SEP Entry Revised
My Stanford Encyclopedia entry on the Church-Fitch paradox of knowability (coauthored with Berit) was recently updated and is now online.
September 22, 2008
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4 comments:
http://www.digitalcosmology.com/Articles/fitch/fitch.html
Hi Efthimios,
Thank for the link to the interesting discussion. You considered my co-authored claim,
"... clearly there are unknown truths; individually and collectively we are non-omniscient."
and you say,
"The above statement can only be true in the past and present time. "
That happens to be false. The claim is that, clearly, there are some truths that will never be known by any human. To deny this is to claim a number of interesting things. It is to claim that it is not clear that we will never know obscure truths about, say, the precise number of breaths taken by Caesar in his lifetime, etc. It is also to claim the following. Allowing for infinitary propositions, we can note that the conjunction of all truths is itself a truth. Hence, you are claiming that it is not obvious that the conjunction of all truths will never be known by someone. That's a pretty strong claim. And even by your own lights, according to your discussion of asymptotic limits, there will never be a time at which all truths are known. Hence, clearly, there will never be a time when our infinite conjunction is known by some human.
Hello,
You said:
"The claim is that, clearly, there are some truths that will never be known by any human."
I think this should be taken as a postulate rather than a self-evident truth. I can propose a counter argument. Assume that our reality is manifested by a computer simulation (see "It from Bit" and pancomputantionalism) and the program keeps record of every event that has taken place in spacetime as well as of all spacetime processes (sequences of events in spacetime). Further assume that there is a possibility of getting access to that program in the future. Then, every truth is knwoable, including Ceasars's birth count. But that is not necessarily omniscience since the future output of the computer may depend on a stochastic process.
I think all the talk about (possibly) knowable truths is a just a red hearing in favor of Fitch's proof and Idealism. The real issue, and maybe the point I did not make clear, is whether the type of omniscience implied by Fitch's proof poses a threat to the anti-realist thesis. I argue it does not, because this type of omniscience is never achieved even if all truths are knowable and this is because of the arrow of time in compination of the true metaphysically speaking nature of reality.
Thus, I argue, that Fitch's proof is an epistemological stand that neglects any ramifications from ontological (metaphysical) content. Such considerations may ideed play an important role in the way that knowability and omniscience are related and a simple proof may only be a naive way of trying to uncover it.
Revised:
http://www.digitalcosmology.com/Articles/fitch/fitch.html
Regards
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