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#37
Mar29-12, 08:23 AM
PF Gold
P: 322
Quote Quote by lugita15 View Post
Sure, I can go on to other ones. (And it's a he by the way.) But let me first explain my preferred resolution to Fitch's paradox. I came up with it on my own soon after reading about the paradox a while back, but then I later found out that Joseph Melia thought of more or less the same solution in 1991; see the attached paper. The key idea is this: Fitch's "argument presupposes that we can discover a statement's truth value without affecting that statement's truth value. But this is not so: there exist statements which are true, yet which would have been false had we performed the procedures necessary to discover that statement's truth value."

To illustrate this point, suppose for sake of argument that it were possible for someone to be omniscient (i.e. knowing literally everything) but that no one was actually omniscient. Now consider the statement "No one is omniscient." That would be a true statement. But could it be known? Well, since we're assuming that omniscience is possible, by definition it would be possible for someone to know literally all true statements. But in that case "no one is omniscient" would not be a true statement, so it obviously wouldn't be known. So the thesis "all truths are knowable" doesn't make much sense, only because if the truth value of some true statements were found out they would no longer be true, and thus no longer be in the set of statements people can know (because you can't know a false statement).

So how do we remedy that? Surely "all truths are knowable" does try to capture some sensible and debatable sentiment, namely the belief that there are no limits to human knowledge. A better way of expressing that sentiment, one that does not fall victim to Fitch's paradox, is to say, "all truths are verifiable" or to put it another way "the truth value of any statement is knowable". To put it in more formal language, "For all statements P, either P is knowable or not P is knowable." You might think that that's equivalent to "For true statements P, P is knowable and for all false statement P, not P is knowable." But that's not true. Because your knowledge of the truth value of P may change the truth value of P (e.g. "the statement "there is no light in the room" becomes false if you turn on the light to test whether there's any light in the room!). But the important point is that Fitch's paradox allows for the possibility that you can find out the truth value of any statement, and if that's the case then surely it does not put any limitations on human knowledge.

Does that make sense to everyone? If not, look at the attached paper, and if you still have questions I'm happy to try and clarify matters.
I do see where you're coming from. Allow me to tell you how it runs with me.

Your statement .. suppose for sake of argument that it were possible for someone to be omniscient (i.e. knowing literally everything) .. seems contradictory. I cannot believe that a person, with a limited brain, intelligence, life span, etc (i.e., finite), can ever literally know everything (i.e., infinite). Can you even imagine someone having infinite knowledge ? He would need an infinite space to put it all in, and probably, an infinite span of time to assimilate it - particularly given that new and further knowledge of infinitely more things and events would be coming up all the time.

Thus, the juxtaposition of 'person' and 'omniscient' in the real world, is to me nonsensical, and if I supposed it, would simultaneously suppose that anything flowing from it would be also.

We cannot take a term such as 'someone', i.e., a human being, and suppose upon him omniscience, because for a start, that is not the ordinary definition of a person. And BTW, I was interested to read on another thread, where a contributor was railing against too narrow a definition of words on these forums, another contributor pointed out that these forums rules require for words to be used only in accordance with their dictionary meaning. And in no dictionary will you find omniscience as a description of a normal person.

Now, I'm NOT trying to pull rules here - I'm sure I sail against the wind myself on the odd occasion. And I do like the odd flight of fancy myself. But it IS a flight of fancy to say 'suppose someone is omniscient'. No logical discourse can follow from that.

I personally believe that these paradoxes (certainly the one in question) arise from different folk attributing different meanings to words - a nuance here, an inflection there, a not so subtle leap of faith elsewhere .. before you know it - confusion and chaos.

But anyway, I do enjoy the interaction and thinking about these things, and by no means am I trying to assert a superiority of view here - I'm just sayin' how I see it.

PS - will read the one on #35 soon.