Phenomenology, Logic, and the Philosophy of Mathematics

Amazing selection of essays which are thematically tied together to create a rather coherent narrative and book. The text is a sustained argument for a Husserlian theory of mathematics that offers itself as a candidate for providing a theoretical foundation for mathematics. To this end about 30-40% of the text looks at Godel's outward appreciation and interest in Husserlian phenomenology for just this reason - namely as the only response viable to his incompleteness theorems which could find a non-formalist foundation for mathematics. In general mathematics is looked at as a particular type of intentional experience and constitution which represent a unique regional ontology. Following Husserl's lead, Tieszen does a wonderful job of providing a phenomenology of mathematics as a form of constitutive experience that deals with "abstract ideas-objects" that are at once immanently constituted in the subject and their lived-experience, but whose inherent meaning as mathematical objects is lived as concepts that are transcendent to the subject and which have inherent constraints which pre-demarcate the horizon of their possiblities. Mathematicians then explore these horizons in the natural attitude of doing math, while phenomenology makes explicit the logic of free variation that is operating in the background. This ends in a form of non-metaphysical platonic realism. Fascinating book, highly recommended to anyone who studies phenomenology or the philosophy of mathematics. Thoughts will be provoked either way. P.s. Learned a ton about formalism, finitism, intuitionalism, nominalism, and other areas of the philsophy of mathematics, the relation of all this to turing machines, and in addition about the Husserlian-mathematics connection throughout his life.

Great book written by my late uncle Rick. Buy it!