And eminent philosophers recognise both the historical significance of maths and science on the discipline of philosophy and the consequences of its absence.
Take, for instance, Daniel Dennett, who likened many philosophical projects to exploring the logical universes of a fictional and irrelevant variant on chess, and the harsher Peter Unger, whose Empty Ideas is devastating to enormous swaths of philosophical pursuit, especially those that are scientifically uninformed. Still, just as good philosophers gain competence by being scientifically informed, good theoretical scientists gain competence by knowing more and deeper mathematics.
This does not imply that all good science is heavily mathematical, as biology is a conspicuous example of good science that isn't primarily mathematical. In On the Origin of Species , for example, there are no equations, but it abounds with observations and inferences. Even evolutionary biology, however, is deepened by the ideas in graph theory the "tree of life," for example , set-subset relationships taxonomy , probability and combinatorics gene inheritance , dynamic modelling differential growth rates of populations to describe effects of environmental pressures, say as modelled by the Lotka-Volterra equations and others , stochastic processes random variation of traits , and the combinatorial approach to thinking about DNA as "mathematical words" in a four-letter alphabet.
No discipline is better than mathematics for tuning an intellect to think in such a manner. Some may object that the onus to develop mathematical competence and habits of thought lays upon theoretical scientists more than on philosophers, but this sells short the capabilities of good philosophers and the demands of good philosophy. The lines that divide theoretical science and good philosophy of the sciences are both blurred and thin, and hence many branches of philosophy necessitate that philosophers are in fact theoreticians.
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In that case, just as theoretical scientists are ultimately beholden to the data, no matter the elegance of their models, so too are good philosophers. When the conclusions of sound argumentation proceeding from evidence conflict with common sense, it should be the latter that we dismiss and not the former. They use maths and science to clarify and inform their philosophy.
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Maths helps hone skills of clear, rigorous thinking, and science is unparalleled at determining facts and explanatory theories describing reality. Maths and science are therefore crucial for philosophy to make contributions of enduring worth, and so those who wish to be good at philosophy should study both. Share This. You can find him on Twitter at PeterBoghossian. James A. Follow him on Twitter: GodDoesnt. You might also like Study Maths and Science.
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The Meaning of "Asshole". Refresh and try again. Open Preview See a Problem? Details if other :. Thanks for telling us about the problem. Return to Book Page. Preview — Philosophies of Mathematics by Alexander George. Philosophies of Mathematics by Alexander George ,. Daniel J. This book provides an accessible, critical introduction to the three main approaches that dominated work in the philosophy of mathematics during the twentieth century: logicism, intuitionism and formalism.
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Oct 02, Darush rated it it was amazing. Apr 26, Peter Mcloughlin rated it really liked it Shelves: philosophy , mathematics , good-things. Probably the clearest exposition on the philosophy of mathematics I have read in a while. It can be comprehended with a minimum of mathematics and philosophy background. It traces out developments in the philosophy of mathematics in the twentieth century. It talks about Frege and Russell's logicist program to reduce mathematics to a branch of logic and Russell's paradox and Godel's incompleteness theorem of It also takes up intuitionism and finitism two alternatives to logicism and realis Probably the clearest exposition on the philosophy of mathematics I have read in a while.
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