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.

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.

Possible Worlds Counterfactual Theories of Causation

1980 ◽  
Vol 6 ◽  
pp. 119-138
Author(s):  
Richard Adler
Keyword(s):  
Alternative Treatment ◽  
Possible Worlds ◽  
Great Length ◽  
Current Interest ◽  
Possible Worlds Semantics ◽  
Causal Relations ◽  
Its Analysis ◽  
Counterfactual Theory ◽  
Causal Theories ◽  
Counterfactual Approach

The numerous difficulties facing the traditional Humean regularity approach to the problem of causation have been discussed in the literature at great length. In view of the current interest in possible worlds semantics, it is not surprising that the only serious alternative treatment of causation presently available, the counterfactual approach, has been explored recently as a means of circumventing the apparently unresolvable difficulties facing regularity causal theories. It is the purpose of this paper to suggest that such a strategy holds little promise. Specifically, I will argue that, in addition to giving rise to problems directly analogous to those facing regularity accounts, the counterfactual approach fails in principle to reflect important properties of causal relations as we understand them intuitively. David Lewis's possible worlds account, the most comprehensive counterfactual theory to date, is further criticized for implicit problems with natural lawhood even more serious than those typically raised for regularity accounts, for additional inadequacies in its analysis of causal relations, and for its failure to satisfy basic empiricist epistemological standards.

scholarly journals Can we have mathematical understanding of physical phenomena?

2018 ◽  
Vol 33 (1) ◽  
pp. 91
Author(s):  
Gabriel Tȃrziu
Keyword(s):  
Affirmative Answer ◽  
Mathematical Understanding ◽  
Explanatory Role ◽  
Mathematical Explanations ◽  
Physical Phenomena

Can mathematics contribute to our understanding of physical phenomena? One way to try to answer this question is by getting involved in the recent philosophical dispute about the existence of mathematical explanations of physical phenomena. If there is such a thing, given the relation between explanation and understanding, we can say that there is an affirmative answer to our question. But what if we do not agree that mathematics can play an explanatory role in science? Can we still consider that the above question can have an affirmative answer? My main aim here is to give an account that takes mathematics, in some of the cases discussed in the literature, as contributing to our understanding of physical phenomena despite not being explanatory.

scholarly journals Regularity and counterfactuality in Hume's treatment of causation

2011 ◽  
Vol 52 (124) ◽  
pp. 355-364 ◽  
Author(s):  
José Oscar de Almeida Marques
Keyword(s):  
David Lewis ◽  
Regularity Theory ◽  
Causal Inferences ◽  
Counterfactual Theory ◽  
Definition Of ◽  
Counterfactual Approach ◽  
Conceptual Resources

Of the several theories of causation current in our days, Hume is said to be the inspiration of two of the most influential and accepted: the regularity theory, first clearly formulated by Thomas Brown in 1822, and the counterfactual theory, proposed by David Lewis in 1973. After a brief outline of the comparative merits and difficulties of these two views, I proceed to examine whether Hume's own treatment of causation actually corresponds to any of them. I will show that his first definition of cause, coupled with his rules by which to judge about causes and effects, contains elements that, properly developed, allow us to address successfully some traditional difficulties of the regularity view of causation, without resorting to the conceptual resources employed in the counterfactual approach. Therefore, we can properly classify Hume as an advocate of the conception of causation as regularity, noting however that his primary goal in his research and definitions of the concept was to provide not so much an analysis of causation as such, but of causation as we apprehend it, in the form of our ability to make causal inferences and refine them to reach the more sophisticated causal reasonings that are required in the theoretical and practical issues of life.

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 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 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 STUDENT EVALUATION MATHEMATICAL EXPLANATION IN DIFFERENTIAL CALCULUS CLASS

2021 ◽  
Vol 6 (1) ◽  
pp. 45-56
Author(s):  
Gabariela Purnama Ningsi ◽  
Fransiskus Nendy ◽  
Lana Sugiarti ◽  
Ferdinandus Ardian Ali
Keyword(s):  
Evaluation Method ◽  
Student Evaluation ◽  
Evaluation Methods ◽  
Mathematical Explanation ◽  
Sociomathematical Norms ◽  
Student Work ◽  
Video Recordings ◽  
Mathematical Explanations ◽  
Field Notes

This study aimed to determine that the failure of students to evaluate mathematical explanations based on mathematics is influenced by sociomathematical norms, teaching authority, and classroom mathematics practice. The research method used is the case study method. The research data were obtained from inside and outside the research class. The data in the research class were in the form of field notes, video recordings of the class, video recordings of student group work, and student work. Data outside the research class is the result of interviews with three interview subjects. By studying the three evaluation methods students used in evaluating explanations, it was found that each student applied a different evaluation method at different times. The three evaluation methods contributed to some of the difficulties students experience in evaluating their mathematical descriptions. The results indicate that the failure of students in evaluating explanations is not solely due to errors in choosing the method, approach, or learning model used but can be caused by sociomathematical norms, authority, and classroom mathematics practices applied in the classroom.

scholarly journals Models, structures, and the explanatory role of mathematics in empirical science

Synthese ◽  
2021 ◽  
Author(s):  
Mary Leng
Keyword(s):  
Physical System ◽  
Mathematical Structure ◽  
Structural Features ◽  
Empirical Science ◽  
Explanatory Role ◽  
Mathematical Objects ◽  
Mathematical Explanations ◽  
Physical Phenomena

AbstractAre there genuine mathematical explanations of physical phenomena, and if so, how can mathematical theories, which are typically thought to concern abstract mathematical objects, explain contingent empirical matters? The answer, I argue, is in seeing an important range of mathematical explanations as structural explanations, where structural explanations explain a phenomenon by showing it to have been an inevitable consequence of the structural features instantiated in the physical system under consideration. Such explanations are best cast as deductive arguments which, by virtue of their form, establish that, given the mathematical structure instantiated in the physical system under consideration, the explanandum had to occur. Against the claims of platonists such as Alan Baker and Mark Colyvan, I argue that formulating mathematical explanations as structural explanations in this way shows that we can accept that mathematics can play an indispensable explanatory role in empirical science without committing to the existence of any abstract mathematical objects.

Mechanisms of Eyewitness Suggestibility: A Test of the Explanatory Role Hypothesis

2014 ◽  
Author(s):  
Eric J. Rindal ◽  
Quin M. Chrobak ◽  
Maria Zaragoza ◽  
Caitlin Weihing
Keyword(s):  
Explanatory Role ◽  
Eyewitness Suggestibility
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