In arithmetic, if only because many of its methods and concepts originated in India, it has been the tradition to reason less strictly than in geometry, ...

Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.

In this festschrift for the eminent philosopher Hilary Putnam, a team of distinguished philosophers write on a broad range of topics and thus reflect the remarkably fertile and provocative research of Putnam himself. The volume is not merely a celebration of a man, but also a report on the state of philosophy in a number of significant areas. The essays fall naturally into three groups: a central core on the theme of conventionality and content in the philosophy of mind, language, (...) and science, and two smaller sections on the relationship of ethics and language, and on the philosophy of logic and aesthetics.In this festschrift for the eminent philosopher Hilary Putnam, a team of distinguished philosophers write on a broad range of topics and thus reflect the remarkably fertile and provocative research of Putnam himself. The volume is not merely a celebration of a man, but also a report on the state of philosophy in a number of significant areas. The essays fall naturally into three groups: a central core on the theme of conventionality and content in the philosophy of mind, language, and science, and two smaller sections on the relationship of ethics and language, and on the philosophy of logic and aesthetics. (shrink)

... as 'logicism') that the content expressed by true propositions of arithmetic and analysis is not something of an irreducibly mathematical character, ...

In "Frege: Philosophy of Mathematics" Dummett recommends the following thesis, (PNP): the correct analysis of any sentence containing a plural noun phrase will show that the phrase is functioning predictively. According to Dummett, (PNP), applied to numerical predications such as the leaves are 1,000' is the key premise in Frege's argument against Mill's theory of numbers. But Frege never subscribed to (PNP) and he rejected such numerical predications, and point out how Frege's own semantic theory for plural noun phrases obscures (...) his idea of a relation. (shrink)

Michael Dummett; Discussions: Chairman's Address: Basic Law V*, Proceedings of the Aristotelian Society, Volume 94, Issue 1, 1 June 1994, Pages 243–252, https:/.