yes, non-life is inconceivable, as is any non-entity, since non-existence is precisely the negation of perceivability. If you notice, I make that point as well at the end of my post.

As for the second part of your criticism, I'm not very pleased with your general tone.

I think you misread; there was no explicit or implicit dismissiveness in what I was saying. You say time cannot be imagined as an idea, with which, at least as you frame the issue, I agree with you. However, my question was, within this framework, what is an example of something that can be imagined as an idea? Only if this collection is non-empty is the statement that time is unimagineable meaningful, and I'm not entirely sure that, by these standards, this collection is non-empty, which is why I (un-ironically and un-dismissively) asked for an example.

Also, you dismiss correspondence, but I'm also curious if consistency is even meaningful absent some connection to correspondence. Again, I'm unsure.

My statement about time being clearly existent was meant to point out that it is dangerous (at least in my view) to characterize something as inconceivable merely because it is inconsistent. Some would say that this is the great shortcoming of the entire rationalist approach, be it the inductive (scientific) or deductive (math/philosophy) branch.

Again, dismissiveness is not part of the program. I'm pretty sure I'm taking you at least as seriously as you're taking yourself.

p.s. Yes, non-life is inconceivable, as is any non-entity, since non-existence is precisely the negation of perceivability. If you notice, I make that point as well at the end of my post.

That's not quite what I meant, since life is not generally considered an "entity" (but, then again, maybe it should be). Admittedly, it's related...

Perhaps more concretely, one might ask the question: "Is there anything which is not alive?" A much harder question to answer than to ask.

However, my question was, within this framework, what is an example of something that can be imagined as an idea?

Something that can be imagined as an idea? Memory. Not memory as it is commonly conceived, i.e. a reconstruction of past events, but rather an imaginative placement of self in an alternative environment. Note that this solves many of the problems that have plagued theorists of memory, such as the question of how a memory can actually be retained when it seems to be cognitively re-created every time it is recalled. Granted it solves the problem but demolishing the chronological relationship which seems to be its most fundamental element, but preserving that is no concern of mine.

Also, you dismiss correspondence, but I'm also curious if consistency is even meaningful absent some connection to correspondence.

Or perhaps correspondence is simply a form of internal consistency that claims to be something higher. And in a sense you're right: whether or not consistency has meaning without correspondence to something external, it certainly would not have value if it diidn't. But the natural question is: "correspondence to what?" If we are speaking about ideas, it seems pretty clear that no matter what the point of correspondence, it is always another idea. Take Locke's rock for example: "The word 'rock' corresponds to a actual rock because the definition of a rock is a firm inanimate mineral body, etc. and rocks are indeed firm, inanimate, composed of minerals, and so forth." A tautology if ever there was one, but that simply illuminates the point that the form of the correspondence is tautological: a definition is compared with a list of supposed properties, which if they correspond is simply the definition. There are of course many more sophisticated examples of correspondence, and other types, but I have yet to see one that breaks out of the linguistic cacoon.

My statement about time being clearly existent was meant to point out that it is dangerous (at least in my view) to characterize something as inconceivable merely because it is inconsistent.

But that's not why I labelled it as inconceivable. I called it inconceivable from a subjective point of view because I cannot form a coherent idea of it. An idea might be conceivable if there are elements of it left unaffected by the conflicting parts, but when it comes to the "present" there seem to be two basic aspects and they are opposed to each other. I simply cannot add one to the other since it is precisely a negation of it.

Again, dismissiveness is not part of the program. I'm pretty sure I'm taking you at least as seriously as you're taking yourself.

Maybe more so. Who said anything about a program?

Perhaps more concretely, one might ask the question: "Is there anything which is not alive?" A much harder question to answer than to ask.

One could ask it, but I'm not sure what the relevance of it would be. I would guess that people generally ask it in lieu of two equally theoretical but more personally affecting questions: "Is there anything different from me?" and "Is communication possible?"

Maybe more so. Who said anything about a program?

You said you thought I was being dismissive, and I was just trying to reiterate that I wasn't intending to be so. Maybe "program" was the wrong word.