4,323 research outputs found
Iterated reflection principles over full disquotational truth
Iterated reflection principles have been employed extensively to unfold
epistemic commitments that are incurred by accepting a mathematical theory.
Recently this has been applied to theories of truth. The idea is to start with
a collection of Tarski-biconditionals and arrive by finitely iterated
reflection at strong compositional truth theories. In the context of classical
logic it is incoherent to adopt an initial truth theory in which A and 'A is
true' are inter-derivable. In this article we show how in the context of a
weaker logic, which we call Basic De Morgan Logic, we can coherently start with
such a fully disquotational truth theory and arrive at a strong compositional
truth theory by applying a natural uniform reflection principle a finite number
of times
On the inevitability of the consistency operator
We examine recursive monotonic functions on the Lindenbaum algebra of
. We prove that no such function sends every consistent
to a sentence with deductive strength strictly between and
. We generalize this result to iterates
of consistency into the effective transfinite. We then prove that for any
recursive monotonic function , if there is an iterate of that
bounds everywhere, then must be somewhere equal to an iterate of
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