Mathematical Explanation in Science

@article{Baker2009MathematicalEI,
  title={Mathematical Explanation in Science},
  author={A. Baker},
  journal={The British Journal for the Philosophy of Science},
  year={2009},
  volume={60},
  pages={611 - 633}
}
  • A. Baker
  • Published 2009
  • Philosophy
  • The British Journal for the Philosophy of Science
Does mathematics ever play an explanatory role in science? If so then this opens the way for scientific realists to argue for the existence of mathematical entities using inference to the best explanation. Elsewhere I have argued, using a case study involving the prime-numbered life cycles of periodical cicadas, that there are examples of indispensable mathematical explanations of purely physical phenomena. In this paper I respond to objections to this claim that have been made by various… Expand
Mathematical Explanations Of Empirical Facts, And Mathematical Realism
A main thread of the debate over mathematical realism has come down to whether mathematics does explanatory work of its own in some of our best scientific explanations of empirical facts. RealistsExpand
Indispensability Arguments and Mathematical Explanation in Science
TLDR
The aim of this thesis is to find a way to undermine the indispensability argument for mathematical platonism by rejecting the first reading and arguing that a second reading, which involves an instance of IBE, is the most plausible. Expand
Unification and mathematical explanation in science
Mathematics clearly plays an important role in scientific explanation. Debate continues, however, over the kind of role that mathematics plays. I argue that if pure mathematical explananda andExpand
Mathematical Indispensability and Arguments from Design
The recognition of striking regularities in the physical world plays a major role in the justification of hypotheses and the development of new theories both in the natural sciences and inExpand
Outlines of a theory of structural explanations
This paper argues that in some explanations mathematics are playing an explanatory rather than a representational role, and that this feature unifies many types of non-causal or non-mechanisticExpand
Indispensability and Explanation
  • S. Bangu
  • Sociology
  • The British Journal for the Philosophy of Science
  • 2013
The question as to whether there are mathematical explanations of physical phenomena has recently received a great deal of attention in the literature. The answer is potentially relevant for theExpand
Scientific Realism and the Indispensability Argument for Mathematical Realism: A Marriage Made in Hell
An emphasis on explanatory contribution is central to a recent formulation of the indispensability argument (IA) for mathematical realism. Because scientific realism is argued for by means ofExpand
Mathematical Explanation by Law
  • Sam Baron
  • Mathematics
  • The British Journal for the Philosophy of Science
  • 2019
Call an explanation in which a non-mathematical fact is explained—in part or in whole—by mathematical facts: an extra-mathematical explanation. Such explanations have attracted a great deal ofExpand
Evidence, explanation and enhanced indispensability
TLDR
The genuineness of mathematical explanations of scientific facts turns out to be dependent on pragmatic constraints and therefore cannot be plugged in EIA and used to establish existential claims about mathematical objects. Expand
Importance and Explanatory Relevance: The Case of Mathematical Explanations
A way to argue that something (e.g. mathematics, idealizations, moral properties, etc.) plays an explanatory role in science is by linking explanatory relevance with importance in the context of anExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 29 REFERENCES
Are there Genuine Mathematical Explanations of Physical Phenomena
Many explanations in science make use of mathematics. But are there cases where the mathematical component of a scientific explanation is explanatory in its own right? This issue of mathematicalExpand
Living in Harmony: Nominalism and the Explanationist Argument for Realism
According to the indispensability argument, scientific realists ought to believe in the existence of mathematical entities, due to their indispensable role in theorising. Arguably the crucial senseExpand
Does the Existence of Mathematical Objects Make a Difference?
In this paper I examine a strategy which aims to bypass the technicalities of the indispensability debate and to offer a direct route to nominalism. The starting-point for this alternative nominalistExpand
Mathematical Explanation: Why it Matters
This chapter offers a broad survey of the literature on mathematical explanation, and shows the importance of this area of work for a philosophical understanding of mathematical practice and forExpand
Inference to the best explanation and mathematical realism
  • S. Bangu
  • Philosophy, Computer Science
  • Synthese
  • 2006
TLDR
It is shown that this example of a genuine mathematical explanation of a physical phenomenon, and the argument built upon it, begs the question against the mathematical nominalist. Expand
Weaseling away the indispensability argument
According to the indispensability argument, the fact that we quantify over numbers, sets and functions in our best scientific theories gives us reason for believing that such objects exist. I examineExpand
Response to Colyvan
In 'Weaseling Away the Indispensability Argument' (Melia 2000) I argued that although quantification over mathematical objects may indeed be indispensable to our scientific theories, it is not alwaysExpand
MATHEMATICAL EXPLANATION AND INDISPENSABILITY ARGUMENTS
We defend Joseph Melia's thesis that the role of mathematics in scientific theory is to ‘index’ quantities, and that even if mathematics is indispensable to scientific explanations of concreteExpand
There Are No Abstract Objects
1 The thesis Suppose you start out inclined towards the hard-headed view that the world of material objects is the whole of reality. You elaborate: 'Everything there is is a material object: the sortExpand
Reducing possibilities to language
The view that possible worlds should be identified with linguistic entities has a long and respectable history: Carnap (1947), Jeffrey (1965) and Hintikka (1969) are but a few philosophers who haveExpand
...
1
2
3
...