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The Explanatory Power of Phase Spaces
"... David Malament argued that Hartry Field’s nominalisation program is unlikely to be able to deal with nonspacetime theories such as phasespace theories. We give a specific example of such a phasespace theory and argue that this presentation of the theory delivers explanations that are not availabl ..."
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David Malament argued that Hartry Field’s nominalisation program is unlikely to be able to deal with nonspacetime theories such as phasespace theories. We give a specific example of such a phasespace theory and argue that this presentation of the theory delivers explanations that are not available in the classical presentation of the theory. This suggests that even if phasespace theories can be nominalised, the resulting theory will not have the explanatory power of the original. Phasespace theories thus raise problems for nominalists that go beyond Malament’s initial concerns.
10. Appendix A: Extracting an ‘Underlying ’ Explanation 11. Appendix B: Another Example of an Explanatory Physical Argument
"... There are lots of arguments for, or justifications of, mathematical theorems that make use of principles from physics. Do any of these constitute explanations? On the one hand, physical principles do not seem like they should be explanatorily relevant; on the other, some particular examples of physi ..."
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There are lots of arguments for, or justifications of, mathematical theorems that make use of principles from physics. Do any of these constitute explanations? On the one hand, physical principles do not seem like they should be explanatorily relevant; on the other, some particular examples of physical justifications do look explanatory. In this paper I defend the idea that (some) physical justifications can and do explain mathematical facts.
Indispensability Arguments and Their Quinean Heritage
"... Indispensability arguments (IA) for mathematical realism are commonly traced back to Quine. We identify two different Quinean strands in the interpretation of IA, what we label the ‘logical point of view ’ and the ‘theorycontribution ’ point of view. Focusing on each of the latter, we offer two min ..."
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Indispensability arguments (IA) for mathematical realism are commonly traced back to Quine. We identify two different Quinean strands in the interpretation of IA, what we label the ‘logical point of view ’ and the ‘theorycontribution ’ point of view. Focusing on each of the latter, we offer two minimal versions of IA. These both dispense with a number of theoretical assumptions commonly thought to be relevant to IA (most notably confirmational holism and naturalism). We then show that the attribution of both minimal arguments to Quine is controversial, and stress the extent to which this is so in both cases, in order to attain a better appreciation of the Quinean heritage of IA.
Mirror Symmetry and Other Miracles in
"... Abstract The dominance of string theory in the research landscape of quantum gravity physics (despite any direct experimental evidence) can, I think, be justified in a variety of ways. Here I focus on an argument from mathematical fertility, broadly similar to Hilary Putnam’s ‘no miracles argument ’ ..."
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Abstract The dominance of string theory in the research landscape of quantum gravity physics (despite any direct experimental evidence) can, I think, be justified in a variety of ways. Here I focus on an argument from mathematical fertility, broadly similar to Hilary Putnam’s ‘no miracles argument ’ that, I argue, many string theorists in fact espouse. String theory leads to many surprising, useful, and wellconfirmed mathematical ‘predictions’—here I focus on mirror symmetry. These predictions are made on the basis of general physical principles entering into string theory. The success of the mathematical predictions are then seen as evidence for framework that generated them. I attempt to defend this argument, but there are nonetheless some serious objections to be faced. These objections can only be evaded at a high (philosophical) price.
Mathematical Explanations in Euler’s Königsberg
, 2014
"... I examine Leonhard Euler’s original solution to the Königsberg bridges problem. Euler’s solution can be interpreted as both an explanation within mathematics and a scientific explanation using mathematics. At the level of pure mathematics, Euler proposes three different solutions to the Königsberg p ..."
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I examine Leonhard Euler’s original solution to the Königsberg bridges problem. Euler’s solution can be interpreted as both an explanation within mathematics and a scientific explanation using mathematics. At the level of pure mathematics, Euler proposes three different solutions to the Königsberg problem. The differences between these solutions can be fruitfully explicated in terms of explanatory power. In the scientific version of the explanation, mathematics aids by representing the explanatorily salient causal structure of Königsberg. Based on this analysis, I defend a version of the socalled “Transmission View” of scientific explanations using mathematics against objections by Alan Baker and Marc Lange, and I discuss Lange’s notion of “distinctively mathematical expla