Philosophy of Mathematics: Set Theory, Measuring Theories, and Nominalism

ISBN-13: 9783110323092 / Angielski / Twarda / 2008 / 184 str.

Gerhard Preyer;Georg Peter

Opis

One main interest of philosophy is to become clear about the assumptions, premisses and inconsistencies of our thoughts and theories. And even for a formal language like mathematics it is controversial if consistency is acheivable or necessary like the articles in the firt part of the publication show. Also the role of formal derivations, the role of the concept of apriority, and the intuitions of mathematical principles and properties need to be discussed. The second part is a contribution on nominalistic and platonistic views in mathematics, like the "indispensability argument" of W. v. O. Quine H. Putnam and the "makes no difference argument" of A. Baker. Not only in retrospect, the third part shows the problems of Mill, Frege's and the unity of mathematics and Descartes's contradictional conception of mathematical essences. Together, these articles give us a hint into the relationship between mathematics and world, that is, one of the central problems in philosophy of mathematics and philosophy of science.

O autorze

Dr. Gerhard Preyer is professor of sociology. Newer publication: Intention and Practical Thought (2007). Together with Georg Peter editions on Context-Sensitivity and Semantic Minimalism (2007), Contextulaism in Philosophy (2005) and Logical Form and Language (2002).Dr. Georg Peter is a member of the Project Protosociology. Together with Gerhard Preyer newer editions on Context-Sensitivity and Semantic Minimalism (2007), Contextulaism in Philosophy (2005) and Logical Form and Language (2002).