Who are the currently active researchers writing and publishing in peer-reviewed technical journals about the use of mathematics to arrive at useful philosophical ideas? By "mathematical philosophy" is NOT meant "philosophy of mathematics," even though Bertrand Russell published a book called "Mathematical Philosophy" which is actually a philosophical summary of basic mathematical concepts. This question is about the use of mathematical intuition, notation, or theorems to declare or to support philosophical ideas. In particular, in metaphysics and in moral philosophy. By "useful philosophical idea" is meant an idea that advances the discussion among a circle of interested parties.
Check out the website at https://www.mcmp.philosophie.uni-muenchen.de/students/math/index.html
Also at https://mathoverflow.net/questions/tagged/mathematical-philosophy
https://www.academia.edu/35504572/CORCORAN_ON_NEW_MATHEMATICAL_PHILOSOPHY
https://www.cairn-int.info/article-E_APHI_682_0315--giordano-bruno-s-mathematical.htm
https://www.nature.com/articles/113741a0
https://www.degruyter.com/view/product/151059
Obviously quite a lot going on ...
There is a lot of philosophy done using formal methods -- symbolic logic, probability, decision and games theory, topology. You might look at the website of the Society for Exact Philosophy.
I have interest in the topic although I am yet to know deep about it.
Dear Ellis D. Cooper,
Since you asked for persons who use mathematics to establish philosophical results, I would recommend to look at the work of Kit Fine. Fine is widely regarded as a leading figure in contemporary metaphysics. My best guess is that his most interesting work four you is his Truthmaker Semantics, because it is based on Mereology. This system binds directly into an intensely debated metaphysical topic called “grounding“ and is relevant to a wide variety of issues in theoretical philosophy.
A published paper that presents the core ideas is Truthmaker Semantics in A Companion to the Philosophy of Language (2017): 556-577.
Perhaps of more interest – because much more detailed - is his unpublished Truthconditional Content - Part I & II which can be found on Academia.
For an introduction into the metaphysical side, see, for example, Fine’s Guide to Ground in Correia and Schnieder, Metaphysical grounding: Understanding the structure of reality (2012): 37-80.
Hope that helps.
Best,
Sven Beecken
Some links for formal methods in ethics:
https://philpapers.org/browse/decision-theory-and-ethics
https://stanford.library.sydney.edu.au/archives/fall2008/entries/game-ethics/
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