scholarly journals Platonic Relations and Mathematical Explanations

2020 ◽  
Author(s):  
Robert Knowles
Keyword(s):  
Mathematical Explanation ◽  
Indispensability Argument ◽  
Scientific Explanations ◽  
Turn On ◽  
Mathematical Explanations ◽  
Mathematical Platonism ◽  
Adequate Understanding ◽  
Enhanced Indispensability Argument

Abstract Some scientific explanations appear to turn on pure mathematical claims. The enhanced indispensability argument appeals to these ‘mathematical explanations’ in support of mathematical platonism. I argue that the success of this argument rests on the claim that mathematical explanations locate pure mathematical facts on which their physical explananda depend, and that any account of mathematical explanation that supports this claim fails to provide an adequate understanding of mathematical explanation.

scholarly journals Unification and mathematical explanation

2021 ◽  
Author(s):  
Robert Knowles
Keyword(s):  
Divide And Conquer ◽  
Mathematical Explanation ◽  
Indispensability Argument ◽  
Mathematical Explanations ◽  
Enhanced Indispensability Argument ◽  
One Step ◽  
The Right

AbstractThis paper provides a sorely-needed evaluation of the view that mathematical explanations in science explain by unifying. Illustrating with some novel examples, I argue that the view is misguided. For believers in mathematical explanations in science, my discussion rules out one way of spelling out how they work, bringing us one step closer to the right way. For non-believers, it contributes to a divide-and-conquer strategy for showing that there are no such explanations in science. My discussion also undermines the appeal to unifying power in support of the enhanced indispensability argument.

scholarly journals Mathematical explanation and indispensability

2018 ◽  
Vol 33 (2) ◽  
pp. 233 ◽  
Author(s):  
Susan Vineberg
Keyword(s):  
Causal Explanation ◽  
Mathematical Explanation ◽  
Indispensability Argument ◽  
Mathematical Realism ◽  
Explanatory Role ◽  
Mathematical Objects ◽  
Scientific Explanations ◽  
Enhanced Indispensability Argument

This paper discusses Baker’s Enhanced Indispensability Argument (EIA) for mathematical realism on the basis of the indispensable role mathematics plays in scientific explanations of physical facts, along with various responses to it. I argue that there is an analogue of causal explanation for mathematics which, of several basic types of explanation, holds the most promise for use in the EIA. I consider a plausible case where mathematics plays an explanatory role in this sense, but argue that such use still does not support realism about mathematical objects.

A Counterfactual Approach to Explanation in Mathematics

2019 ◽  
Vol 28 (1) ◽  
pp. 1-34 ◽  
Author(s):  
Sam Baron ◽  
Mark Colyvan ◽  
David Ripley
Keyword(s):  
Scientific Explanation ◽  
Mathematical Explanation ◽  
Test Case ◽  
Mathematical Explanations ◽  
Counterfactual Theory ◽  
Explanatory Structure ◽  
Counterfactual Approach

ABSTRACT Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines.

scholarly journals Counterfactual Scheming

Mind ◽  
2019 ◽  
Vol 129 (514) ◽  
pp. 535-562
Author(s):  
Sam Baron
Keyword(s):  
Mathematical Explanation ◽  
Explanatory Role ◽  
Unification Theory ◽  
Mathematical Explanations ◽  
Counterfactual Theory ◽  
Counterfactual Approach

Abstract Mathematics appears to play a genuine explanatory role in science. But how do mathematical explanations work? Recently, a counterfactual approach to mathematical explanation has been suggested. I argue that such a view fails to differentiate the explanatory uses of mathematics within science from the non-explanatory uses. I go on to offer a solution to this problem by combining elements of the counterfactual theory of explanation with elements of a unification theory of explanation. The result is a theory according to which a counterfactual is explanatory when it is an instance of a generalized counterfactual scheme.

Proof of critical speed of high-speed rail underlain by stratified media

2020 ◽  
Vol 476 (2240) ◽  
pp. 20200083
Author(s):  
Eduardo Kausel ◽  
José Estaire ◽  
Inés Crespo-Chacón
Keyword(s):  
Twentieth Century ◽  
Upper Bound ◽  
High Speed ◽  
Critical Speed ◽  
Complete System ◽  
Stratified Media ◽  
High Speed Rail ◽  
Turn On ◽  
Mathematical Explanations ◽  
First Time

As is well known, the safe travel velocity of high-speed rail must remain below a well-defined limit commonly referred to as the critical speed . This upper bound depends, in turn, on the speed at which waves propagate in the ground. But as models for trains in motion have increased in complexity, over the years the concept of critical speed has grown in obscurity. It was not until late in the twentieth century that it was realized that the critical speed was somehow connected to the so-called dispersion spectrum for the complete system, but until now, the justification for its application in practice has remained empirical and lacking in rigorous mathematical explanations. This task is taken up in this article, where for the first time a most general proof is provided for the problem at hand that is applicable to any layered soil configuration when one such system is subjected to one or more loads in motion.

scholarly journals A deductive-nomological model for mathematical scientific explanation

2020 ◽  
Vol 24 (1) ◽  
pp. 1-27
Author(s):  
Eduardo Castro
Keyword(s):  
Hamiltonian Systems ◽  
North American ◽  
Scientific Explanation ◽  
Laws Of Nature ◽  
Mathematical Explanation ◽  
Causal Explanations ◽  
Scientific Explanations ◽  
The North

I propose a deductive-nomological model for mathematical scientific explanation. In this regard, I modify Hempel’s deductive-nomological model and test it against some of the following recent paradigmatic examples of the mathematical explanation of empirical facts: the seven bridges of Königsberg, the North American synchronized cicadas, and Hénon-Heiles Hamiltonian systems. I argue that mathematical scientific explanations that invoke laws of nature are qualitative explanations, and ordinary scientific explanations that employ mathematics are quantitative explanations. I analyse the repercussions of this deductivenomological model on causal explanations.

scholarly journals Mathematical Explanations in Evolutionary Biology or Naturalism? A Challenge for the Statisticalist

2021 ◽  
Author(s):  
Fabio Sterpetti
Keyword(s):  
Population Genetics ◽  
Natural Selection ◽  
Evolutionary Biology ◽  
Causal Interpretation ◽  
Causal Explanations ◽  
Scientific Explanations ◽  
Mathematical Explanations

AbstractThis article presents a challenge that those philosophers who deny the causal interpretation of explanations provided by population genetics might have to address. Indeed, some philosophers, known as statisticalists, claim that the concept of natural selection is statistical in character and cannot be construed in causal terms. On the contrary, other philosophers, known as causalists, argue against the statistical view and support the causal interpretation of natural selection. The problem I am concerned with here arises for the statisticalists because the debate on the nature of natural selection intersects the debate on whether mathematical explanations of empirical facts are genuine scientific explanations. I argue that if the explanations provided by population genetics are regarded by the statisticalists as non-causal explanations of that kind, then statisticalism risks being incompatible with a naturalist stance. The statisticalist faces a dilemma: either she maintains statisticalism but has to renounce naturalism; or she maintains naturalism but has to content herself with an account of the explanations provided by population genetics that she deems unsatisfactory. This challenge is relevant to the statisticalists because many of them see themselves as naturalists.

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