By Marc Lange
Now not 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 types of non-causal motives in technological know-how and arithmetic. those themes were unjustly ignored within the philosophy of technological know-how and mathematics.
One vital type of non-causal clinical rationalization is named rationalization by means of constraint. those reasons paintings by means of delivering information regarding what makes yes proof particularly inevitable - extra invaluable than the standard legislation of nature connecting reasons to their results. proof defined during this means go beyond the hurly-burly of reason and impression. Many physicists have appeared the legislation of kinematics, the good conservation legislation, the coordinate ameliorations, and the parallelogram of forces as having motives via constraint. This ebook provides an unique account of factors via constraint, focusing on quite a few examples from classical physics and specific relativity.
This booklet additionally bargains unique money owed of a number of different sorts of non-causal medical clarification. Dimensional causes paintings via exhibiting how a few legislations of nature arises in simple terms from the dimensional family one of the amounts concerned. rather statistical motives contain factors that attract regression towards the suggest and different canonical manifestations of likelihood. Lange presents an unique account of what makes sure mathematical proofs yet now not others clarify what they end up. Mathematical clarification connects to a bunch of different vital mathematical principles, together with coincidences in arithmetic, the importance of giving a number of proofs of an analogous outcome, and traditional 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 time table for destiny paintings on non-causal explanation.
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Extra info for Because without cause: non-causal explanations in science and mathematics
This is a non-causal explanation because it does not work by describing some aspect of the world’s network of causal relations. No aspect of the particular forces operating on or within the system (which would make a difference to U(α,β)) matters to this explanation. Rather, the explanation exploits merely the fact that by virtue of the system’s being a double pendulum, its configuration space is the surface of a torus—that is, that U is a function of α and β. 4 The topology of the configuration space of a simple double pendulum.
Pincock (2007) offers another example. Why has no one ever succeeded (or, in particular, why did a given person on a given occasion not succeed) in crossing all of the bridges of Königsberg exactly once (while remaining always on land or on a bridge rather than in a boat, for instance, and while crossing any bridge completely once having begun to cross it)? Here it is understood that the problem concerns the town’s bridges as they were arranged when Euler considered this problem in 1735 (see fig.
7 For example, as Beebee (2004, 301–304) emphasizes, a typical explanation that appeals only to an omission or absence (along with laws of nature) is causal even though strictly speaking (according to many philosophers), an omission is not a cause since it is not even an event; it involves nothing happening. For 13 What Makes a Scientific Explanation Distinctively Mathematical? , not accelerating) by citing the absence of any forces on it, we give a causal explanation that cites no causes since it cites no forces.