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.

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 Indispensability, causation and explanation

2018 ◽  
Vol 33 (2) ◽  
pp. 219
Author(s):  
Sorin Bangu
Keyword(s):  
Indispensability Argument ◽  
Methodological Naturalism ◽  
Mathematical Realism ◽  
Mathematical Objects ◽  
The Road ◽  
Realist Position ◽  
Opposite View ◽  
Mathematical Nominalism

When considering mathematical realism, some scientific realists reject it, and express sympathy for the opposite view, mathematical nominalism; moreover, many justify this option by invoking the causal inertness of mathematical objects. The main aim of this note is to show that the scientific realists’ endorsement of this causal mathematical nominalism is in tension with another position some (many?) of them also accept, the doctrine of methodological naturalism. By highlighting this conflict, I intend to tip the balance in favor of a rival of mathematical nominalism, the mathematical realist position supported by the ‘Indispensability Argument’ – but I do this indirectly, by showing that the road toward it is not blocked by considerations from causation.

Colloquium 5 The Birds and the Bees: Aristotle on the Biologcial Concept of ἀνάλογον

2014 ◽  
Vol 29 (1) ◽  
pp. 145-169
Author(s):  
Devin Henry
Keyword(s):  
Natural Kind ◽  
Natural Kinds ◽  
Causal Explanation ◽  
Explanatory Role ◽  
Common Causes ◽  
Similar Location ◽  
Different Parts ◽  
Second Analogy

In this paper I examine Aristotle’s biological use of the concept of analogy. On the reading I defend, biological analogues are parts that realize the same capacity of soul or occupy a similar location in the animals whose parts they are but are not specific (“more-and-less”) modifications of the same underlying material substratum. The concept of analogy serves two principal functions in Aristotle’s biology. First, Aristotle uses analogy as a tool for classifying animals into separate natural kinds (Part 3). Second, analogy plays an explanatory role in which the same causal explanation is transferred to “φ and its analogue” (Part 4). Here the function of analogy is to group different parts into a single explanatory class unified on the basis of shared causes. One of the upshots of my interpretation is that, while analogical unity may allow us to posit a common explanation for φ and its analogue, it is not grounds for treating the class of animals that ­possess those parts as a natural kind. For Aristotle, natural kinds are groups whose shared similarities must result from common causes operating on a common material substratum.


scholarly journals Action explanation and its presuppositions

2019 ◽  
Vol 49 (1) ◽  
pp. 123-146
Author(s):  
Lilian O’Brien
Keyword(s):  
Causal Explanation ◽  
Intentional Action ◽  
Explanatory Role ◽  
Psychological States ◽  
Action Explanation

AbstractIn debates about rationalizing action explanation causalists assume that the psychological states that explain an intentional action have both causal and rational features. I scrutinize the presuppositions of those who seek and offer rationalizing action explanations. This scrutiny shows, I argue, that where rational features play an explanatory role in these contexts, causal features play only a presuppositional role. But causal features would have to play an explanatory role if rationalizing action explanation were a species of causal explanation. Consequently, it is not a species of causal explanation.

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.

scholarly journals Searching for Non-Causal Explanations in a Sea of Causes

2018 ◽  
Author(s):  
Alisa Bokulich
Keyword(s):  
Scientific Explanation ◽  
Causal Explanation ◽  
Causal Explanations ◽  
Explanatory Pluralism ◽  
Sand Ripples ◽  
Scientific Explanations ◽  
Model Based ◽  
Aeolian Geomorphology

In the spirit of explanatory pluralism, this chapter argues that causal and non-causal explanations of a phenomenon are compatible, each being useful for bringing out different sorts of insights. First the chapter reviews the author’s model-based account of scientific explanation, which can accommodate causal and non-causal explanations alike. Then it distills from the literature an important core conception of non-causal explanation. This non-causal form of model-based explanation is illustrated using the example of how Earth scientists in a subfield known as aeolian geomorphology are explaining the formation of regularly-spaced sand ripples. The chapter concludes that even when it comes to everyday “medium-sized dry goods” such as sand ripples, where there is a complete causal story to be told, one can find examples of non-causal scientific explanations.

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