Certain Doubts

Green is in the good case so he knows all sorts of stuff about how things are and ought to be.  Green knows that he ought to keep his promises when there’s no overriding reason not to, knows that he cannot keep his promises without visiting his friend Plum, knows that he cannot get to see Plum unless he gets his tickets for the train, and so knows that he ought to get his tickets for the train.  Mustard is in the bad case.  While Mustard is Green’s epistemic counterpart (i.e., the two are in precisely the same non-factive mental states and have been since the cradle), Mustard is deceived at nearly every turn by a deceiving demon.  It seems to Mustard that he has friends and that he’s made promises to them that can be kept only if tickets are purchased, but Mustard’s only companion is the demon.  His beliefs don’t constitute knowledge as they tend to be false.  Unless you like abusing a perfectly good word, you should probably say that the processes that produce his beliefs aren’t reliable.  Things seem precisely the same to them and they reason in just the same way. (more…)

Walter Dean and Hidenori Kurokawa have a new paper in Synthese, ‘From the Knowability Paradox to the existence of proofs’:

Abstract: The Knowability Paradox purports to show that the controversial but not patently absurd hypothesis that all truths are knowable entails the implausible conclusion that all truths are known. The notoriety of this argument owes to the negative light it appears to cast on the view that there can be no verification-transcendent truths. We argue that it is overly simplistic to formalize the views of contemporary verificationists like Dummett, Prawitz or Martin-Löf using the sort of propositional modal operators which are employed in the original derivation of the Paradox. Instead we propose that the central tenet of verificationism is most accurately formulated as follows: if φ is true, then there exists a proof of φ. Building on the work of Artemov (Bull Symb Log 7(1): 1–36, 2001), a system of explicit modal logic with proof quantifiers is introduced to reason about such statements. When the original reasoning of the Paradox is developed in this setting, we reach not a contradiction, but rather the conclusion that there must exist non-constructed proofs. This outcome is evaluated relative to the controversy between Dummett and Prawitz about proof existence and bivalence.

HT: Rasmus Rendsvig at Logic & Rational Interaction.

Update 5/13: I’m back from a trip to discover that Plato won the pre-modern contest, edging out Aristotle by just 2 votes.  However, the final round has begun to determine the most important philosopher of all time, and as of right now, Aristotle has a small but significant lead in that contest (results so far).  The poll ends in a couple of days (May 15).

——

Like a good basketball game, it’s been close all the way, with lots of ties and lead changes.  But right now (10:30 Eastern, 5/8), one of the main “footnotes to Plato” (Aristotle) is beating Plato himself in the Leiter-sponsored poll concerning “The Most Important Philosophers of the Pre-Modern Era.”

Results.

Take the poll.

Next, of course, one supposes there will have to be a championship round of the most important philosophers of all time in which Kant, who came out on top of the poll about the “Most Important Philosopher of the Modern Era” (results), will square off against the Plato and Aristotle, no doubt hoping to avenge a controversial soccer loss that his German team suffered at the hands of the Greeks.

May 15-17th, conference webpage here. Looks really interesting!

Frege believed that the unrestricted comprehension axiom is true, and it is sad, since the axiom leads to paradox. If you are inclined toward coherentism, the rationality of Frege’s belief causes a problem, since it is logically inconsistent.

I’ve been working on the problem for coherentism of justified inconsistent beliefs, and this is one version of the problem. I’m tempted, though, to think it isn’t an epistemological problem, but rather a philosophy of language issue. Here’s why.
(more…)