PHIL 439

Spring 2023 Part of Term 1

Part of Term 1
Jan 17-May 3

Philosophy of Mathematics

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Credit: 3 OR 4 hours.

Introduction to some of the main philosophical problems and contemporary viewpoints concerning mathematical concepts, mathematical methods, and the nature of mathematical truth.

Same as MATH 439. 3 undergraduate hours. 3 or 4 graduate hours. Prerequisite: One course in philosophy.

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PHIL 439 class schedule data for spring 2023
	CRN	Type	Section	Time	Day	Location	Instructor	Section Details
	39169	Lecture-Discussion	G	9:30AM -10:50AM	TR	111 Gregory Hall	Kishida, K	Part of Term: 1 Date Range: 01/17/23-05/03/23 Credit: 4 hours Section Info: Graduate Section We shall discuss some basic issues in the foundations and philosophy of mathematics. The basic philosophical issues concern the nature of mathematical truth and the possibility and conditions of mathematical knowledge. Among the questions to be considered are the following: are the theorems of pure mathematics objectively true or false, independently of the mental? If so, what makes them true or false? In particular, are there specifically “mathematical” objects and, if so, how can we know about them? Are there properly basic concepts in mathematics – concepts from which all other mathematical notions can somehow be derived – and, if so, what are they? In particular, does a theory unfolding the concept of a set or class provide a satisfactory foundation for mathematics? Are there limits to our mathematical knowledge? Finally, we will join an ongoing discussion sparked by the logician Kurt Gödel, who famously claimed “Either mathematics is too big for the human mind, or the human mind is more than a machine.” Restriction(s): Restricted to Graduate - Urbana-Champaign.
	39168	Lecture-Discussion	UG	9:30AM -10:50AM	TR	111 Gregory Hall	Kishida, K	Part of Term: 1 Date Range: 01/17/23-05/03/23 Credit: 3 hours Section Info: Undergraduate Section We shall discuss some basic issues in the foundations and philosophy of mathematics. The basic philosophical issues concern the nature of mathematical truth and the possibility and conditions of mathematical knowledge. Among the questions to be considered are the following: are the theorems of pure mathematics objectively true or false, independently of the mental? If so, what makes them true or false? In particular, are there specifically “mathematical” objects and, if so, how can we know about them? Are there properly basic concepts in mathematics – concepts from which all other mathematical notions can somehow be derived – and, if so, what are they? In particular, does a theory unfolding the concept of a set or class provide a satisfactory foundation for mathematics? Are there limits to our mathematical knowledge? Finally, we will join an ongoing discussion sparked by the logician Kurt Gödel, who famously claimed “Either mathematics is too big for the human mind, or the human mind is more than a machine.” Restriction(s): Restricted to Undergrad - Urbana-Champaign.