Absolute identity seems at first sight to be presupposed in the branch of formal logic called identity theory. Classical identity theory may be obtained by adjoining a single schema to ordinary quantification theory.

Ordinary usage gives a way to think of identity through time: the Pittsburgh of 1946 was the same city as the Pittsburgh of today is--namely Pittsburgh. Problem: The Pittsburgh of 1946 does not exist; Pittsburgh still does. How can they have been identical? I reject the temporal parts view on which they were not but we may speak as though they were. Rather I argue that claiming their identity is not contradictory. I interpret ‘the Pittsburgh of 1946’ as ‘Pittsburgh as (...) it was in 1946’ and suggest that the apparent contradiction results from an ambiguity in the scope of ‘as’. (shrink)

Timothy Williamson; VII*—Equivocation and Existence, Proceedings of the Aristotelian Society, Volume 88, Issue 1, 1 June 1988, Pages 109–128, https://doi.org/10.

§ i. After deserting for a time the old Euclidean standards of rigour, mathematics is now returning to them, and even making efforts to go beyond them. ...

Antoine Arnauld and Pierre Nicole were philosophers and theologians associated with Port-Royal Abbey, a centre of the Catholic Jansenist movement in seventeenth-century France. Their enormously influential Logic or the Art of Thinking, which went through five editions in their lifetimes, treats topics in logic, language, theory of knowledge and metaphysics, and also articulates the response of 'heretical' Jansenist Catholicism to orthodox Catholic and Protestant views on grace, free will and the sacraments. In attempting to combine the categorical theory of the (...) proposition with a Cartesian account of knowledge, their Logic represents the classical view of judgment which inspired the modern transformation in logic and semantic theory by Frege, Russell, Wittgenstein and recent philosophers. This edition presents a new translation of the text, together with a historical introduction and suggestions for further reading. (shrink)

Contents PART I: INTRODUCTION 1 John Perry: The Problem of Personal Identity, 3 PART II: VERSIONS OF THE MEMORY THEORY 2 John Locke: Of Identity and ...

Locke notoriously included number amongst the primary qualities of bodies and was roundly criticized for doing so by Berkeley. Frege echoed some of Berkeley's criticisms in attacking the idea that ‘Number is a property of external things’, while defending his own view that number is a property of concepts. In the present paper, Locke's view is defended against the objections of Berkeley and Frege, and Frege's alternative view of number is criticized. More precisely, it is argued that numbers are assignable (...) to pluralities of individuals. However, it is also argued that Locke went too far in asserting that ‘Number applies itself to ... everything that either doth exist, or can be imagined’. (shrink)

There will be a few themes. One to get us going: expansion versus contraction. About an object, o, and the region, R, of space(time) in which o is exactly located,1 we may ask: i) must there exist expansions of o: objects in filled superregions2 of R? ii) must there exist contractions of o: objects in filled subregions of..

Armstrong has loose identity be an equivalence relation, yet in cases of something becoming something else, loose identity is not transitive. My alternate account has an attribution of loose identity be really two: a true attribution of an underlying relation (perhaps not transitive) and a false attribution--a Humean feigning-of strict identity. The feigning may become less appropriate as the underlying relation grows more distant. What makes it appropriate initially is that the underlying relation supports a predictable change in some collective. (...) The importance of the predictably changing collective is signaled by regarding it as a single thing. (shrink)

This essay interprets Butler’s distinction between identity in the loose and popular sense and in the strict and philosophical sense. Suppose there are different standards for counting the same things. Then what are two distinct things counting strictly may be one and the same thing counting loosely. Within a given standard identity is one-one. But across standards it is many-one. An alternative interpretation using the parts-whole relation fails, because that relation should be understood as many-one identity. Another alternative making identity (...) relative to sort fails, because whole and parts can be of the same sort. (shrink)