Naturalism in mathematics
Mathematics Naturalism e-böcker
Oxford University Press
1997
EISBN 9780198235736
Part I, The problem. The origins of set theory.
Set theory as a foundation.
The standard axioms.
Independent questions.
New axiom candidates.
Part II, Realism. Gödelian realism.
Quinean realism.
Set theoretic realism.
A realist's case against.
Hints of trouble.
Indispensability and scientific practice.
Indispensability and mathematical practice.
Part III, Naturalism. Wittgensteinian anti-philosophy.
A second Gödelian theme.
Quinean naturalism.
Mathematical naturalism.
The problem revisited.
A naturalist's case against.
Set theory has rendered the notion of self-evident truths to be obsolete in mathematics. Penelope Maddy examines this dilemma using the minimum of technical jargon. Set theory is explained in a manner that can be understood by non-mathematicians.
Set theory as a foundation.
The standard axioms.
Independent questions.
New axiom candidates.
Part II, Realism. Gödelian realism.
Quinean realism.
Set theoretic realism.
A realist's case against.
Hints of trouble.
Indispensability and scientific practice.
Indispensability and mathematical practice.
Part III, Naturalism. Wittgensteinian anti-philosophy.
A second Gödelian theme.
Quinean naturalism.
Mathematical naturalism.
The problem revisited.
A naturalist's case against.
Set theory has rendered the notion of self-evident truths to be obsolete in mathematics. Penelope Maddy examines this dilemma using the minimum of technical jargon. Set theory is explained in a manner that can be understood by non-mathematicians.
