By Marc Lange
Now not all clinical factors paintings by way of 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 booklet, Marc Lange proposes philosophical debts of many forms of non-causal motives in technological know-how and arithmetic. those themes were unjustly ignored within the philosophy of technology and mathematics.
One very important form of non-causal clinical rationalization is named clarification through constraint. those motives paintings by means of delivering information regarding what makes convinced evidence in particular inevitable - extra priceless than the standard legislation of nature connecting motives to their results. proof defined during this method go beyond the hurly-burly of reason and impression. Many physicists have looked the legislation of kinematics, the nice conservation legislation, the coordinate variations, and the parallelogram of forces as having reasons through constraint. This publication offers an unique account of factors by way of constraint, focusing on various examples from classical physics and distinct relativity.
This e-book additionally deals unique money owed of numerous different kinds of non-causal medical rationalization. Dimensional motives paintings by way of exhibiting how a few legislations of nature arises purely from the dimensional kin one of the amounts concerned. particularly statistical factors contain factors that entice 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 turn out. Mathematical clarification connects to a number of alternative very important mathematical principles, together with coincidences in arithmetic, the importance of giving a number of proofs of a similar outcome, and usual houses 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 no Cause's proposals and examples should still set the schedule for destiny paintings on non-causal explanation.
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Additional info for Because without cause: non-causal explanations in science and mathematics
Nevertheless, I maintain that this explanation is non-causal because it does not work by virtue of describing the outcome’s causes or, more broadly, the world’s network of causal relations. The causal mechanism by which Mother distributed her strawberries does not enter into it. The numbers of children and strawberries do not figure in this explanation as causes of the outcome. A distinctively mathematical scientific explanation may happen to cite causes, but it does not appeal to them as causes.
This is a causal explanation of neon’s inertness even though (as Kitcher 1985, 637 says) it does not describe any causal processes at work in neon. It explains by virtue of describing the world’s network of causal relations (in particular, the causes of other atoms’ chemical activity). Similarly, when a disposition is explained by its categorical base (and natural laws), the categorical base does not cause the disposition (as I mentioned earlier). The explanation does not supply information about the disposition’s causal history 17 What Makes a Scientific Explanation Distinctively Mathematical?
21 What Makes a Scientific Explanation Distinctively Mathematical? ■ 21 As I showed earlier, there is a non-causal explanation for the existence at a given moment of antipodal equatorial points having the same temperature. Perhaps this occurrence also has a causal explanation that appeals to whatever prior meteorological conditions (and natural laws) explain why those particular antipodal equatorial points have the same temperature (rather than different temperatures) at the given moment. Of course, the non-causal explanation shows that even if meteorological conditions had been different so that the temperatures at those particular antipodal points had been unequal, there would still have been a pair of antipodal equatorial points at the same temperature.