Handouts
This is the list of handouts that were distributed in class.
Kinds of reasoning
- Dirk Schlimm: Terminology for proofs and arguments. PDF
-
Anthony Weston: A Rulebook for Arguments, 1992.
- Chapter IV: Deductive Arguments, pages 46-59.
-
Clark Glymour: Thinking Things Through, 1992.
- Chapter 1: Proofs, pages 3-15.
The structure of mathematical theories
-
Berlinghoff, Grant, Skrien: A Mathematics Sampler - Topics for the liberal arts, 1996.
- Sections 3.3-3.5: Axiom systems. Models. Consistency and Independence., pages 85-103.
-
David Hilbert: Foundations of Geometry, 1899.
- Chapter I: The five groups of axioms, pages 1-5.
-
Edmund Landau: Foundations of Analysis - The Arithmetic of Whole, Rational, Irrational, and Complex Numbers. A Supplement to Text-Books on the Differential and Integral Calculus, 1926.
- Chapter I: Natural numbers, pages 1-13.
-
J.M. Bochenski: The Method of Contemporary Thought, 1964.
- Chapter VI: The Axiomatic Method, Section 16: Example
of the axiomatic method in practice - Axiomatization of the
sentential logic of Hilbert and Ackermann, pages 87-90.
-
Bertrand Russell: Introduction to Mathematical Philosophy, 1919.
- Chapter I: The series of natural numbers, pages 1-10.
-
Dirk Schlimm: Hilbert and Gödel. PDF
- Containing quotes from Constance Reid, Hilbert (1970) and
Kurt Gödel, On formally undecidable propositions of Principia
Mathematica and related formal systems I (1931).
Case Study I: Theory of Probability
-
Robert Audi (ed.): The Cambridge Dictionary of Philosophy, 1995.
- Probability by E.Eels, pages 649-651.
-
Dirk Schlimm: Conditional probabilities and Cherry pies. PDF
Logic & Formal proofs
-
Clark Glymour: Thinking Things Through, 1992.
- Chapter 2: Aristotle's logic, pages 44-61.
-
Dirk Schlimm: Natural Deduction rules. PDF
-
Dirk Schlimm: Mathematical induction problems.
Theory of the infinite
-
Dirk Schlimm: Important definitions: Sets & Functions. PDF
-
William Dunham: Journey through Genius, 1990.
- Chapter 11: The Non-Denumerability of the Continuum, pages
245-266.
© Dirk Schlimm, Last
modified: 4/24/02