By Marc Lange
Now not all medical factors 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 ebook, Marc Lange proposes philosophical debts of many types of non-causal factors in technology and arithmetic. those themes were unjustly ignored within the philosophy of technological know-how and mathematics.
One vital form of non-causal medical clarification is named rationalization through constraint. those factors paintings by way of offering information regarding what makes convinced proof particularly inevitable - extra priceless than the standard legislation of nature connecting explanations to their results. proof defined during this means go beyond the hurly-burly of reason and influence. Many physicists have looked the legislation of kinematics, the nice conservation legislation, the coordinate changes, and the parallelogram of forces as having motives through constraint. This booklet offers an unique account of factors by means of constraint, targeting various examples from classical physics and unique relativity.
This publication additionally deals unique bills of numerous different forms of non-causal medical clarification. Dimensional reasons paintings by means of displaying how a few legislation of nature arises in simple terms from the dimensional relatives one of the amounts concerned. rather statistical reasons comprise causes that attract regression towards the suggest and different canonical manifestations of likelihood. Lange presents an unique account of what makes yes mathematical proofs yet no longer others clarify what they turn out. Mathematical rationalization connects to a bunch of different very important mathematical rules, together with coincidences in arithmetic, the importance of giving a number of proofs of an analogous consequence, and normal houses in arithmetic. Introducing many examples drawn from real technological know-how 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 time table for destiny paintings on non-causal explanation.
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Additional info for Because without cause: non-causal explanations in science and mathematics
3 that distinctively mathematical explanations are non-causal. I will also argue that we must refine the explanatory target very carefully before we can agree with those philosophers who characterize certain explanations appealing to natural selection as distinctively mathematical. 5, I will elaborate and defend my account of how distinctively mathematical explanations work. I will argue that even when such an explanation appeals to a contingent law of nature, it works by showing the explanandum to be necessary in a stronger sense than any causal explanation could.
If, on the other hand, a population contains more females than males, then the heritable tendency to produce more male than female offspring will be selectively advantageous, tending to restore the 1:1 ratio. Sober correctly emphasizes that such an equilibrium explanation of a population’s current 1:1 ratio does not describe the particular causal path by which the population arrived at that ratio; it does not specify the varying sex ratios or selection pressures at earlier moments. Rather, the explanation works by showing how the tendency to return to a 1:1 ratio arises from various unchanging features of the population, including that the only selection pressure on the sex ratio is selection for individuals who have a tendency to overproduce the minority sex, that such a heritable tendency is present among some members of the population, and that male and female offspring require the same resources.
Any causes cited by a causal explanation explain by virtue of being causes and thereby supplying information about the network of causal relations—and since even non-causes can supply such information, they can figure in causal explanations, too. As I will show, when causes figure in non-causal explanations, the source of their explanatory power is not their status as causes. Of course, this is not to say that in a causal explanation, any information whatever about the world’s network of causal relations (or even about the explanandum’s causes in particular) is explanatory.