Clutch

Thought I'd mention this here, having raised it tangentially over on EoG. A lot of logicians and metaphysicians are very interested in this puzzle nowadays; folks here might be interested too.

Basically it started with an argument floated by Frederic Fitch in a 1963 paper in The Journal of Symbolic Logic. Fitch showed that for any notion O that is both factive and distributive, and given only radically minimal assumptions about modality (viz, that logically absurd propositions are necessarily false), you can first prove the absurdity of

O(p & not-Op)

And then it (classically) follows that if you hold the principle "If p, then it is possible that Op", you are committed to "If p, then Op".

Here's the kicker: knowledge is just such a notion. In other words, if you hold that any truth can in principle be known, then you are logically committed to holding that all truths are actually known. (At least, that they will all be known eventually).

Plantinga actually recruits this as an argument for theism. If you have grounds (say, meaning-theoretic grounds) to hold that all truths are knowable in principle, then, says AP, you should bite the bullet and postulate an omniscient agent.

tronvillain

Would that problem still arise if knowledge was treated as probablistic? It seems that if you hold that no truth can be known for certain, you are not committed to holding that all truths are actually known.

Clutch

Right; that's to give up the factivity of knowledge.

Comes down to semantics, but the consensus seems to be that this would be tantamount to giving up the notion of knowledge, strictu dictu, and just talking about degrees of warrant. Yes, that would work.

(In fact, you'd also give up distributivity in its simplest form, now that I think of it.)

tronvillain

Ah. Well, as far as I can tell, that is what everyone actually does.

Bill Snedden

What does it mean to hold that all truths will be known eventually? Doesn't that assume that there are a finite number of truths to be known? Is that possible? Couldn't the knowledge of some number of truths create additional truths to be known (and so on, ad infinitum)?

If there are in fact a finite number of truths, then I don't see any problem in believing that they will all be known eventually, but I wonder if changing eventually to "never" given an infinite number of truths actually changes the nature of the argument.

I wonder also how this sort of notion squares with Cantorian set theory, which seems to suggest (ala Patrick Grim) that the power set of all truths cannot exist and thus the very existence of an omniscient agent is called into question.

Regards,

Bill Snedden

Clutch

Bill, I guess it means that there exists no truth that is never known. If this is incoherent, then Plantinga's argument fails, but the supporter of principled knowability is in even worse shape than inadvertently having an argument for theism!

John Page

Depends on your definition of truth:

1. If you hold that truth is an absolute then you get the kind of results you indicate. Indeed, these results argues against the validity of the "absolute truth" concept because there is evidence that we do, in fact, acquire knowledge.

2. If however, you hold that truth is only a relation held in the mind (IMO "known" in the brain), all you are doing is saying we hold true what we hold true (a non-contradictory tautology).

Cheers, John

Clutch

John, I don't know what to make of that. Neither what the contrast is supposed to be (is truth *absolutely* "only a relation held in the mind"?), nor how that view could possibly recover the functions of the natural language term "truth".

Anyhow, adopting that view, whatever it is, might well block the Fitch argument. But then, so might adopting the view that truth is a cheese sandwich.

John Page

Truth is something you think. You see an object, maybe the Law of Identity, or an apple, and you think "That is a true <language label>" You arrive at "truth" by comparing things and this is a mental act.

You can see a dog running down the street but you can't see truth. Truth is a meta-object that you perceive - once you stop perceiving that "truth" the event is over. Our senses and experience, however, tell us that the dog is still there even when we're not looking.

Logic truth functions assume extentionality - but this only ranges over identical variables[Deliberate oxymoron]. In "real" life extentionality cannot be assumed because the variables are not identical - they merely conform to the archetype in your mind. Back to dogs, all dogs have four legs except those with three legs. True but illogical.

Not as precise as I had hoped but I hope the above points show why logical truths cannot be assumed to apply directly to actual existence. As to your cheese sandwich, I seems more logical that it equate to another cheese sandwich than the truth function that makes them equivlent. Hope this demystifies the truth and other lies.

Cheers, John

Vorkosigan

It's a philosophical proof. Like all other philosophical proofs, it is meaningless as far as the real world is concerned, until empirically supported.

What it says is that if you hold that any truth can be known.....but most of us are committed to the concept of provisional truth, and are therefore not committed to the concept of capital-T truth.

Vorkosigan