Philosophy, linguistics, mathematics and computer science are just stupid names for the bureaucrats. As Árpád Szabó showed in his works (e.g. in The Beginnings of Greek Mathematics) the logical investigations of the Eleatics school were a necessary precondition of the birth of axiomatic mathematics. Euclid's Elements is a real gem (Smullyan writes in superlatives about the book in his autobiography, and according to him, it is still the best introduction into geometry and mathematical thinking) and it was unquestionable till the 19th century.
In 1637 Descartes published the Discours de la méthode with a less known appendix titled La Géomtérie in which he showed his calcul géométrique, today this field is called analytic geometry or coordinate geometry, sometimes Cartesian geometry. The axiomatic method of geometry deeply influenced Descartes, and I guess Descartes mathematics was influenced by the Cartesianism too. Spinoza continued the Cartesian line and built up his ethics more geometrico (in the geometrical manner).
The foundational crisis of mathematics was preceded by "mini-crisis" in geometry. János Bolyai and Nikolai Lobachevsky "discovered" the non-euclidian geometry almost at the same time. Bolyai wrote in a letter to his father "by denying the axiom of parallels i made a wonderful new world from nothing". The philosopher of mathematics and mathematician Imre Toth calls this process of "creating negation", and he thinks this is the differencia specifica of mankind; we can make new worlds by the power of thinking (if you want to read non-analytic philosophy of maths you should read Toth's books, my personal favorites Platon et l'irrationnel mathématique and Liberté et vérité: Pensée mathématique et spéculation philosophique. If you want to read a postmodern quasi-literary maths book, I recommend you Toth's Palimpseste: Propos avant un triangle ).
As Wadler says in his Proofs Are Programs "For my money, Gentzen’s natural deduction and Church’s lambda calculus are on a par with Einstein’s relativity and Dirac’s quantum physics for elegance and insight." The foundational crisis brought us Frege's works. The logicisim was a reaction to psychologism and neo-kantianism, not "just" yet another mathematical theory. The early 20th century was about finding new ways. The Vienna Circle, the Prague Circle and the Polish School of Mathematics along the flourishing Geman and Hungarian mathematics were exploring the new more geometrico. These schools left the old continent and new ones emerged. For me, generative linguistics is the descendant of the Vienna and Prague circles, highly influenced by the Polish school.
Ethics and political philosophy went back to its roots when Rawls' A Theory of Justice was published.Rawls' linguistic analogy is just one member of the bestiary of formal methods in ethics and political philosophy. These days, you can find "hard core techniques" if you search for social software and dynamic epistemic logic.
During the the second half of the last century new sciences born like computer science, artificial intelligence, cognitive science. These brand new sciences are trying to answer old philosophical questions more geometrico but can we draw a line between science and philosophy?
