Phenomenology, Logic, and the Philosophy of Mathematics 1st Edition by Richard Tieszen (PDF)

Description

Offering a collection of fifteen essays that deal with issues at the intersection of phenomenology, logic, and the philosophy of mathematics, this 2005 book is divided into three parts. Part I contains a general essay on Husserl’s conception of science and logic, an essay of mathematics and transcendental phenomenology, and an essay on phenomenology and modern pure geometry. Part II is focused on Kurt Godel’s interest in phenomenology. It explores Godel’s ideas and also some work of Quine, Penelope Maddy and Roger Penrose. Part III deals with elementary, constructive areas of mathematics. These are areas of mathematics that are closer to their origins in simple cognitive activities and in everyday experience. This part of the book contains essays on intuitionism, Hermann Weyl, the notion of constructive proof, Poincaré and Frege.

User’s Reviews

Editorial Reviews: Book Description In this 2005 book, logic, mathematical knowledge and objects are explored alongside reason and intuition in the exact sciences.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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!

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