NECESSARY AND SUFFICIENT TESTS OF TRUTH

Necessary Truth and Proof

What makes necessary truths true? I argue that all truth supervenes on how things are, and that necessary truths are no exception. What makes them true are proofs. But if so, the notion of proof needs to be generalized to include verification-transcendent proofs, proofs whose correctness exceeds our ability to verify it. It is incumbent on me, therefore, to show that arguments, such as Dummett’...

Necessary Truth and Grammatical Propositions

Estimation of -Cell Mass by Metabolic Tests Necessary, but How Sufficient?

This Perspectives in Diabetes addresses the accuracy of metabolic testing as a measure of pancreatic islet -cell mass in vivo in animals and in humans. The impetus for framing this question lies in the current intense interest in determining the fate of -cell mass in transplanted islets, i.e., does it decrease, increase, or remain the same over time, as well as ascertaining whether drugs that e...

A Necessary and Sufficient Condition for Transcendency

As has been known for many years (see, e.g., K. Mahler, /. Reine Angew. Math., v. 166, 1932, pp. 118-150), a real or complex number f is transcendental if and only if the following condition is satisfied. To every positive number co there exists a positive integer n and an infinite sequence of distinct polynomials {p,(z)} = {pr + pr z + • • • + p z } at most of 0 1 n degree n with integral coef...

A Necessary and Sufficient Condition for Peace∗

This paper examines the possibility for two contestants to agree on a peace settlement thereby avoiding a contest, in which each would exert a costly effort given the posterior distributions inferred from the negotiation. I find a necessary and sufficient condition of the prior distributions for there to exist a negotiation mechanism that admits a peace-ensuring perfect Bayesian equilibrium. Th...