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**Poincaré’s conventionalism and the logical positivists.**
*(English)*
Zbl 0949.83501

Summary: The logical positivists adopted Poincaré’s doctrine of the conventionality of geometry and made it a key part of their philosophical interpretation of relativity theory. The author argues however, that the positivists deeply misunderstood Poincaré’s doctrine. For Poincaré’s own conception was based on the group-theoretical picture of geometry expressed in the Helmholtz-Lie solution of the “space problem”, and also on a hierarchical picture of the sciences according to which geometry must be presupposed by any properly physical theory. But both of these pictures are entirely incompatible with the radically new conception of space and geometry articulated in the general theory of relativity. The logical positivists’s attempt to combine Poincaré’s conventionalism with Einstein’s new theory was therefore, in the end, simply incoherent. Underlying this problem, moreover, was a fundamental philosophical difference between Poincaré’s and the positivists concerning the status of synthetic a priori truths.

### MSC:

83-03 | History of relativity and gravitational theory |

83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |

### Keywords:

conventionalism; geometry; logical positivism; relativity theory; group theory; synthetic a priori; philosophical interpretation of relativity theory; Poincaré’s conventionalism
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\textit{M. Friedman}, Found. Sci. 1(1995--96), No. 2, 299--314 (1996; Zbl 0949.83501)

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### References:

[1] | Carnap, R. (1937), The Logical Syntax of Language, London, Routledge & Kegan Paul, (Originally published in 1934 as Logische Syntax der Sprache). |

[2] | Carnap, R. (1974), An Introduction to the Philosophy of Science, New York, Basic Books, (Originally published in 1966 as Philosophical Foundations of Physic). |

[3] | Poincaré, H. (1913), Science and Hypothesis in: The Foundations of Science, Lancaster, Pa, The Science Press, (Originally published in 1902 as La Science et l’Hypothèse). |

[4] | Reichenbach, R. (1965), The Theory of Relativity and A Priori Knowledge, Berkeley and Los Angeles, University of California Press, (Originally published in 1920 as Relativitätstheorie und Erkenntnis Apriori). |

[5] | Schlick, M. (1979), ’The Philosophical Significance of the Principle of Relativity,’ in: Philosophical Papers Volume I (1909–1922), Dortrecht, Reidel, (Originally published in 1915 as ’Die philosophische Bedeutung des Relativitätsprinzips’, Zeitschrift für Philosophie und philosophische Kritik 159, 129–175). |

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