Book contents
- Frontmatter
- Contents
- Dedication
- Introduction
- 1 Models and reality
- 2 Equivalence
- 3 Possibility and necessity
- 4 Reference and truth
- 5 ‘Two dogmas’ revisited
- 6 There is at least one a priori truth
- 7 Analyticity and apriority: beyond Wittgenstein and Quine
- 8 Computational psychology and interpretation theory
- 9 Reflections on Goodman's Ways of Worldmaking
- 10 Convention: a theme in philosophy
- 11 Philosophers and human understanding
- 12 Why there isn't a ready-made world
- 13 Why reason can't be naturalized
- 14 Quantum mechanics and the observer
- 15 Vagueness and alternative logic
- 16 Beyond historicism
- Bibliography
- Acknowledgements
- Index
1 - Models and reality
Published online by Cambridge University Press: 06 January 2010
- Frontmatter
- Contents
- Dedication
- Introduction
- 1 Models and reality
- 2 Equivalence
- 3 Possibility and necessity
- 4 Reference and truth
- 5 ‘Two dogmas’ revisited
- 6 There is at least one a priori truth
- 7 Analyticity and apriority: beyond Wittgenstein and Quine
- 8 Computational psychology and interpretation theory
- 9 Reflections on Goodman's Ways of Worldmaking
- 10 Convention: a theme in philosophy
- 11 Philosophers and human understanding
- 12 Why there isn't a ready-made world
- 13 Why reason can't be naturalized
- 14 Quantum mechanics and the observer
- 15 Vagueness and alternative logic
- 16 Beyond historicism
- Bibliography
- Acknowledgements
- Index
Summary
In 1922 Skolem delivered an address before the Fifth Congress of Scandinavian Mathematicians in which he pointed out what he called a ‘relativity of set theoretic notions’. This ‘relativity’ has frequently been regarded as paradoxical; but today, although one hears the expression ‘The Löwenheim–Skolem paradox’, it seems to be thought of as only an apparent paradox, something the cognoscenti enjoy but are not seriously troubled by. Thus van Heijenoort writes, ‘The existence of such a “relativity” is sometimes referred to as the Löwenheim–Skolem paradox. But, of course, it is not a paradox in the sense of an antinomy; it is a novel and unexpected feature of formal systems.’ In this paper I want to take up Skolem's arguments, not with the aim of refuting them but with the aim of extending them in somewhat the direction he seemed to be indicating. It is not my claim that the ‘Löwenheim–Skolem paradox’ is an antinomy in formal logic; but I shall argue that it is an antinomy, or something close to it, in philosophy of language. Moreover, I shall argue that the resolution of the antinomy – the only resolution that I myself can see as making sense – has profound implications for the great metaphysical dispute about realism which has always been the central dispute in the philosophy of language.
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- Philosophical Papers , pp. 1 - 25Publisher: Cambridge University PressPrint publication year: 1983
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