Online research in philosophy

CHAPTER ONE INTRODUCTION This investigation seeks to make a modest contribution to the debate on the changes which took place in Reformed theology in the ...

David Lewis, Michael Thau, and Ned Hall have recently argued that the Principal Principle—an inferential rule underlying much of our reasoning about probability—is inadequate in certain respects, and that something called the ‘New Principle’ ought to take its place. This paper argues that the Principle Principal need not be discarded. On the contrary, Lewis et al. can get everything they need—including the New Principle—from the intuitions and inferential habits that inspire the Principal Principle itself, while avoiding the problems that originally caused them to abandon that principle.

In this article, Sandis defends four of the most notorious doctrines which Plato attributes to Socrates. The first is the ‘theory’ of forms, the second is the doctrine of recollection, the third Socrates'contention that philosophers ought to be the guardian-kings of the ideal state, and the fourth his rejection of rhetoric. Sandis does not claim that his interpretation (which owes a lot to Wittgenstein) is correct, but only that it renders the doctrines both relevant and plausible.

For quasivarieties of algebras, we consider the property of having definable relative principal subcongruences, a generalization of the concepts of definable relative principal congruences and definable principal subcongruences. We prove that a quasivariety of algebras with definable relative principal subcongruences has a finite quasiequational basis if and only if the class of its relative (finitely) subdirectly irreducible algebras is strictly elementary. Since a finitely generated relatively congruence-distributive quasivariety has definable relative principal subcongruences, we get a new proof of the result due to D. Pigozzi: a finitely generated relatively congruence-distributive quasivariety has a finite quasi-equational basis.

A principal type-scheme of a -term is the most general type-scheme for the term. The converse principal type-scheme theorem (J.R. Hindley, The principal typescheme of an object in combinatory logic, Trans. Amer. Math. Soc. 146 (1969) 29–60) states that every type-scheme of a combinatory term is a principal type-scheme of some combinatory term.This paper shows a simple proof for the theorem in -calculus, by constructing an algorithm which transforms a type assignment to a -term into a principal type assignment to another -term that has the type as its principal type-scheme. The clearness of the algorithm is due to the characterization theorem of principal type-assignment figures. The algorithm is applicable to BCIW--terms as well. Thus a uniform proof is presented for the converse principal type-scheme theorem for general -terms and BCIW--terms.