"Belief, Knowledge and Tracking the Truth"

Horacio Arlo-Costa & Rohit Parikh

The talk will be given by Parikh and it will consist of two parts.

The first (somewhat longer) part will look at the possibility of
formally implementing Nozick's `Tracking the Truth' suggestion in his
book Philosophical Explanations. There he suggested that the usual
requirements of belief and truth for knowledge be supplemented by a
`tracking the truth' requirement according to which, for true beliefs to
count as knowledge, they have to be sensitive to both the truth and
falsehood of the proposition in question. Since Nozick makes essential
use of conditionals (interpreted somewhat differently from the way that
Lewis and Stalnaker interpret them), we will discuss formal properties
of conditionals and the resulting formal properties of knowledge. (This
part is jointly due to Horacio Arlo Costa and Parikh).

The second part of the talk will no longer take the notion of belief for
granted, but will go into the issue of what it is to believe something,
and what it is that we believe in the first place. Do we believe
sentences? Or do we believe propositions? And if the latter, what are
propositions? We will suggest that actually we believe, in somewhat
different senses of "believe," both "propositions" and sentences (but
that inanimate devices like thermostats "believe" only propositions).
Once we take this stance, we immediately enter the thicket of Frege's
problem, the question of logical omniscience, and the problem of
explaining the mental states of people who "believe" one sentence, but
fail to believe another, "equivalent" one. These issues can be resolved
if we take seriously the fact that there are actually (at least) two
varieties of belief. Propositional beliefs do not "suffer" from logical
omniscience as it is not a problem. Sentential beliefs, on the other
hand, are not closed under logical deduction, nor should we expect them
to be. If they are closed under deduction to some extent, it is for
pragmatic reasons, rather than because such closure is somehow logically
necessary.