The question 'What is the criterion of identity for directions?' might be construed as asking either 'When do lines have the same direction?' or 'When are directions identical?'. Frege's answer 'When they are parallel' fits the former question, not the latter, for it specifies a relation other than identity between lines, not directions. Jonathan Lowe thinks the latter question more fundamental, and claims that Frege's criterion can be reformulated to answer it: 'When some line with one is parallel to some (...) line with the other'. At p. 147 of Identity and Discrimination I make three points against this view: Lowe's construal does not permit a principled rejection of an intuitively unacceptable answer to the original question, On pain of circularity, Lowe's answer uses conceptual resources beyond those of Frege's, and thus is not a mere reformulation, Lowe's question seems to make the hopeless demand for something more basic than 'x = y Lowe's reply 'One-level versus two-level identity criteria' does not address or . I shall follow him in discussing only. (shrink)

The aim of this paper is to derive a perfectly general criterion of identity through time from Locke’s Principle, which says that two things of the same kind cannot occupy the same space at the same time. In this way, the paper pursues a suggestion made by Peter F. Strawson almost thirty years ago in an article called ‘Entity and Identity’. The reason why the potential of this suggestion has so far remained unrealized is twofold: firstly, the suggestion was never (...) properly developed by Strawson, and secondly, it seemed vulnerable to an objection that he himself raised against it. Consequently, the paper’s aim is to further develop Strawson’s suggestion, and to show that the result is not vulnerable to the objection that seemed fatal to its underdeveloped predecessor. In addition, the paper aims to defend Locke’s Principle against alleged counterexamples such as those produced by Leibniz, Fine and Hughes. (shrink)

Reminiscences of Peter, by P. Oppenheim.--Natural kinds, by W. V. Quine.--Inductive independence and the paradoxes of confirmation, by J. Hintikka.--Partial entailment as a basis for inductive logic, by W. C. Salmon.--Are there non-deductive logics?, by W. Sellars.--Statistical explanation vs. statistical inference, by R. C. Jeffre--Newcomb's problem and two principles of choice, by R. Nozick.--The meaning of time, by A. Grünbaum.--Lawfulness as mind-dependent, by N. Rescher.--Events and their descriptions: some considerations, by J. Kim.--The individuation of events, by D. Davidson.--On properties, by (...) H. Putnam.--A method for avoiding the Curry paradox, by F. B. Fitch.--Publications (1934-1969) by Carl G. Hempel (p. [266]-270). (shrink)

§ 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. ...

The book also includes a chronological table of significant events, select bibliography, succinct explanatory notes, and an index--all of which supply ...

Here, Bob Hale and Crispin Wright assemble the key writings that lead to their distinctive neo-Fregean approach to the philosophy of mathematics. In addition to fourteen previously published papers, the volume features a new paper on the Julius Caesar problem; a substantial new introduction mapping out the program and the contributions made to it by the various papers; a section explaining which issues most require further attention; and bibliographies of references and further useful sources. It will be recognized as the (...) most powerful presentation yet of a neo-Fregean program. (shrink)

P. F. Strawson here presents a selection of his shorter writings from the 1970s to the 1990s in the two areas of philosophy to which he has contributed most notably: philosophy of language and Kantian studies. One of these essays is published here for the first time, and one for the first time in English; several others have been difficult to find. A new introduction offers an overview of the essays, their topics, and their interrelations. This book represents some of (...) the most fascinating work of one of the foremost philosophers of the late twentieth century. (shrink)

Frege Arithmetic (FA) is the second-order theory whose sole non-logical axiom is Hume’s Principle, which says that the number of F s is identical to the number of Gs if and only if the F s and the Gs can be one-to-one correlated. According to Frege’s Theorem, FA and some natural definitions imply all of second-order Peano Arithmetic. This paper distinguishes two dimensions of impredicativity involved in FA—one having to do with Hume’s Principle, the other, with the underlying second-order logic—and (...) investigates how much of Frege’s Theorem goes through in various partially predicative fragments of FA. Theorem 1 shows that almost everything goes through, the most important exception being the axiom that every natural number has a successor. Theorem 2 shows that the Successor Axiom cannot be proved in the theories that are predicative in either dimension. (shrink)

E. J. Lowe; Impredicative identity criteria and Davidson's criterion of event identity, Analysis, Volume 49, Issue 4, 1 October 1989, Pages 178–181, https://doi.

Jonathan Lowe argues that metaphysics should be restored to a central position in philosophy, as the most fundamental form of inquiry, whose findings underpin those of all other disciplines. He portrays metaphysics as charting the possibilities of existence, by identifying the categories of being and the relations between them. He sets out his own original metaphysical system, within which he seeks to answer many of the deepest questions in philosophy. 'a very rich book... deserves to be read carefully by anyone (...) interested in any of the many subjects he discusses.' Katherine Hawley, British Journal of the Philosophy of Science. (shrink)

What kinds of sentences with truth predicate may be inserted plausibly and consistently into the T-scheme? We state an answer in terms of dependence: those sentences which depend directly or indirectly on non-semantic states of affairs (only). In order to make this precise we introduce a theory of dependence according to which a sentence φ is said to depend on a set Φ of sentences iff the truth value of φ supervenes on the presence or absence of the sentences of (...) Φ in/from the extension of the truth predicate. Both φ and the members of Φ are allowed to contain the truth predicate. On that basis we are able define notions such as ungroundedness or self-referentiality within a classical semantics, and we can show that there is an adequate definition of truth for the class of sentences which depend on non-semantic states of affairs. (shrink)

_Identity and Discrimination_, originally published in 1990 and the first book by respected philosopher Timothy Williamson, is now reissued and updated with the inclusion of significant new material. Williamson here proposes an original and rigorous theory linking identity, a relation central to metaphysics, and indiscriminability, a relation central to epistemology.__ Updated and reissued edition of Williamson’s first publication, with the inclusion of significant new material Argues for an original cognitive account of the relation between identity and discrimination that has been (...) influential in the philosophy of perception Pioneers the use of epistemic logic to solve puzzles about indiscriminability Develops the application of techniques from mathematical logic to understand issues about identity over time and across possible worlds. (shrink)

According to realist structuralism, mathematical objects are places in abstract structures. We argue that in spite of its many attractions, realist structuralism must be rejected. For, first, mathematical structures typically contain intra-structurally indiscernible places. Second, any account of place-identity available to the realist structuralist entails that intra-structurally indiscernible places are identical. Since for her mathematical singular terms denote places in structures, she would have to say, for example, that 1 = − 1 in the group (Z, +). We call this (...) the identity problem and conclude that nominalism is presently the safest route for the structuralist. (shrink)

Criteria of identity should mirror the identity relation in being reflexive, symmetrical, and transitive. However, this logical requirement is only rarely met by the criteria that we are most inclined to propose as candidates. The present paper addresses the question how such obvious candidates are best approximated by means of relations that have all of the aforementioned features, i.e., which are equivalence relations. This question divides into two more basic questions. First, what is to be considered a ‘best’ approximation. And (...) second, how can these best approximations be found? In answering these questions, we both rely on and constructively criticize ground-breaking work done by Timothy Williamson. Guiding ideas of our approach are that we allow approximations by means of overlapping equivalence-relations, and that closeness of approximation is measured in terms of the number of mistakes made by the approximation when compared to the obvious candidate criterion. (shrink)

E. J. Lowe; One-level versus two-level identity criteria, Analysis, Volume 51, Issue 4, 1 October 1991, Pages 192–194, https://doi.org/10.1093/analys/51.4.192.