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This Ockhamist move is illustrative of and influential on an important development in late medieval physics: the application of mathematics to non-mathematical things, culminating in Galileo's famous statement that the "book of nature" is written in the "language of mathematics".
Similarly to the epistemological problem, the problem of the application of mathematics is partially solved by the mathematical fictionalist.
But even if these difficulties can all be addressed, it is unclear that the mathematical fictionalist has offered an account of the application of mathematics that allows us to make sense of how mathematical theories are actually applied.
Field provides an account of the application of mathematics that does not require the truth of mathematical theories.
There is, of course, a correct intuition underlying the use of isomorphism at this level, and this relates to the idea of justifying the application of mathematics: the isomorphism does guarantee that applied mathematical structures S and the structures M which represent the material situation are mathematically the same.
Edgeworth introduced mathematical elements to Economics explicitly in Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences, published in 1881.
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For those of us interested in the applications of mathematics to the real world, this makes pi indispensable.
By the early 2000s, "tech-savvy investors had come to dominate Wall Street, helped by theoretical breakthroughs in the applications of mathematics to financial markets," Scott Patterson wrote in "The Quants," a book about the bankers who wield those tools.
Opus maius, Part four, deals with mathematics and the applications of mathematics.
The applications of mathematics can in turn be used in religion and theology.
Logic is reduced to mathematics, and the applications of mathematics become central to an understanding of the sciences (Perler, 2005).
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