The Limits of Logic: Higher-Order Logic and the L÷wenheim-Skolem Theorem

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ISBN: 9781855217317 | 1855217317
Cover: Hardcover
Copyright: 10/28/1996

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The International research Library of Philosophy collects in book form a wide range of important and influential essays in philosophy, drawn predominantly from English-language journals. Each volume in the library deals with a field of enquiry which has received significant attention in philosophy in the last 25 years and is edited by a philosopher noted in that field.

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Is Second-Order Logic Logic?
Beyond first-order logic: the historical interplay between mathematical logic and axiomatic set theory
Which logic is the right logic?
On second-order logic
Second-order languages and mathematical practice
What are logical notions?
A curious inference
The rationalist conception of logic
A critical appraisal of second-order logic
Who's afraid of higher-order logic?
Ontological Reduction, Intended Interpretations and the Löwenheim-Skolem Theorems: Ontological reduction
Intended models and the Löwenheim-Skolem theorem
Categoricity
Skolem's paradox and constructivism
Second-order logic, foundations and rules
Plural Quantification
To be is to be a value of a variable (or to be some values of some variables)
Nominalist Platonism
Second-order logic still wild
Philosophy of Set Theory: Kreisel, the continuum hypothesis, and second-order set theory
Skolem and the Löwenheim-Skolem theorem: a case study of the philosophical significance of mathematical results
Skolem and the skeptic
Skolem and the skeptic
Predication versus membership in the distinction between logic as language and logic as calculus
Logicism, the continuum and anti-realism
Name index
Table of Contents provided by Publisher. All Rights Reserved.

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The Limits of Logic: Higher-Order Logic and the L÷wenheim-Skolem Theorem

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