Philosophia Mathematica - current issue

Introduction

Tennant, N. — 2008-03-20

Carnap, Formalism, and Informal Rigour{dagger}

Gregory, L. — 2008-03-20

Carnap's position on mathematical truth in The Logical Syntax of Language has been attacked from two sides: Kreisel argues that it is formalistic but should not be, and Friedman argues that it is not formalistic but needs to be. In this paper I argue that the Carnap of Syntax does not eliminate our ordinary notion of mathematical truth in favour of a formal analogue; so Carnap's notion of mathematical truth is not formalistic. I further argue that there is no conflict between Carnap's use of informal notions and his principle of tolerance; so Carnap's definition of mathematical truth need not be formalistic.

Intuition Between the Analytic-Continental Divide: Hermann Weyl's Philosophy of the Continuum

Folina, J. — 2008-03-20

Though logical positivism is part of Kant's complex legacy, positivists rejected both Kant's theory of intuition and his classification of mathematical knowledge as synthetic a priori. This paper considers some lingering defenses of intuition in mathematics during the early part of the twentieth century, as logical positivism was born. In particular, it focuses on the difficult and changing views of Hermann Weyl about the proper role of intuition in mathematics. I argue that it was not intuition in general, but his commitment to twodifferent types of intuition, which explains his rather unusual and tormented philosophy of the mathematical continuum.

Intuitionism and Logical Syntax

McCarty, C. — 2008-03-20

In Logical Syntax of Language, Rudolf Carnap became a chief proponent of the doctrine that the statements of intuitionism carry nonstandard intuitionistic meanings. This doctrine is linked to Carnap's ‘Principle of Tolerance’ and claims he made on behalf of his notion of pure syntax. From premises independent of intuitionism, we argue that the doctrine, the Principle, and the attendant claims are mistaken, especially Carnap's repeated insistence that, in defining languages, logicians are free of commitment to mathematical statements intuitionists would reject.

Logic and Metaphysics: Heinrich Scholz and the Scientific World View{dagger}

Peckhaus, V. — 2008-03-20

The anti-metaphysical attitude of the neo-positivist movement is notorious. It is an essential mark of what its members regarded as the scientific world view. The paper focuses on a metaphysical variation of the scientific world view as proposed by Heinrich Scholz and his Münster group, who can be regarded as a peripheral part of the movement. They used formal ontology for legitimizing the use of logical calculi. Scholz's relation to the neo-positivist movement and his contributions to logic and foundations are discussed. His heuristic background can be drawn from a set of six methodological ‘articles of faith’, formulated in 1942 and published here for the first time.

Carnap, Godel, and the Analyticity of Arithmetic

Tennant, N. — 2008-03-20

Michael Friedman maintains that Carnap did not fully appreciate the impact of Gödel's first incompleteness theorem on the prospect for a purely syntactic definition of analyticity that would render arithmetic analytically true. This paper argues against this claim. It also challenges a common presumption on the part of defenders of Carnap, in their diagnosis of the force of Gödel's own critique of Carnap in his Gibbs Lecture.

LEO CORRY. David Hilbert and the Axiomatization of Physics (1898-1918)

Brading, K. — 2008-03-20

MATTHIAS WILLE. Mathematics and the Synthetic A Priori: Epistemological Investigations into the Status of Mathematical Axioms

Beisbart, C. — 2008-03-20

TATIANA ARRIGONI. What is meant by V?: Reflections on the universe of all sets

Tiles, M. — 2008-03-20

THOMAS MCKAY. Plural Predication

Burgess, J. P. — 2008-03-20

Jesper Lutzen. Mechanistic Images in Geometric Form: Heinrich Hertz's Principles of Mechanics

Pincock, C. — 2008-03-20

ALAN RICHARDSON and THOMAS UEBEL. The Cambridge Companion to Logical Empiricism

2008-03-20

BART VAN KERKHOVE and JEAN PAUL VAN BENDEGEM, eds. Perspectives on Matmatical Practices: Bringing Together Philosophy of Mathematics, Sociology of Mathematics, and Mathematics Education

2008-03-20

AGUSTIN RAYO and GABRIEL UZQUIANO, eds. Absolute Generality

2008-03-20

MICHAEL FRIEDMAN and ALFRED NORDMANN, editors. The Kantian Legacy in Nineteenth-Century Science

2008-03-20

NATHALIE SINCLAIR, DAVID PIMM, and WILLIAM HIGGINSON, eds. Mathematics and the Aesthetic: New Approaches to an Ancient Affinity

2008-03-20

KAREN FRANCOIS and JEAN PAUL VAN BENDEGEM, eds. Philosophical Dimensions in Mathematics Education

2008-03-20