Abstract
I want to begin by considering a case in which ‘necessary’ truths (or rather ‘truths’, turned out to be falsehoods: the case of Euclidean geometry. I then want to raise the question: could some of the ‘necessary truths’ of logic ever turn out to be false for empirical reasons? I shall argue that the answer to this question is in the affirmative, and that logic is, in a certain sense, a natural science.
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The physics of this example is deliberately oversimplified. In the GTR it is the four-dimensional ‘path’ of the light-ray that is a geodesic. To speak of (local) ‘three-dimensional space’ presupposes that a local reference system has been chosen. But even the geodesics in three-dimensional space exhibit non-Euclidean behavior of the kind described.
This is so only because we are quantizing a particle theory. If we quantize a field theory, we will say ‘the world consists of fields’, etc.
By a ‘differential’ force what is meant is that one has a source, that affects different bodies differently (depending on their physical and chemical composition), etc. The ‘forces’ that one has to postulate to account for the behavior of rigid rods if one uses an unnatural metric for a space are called ‘universal forces’ by Reichenbach (who introduced the terminology “differential/universal”); these have no assignable source, affect all bodies the same way, etc.
David Finkelstein, ‘Matter, Space, and Logic’, in Boston Studies in the Philosophy of Science, vol. V.
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© 1969 D. Reidel Publishing Company, Dordrecht, Holland
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Putnam, H. (1969). Is Logic Empirical?. In: Cohen, R.S., Wartofsky, M.W. (eds) Boston Studies in the Philosophy of Science. Boston Studies in the Philosophy of Science, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-3381-7_5
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