Luca Incurvati's Books

Conceptions of Set and the Foundations of Mathematics

By: Luca Incurvati

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Conceptions of Set and the Foundations of Mathematics

By: Luca Incurvati

Sets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naïve and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the graph conception. In addition, he presents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics.

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Page Count

255

Publisher

Cambridge University Press

Published Date

ISBN 10

1108758355

ISBN 13

9781108758352

Reasoning with Attitude

Foundations and Applications of Inferential Expressivism

By: Luca Incurvati,Julian J. Schlöder

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Reasoning with Attitude

Foundations and Applications of Inferential Expressivism

By: Luca Incurvati,Julian J. Schlöder

Certain combinations of sounds or signs on paper are meaningful. What makes it the case that, unlike most combinations of sounds or signs, they have meaning? What is this meaning that they have? And what is it to understand this meaning? The traditional answers to these questions are based on the idea that words stand for something, but it is difficult to say what words such as good, if, or probable stand for. This book advances novel answers based on the idea that words get their meaning from the way they are used to express states of mind and what follows from them. It articulates a precise version of this idea, at a time when the shortcomings of the traditional answers are hotly discussed.

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