By Marc Lange

ISBN-10: 0190269480

ISBN-13: 9780190269487

ISBN-10: 0190269502

ISBN-13: 9780190269500

ISBN-10: 1891891901

ISBN-13: 9781891891908

No longer all clinical reasons paintings through describing causal connections among occasions or the world's total causal constitution. a few mathematical proofs clarify why the theorems being proved carry. during this publication, Marc Lange proposes philosophical money owed of many varieties of non-causal causes in technology and arithmetic. those themes were unjustly overlooked within the philosophy of technology and mathematics.

One very important form of non-causal medical rationalization is named rationalization by means of constraint. those reasons paintings by way of supplying information regarding what makes sure proof particularly inevitable - extra priceless than the standard legislation of nature connecting factors to their results. proof defined during this means go beyond the hurly-burly of reason and impression. Many physicists have seemed the legislation of kinematics, the nice conservation legislation, the coordinate changes, and the parallelogram of forces as having causes by way of constraint. This publication offers an unique account of reasons through constraint, focusing on a number of examples from classical physics and distinctive relativity.

This ebook additionally bargains unique money owed of a number of different forms of non-causal medical clarification. Dimensional causes paintings via exhibiting how a few legislations of nature arises in basic terms from the dimensional family one of the amounts concerned. particularly statistical factors contain reasons that attract regression towards the suggest and different canonical manifestations of probability. Lange presents an unique account of what makes yes mathematical proofs yet now not others clarify what they end up. Mathematical rationalization connects to a number of different vital mathematical rules, together with coincidences in arithmetic, the importance of giving a number of proofs of an identical end result, and common homes in arithmetic. Introducing many examples drawn from genuine technology and arithmetic, with prolonged discussions of examples from Lagrange, Desargues, Thomson, Sylvester, Maxwell, Rayleigh, Einstein, and Feynman, *Because with out Cause*'s proposals and examples may still set the schedule for destiny paintings on non-causal explanation.

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**Extra resources for Because without cause: non-causal explanations in science and mathematics**

**Example text**

But since the similarity between the two moments is in fact no coincidence, any genuine explanation must so characterize it. 3 MATHEMATICAL EXPL ANATIONS DO NOT EXPLOIT CAUSAL POWERS I have just suggested that distinctively mathematical explanations are non-causal, even if some of them appeal to causes of what they explain, because they do not appeal to them as causes; they do not exploit their causal powers. 20 In this way, mathematics enters distinctively mathematical explanations. It may be objected that although a distinctively mathematical explanation appeals to mathematical facts, it also exploits the causal powers of some of the explanandum’s causes.

17 That a distinctively mathematical explanation happens to cite facts about the explanandum’s causes does not mean that it works by virtue of describing the explanandum’s causes. In the distinctively mathematical explanation, Mother’s having 3 children helps to explain her failure to distribute the strawberries evenly not by virtue of being a cause of her failure, but rather by virtue of helping to make her success mathematically impossible. By the same token, the fact that 23 cannot be divided evenly by 3 supplies information about the world’s network of causal relations: it entails that there are no causal processes by which 23 things are distributed evenly (without being cut) into 3 groups.

These necessities are stronger than the variety of necessity possessed by ordinary laws of nature, setting explanations like these apart from ordinary scientific explanations. Ultimately, I will suggest that distinctively mathematical scientific explanations work by appealing only to facts (including but not always limited to mathematical facts) that are 10 10 ■ Scientific Explanations by Constraint modally stronger than ordinary laws of nature, together with contingent conditions that are contextually understood to be constitutive of the arrangement or task at issue in the why question.

### Because without cause: non-causal explanations in science and mathematics by Marc Lange

by Donald

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