Math Philosophy Lecture Notes PDF

Welcome to our MATH class!  MATHEMATICS and Philosophy Prepared by: VHERLINE A. DOORIN,LPT INSTRUCTOR I  OBJECTIVES Explain the philosophy of mathematics, 1 including mathematical logic and reasoning. Recognize the significance of philosophical 2 perspect...

Welcome to our MATH class!  MATHEMATICS and Philosophy Prepared by: VHERLINE A. DOORIN,LPT INSTRUCTOR I  OBJECTIVES Explain the philosophy of mathematics, 1 including mathematical logic and reasoning. Recognize the significance of philosophical 2 perspectives on mathematics and its logical foundations.. Use mathematical logic and reasoning to 3 explore and discuss philosophical questions about infinity and the nature of mathematics.  THE PHILOSOPHY OF 1 MATHEMATICS  The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics.  THE PHILOSOPHY OF 1 MATHEMATICS FOUR SCHOOLS OF MATHEMATICAL PHILOSOPHY  Logicism  Formalism  Intuitionism  Predicativism  THE PHILOSOPHY OF 1 MATHEMATICS LOGICISM  It holds that mathematics is reducible to principles of pure logic.  THE PHILOSOPHY OF 1 MATHEMATICS RICHARD DEDEKIND  Dedekind’s “logicism” embraced all mathematical concepts: the concepts of number – natural, rational, real, complex – and geometric concepts such as continuity.  THE PHILOSOPHY OF 1 MATHEMATICS QUINE  Logicism, a mathematical truth and logical demonstration go hand in hand..  THE PHILOSOPHY OF 1 MATHEMATICS GOTTLOB FREGE  He devoted much of his career to trying to show how mathematics can be reduced to logic.  THE PHILOSOPHY OF 1 MATHEMATICS FORMALISM  It is the view that much or all of mathematics is devoid of content and a purely formal study of strings of mathematical language/medium of formal symbols.  THE PHILOSOPHY OF 1 MATHEMATICS DAVID HILBERT  He developed the formalist perspective.  He published his epoch- making work Grundlagen der Geometrie (Foundations of Geometry  THE PHILOSOPHY OF 1 MATHEMATICS KURT GODEL  He demonstrates his celebrated Incompleteness Theorems, that there would always be real propositions provable by ideal means which cannot be proved by concrete means.  THE PHILOSOPHY OF 1 MATHEMATICS INTUITIONISM  It holds that mathematics is concerned with mental constructions and defends a revision of classical mathematics and logic.  THE PHILOSOPHY OF 1 MATHEMATICS L.E.J BROUWER  Brouwer held that mathematical theorems are synthetic a prior truths.  He is the proponent of intuitionism.  THE PHILOSOPHY OF 1 MATHEMATICS PREDICATIVISM  There emerged in the beginning of the 20th century also a fourth program.  THE PHILOSOPHY OF 1 MATHEMATICS WEYL  He developed a philosophical stance that is in a sense intermediate between intuitionism and platonism.  He took the collection of natural numbers as unproblematically given. ACTIVITY ASSESSMENT THANK YOU!