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The strength of Mac Lane set theory
 ANNALS OF PURE AND APPLIED LOGIC
, 2001
"... SAUNDERS MAC LANE has drawn attention many times, particularly in his book Mathematics: Form and Function, to the system ZBQC of set theory of which the axioms are Extensionality, Null Set, Pairing, ..."
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SAUNDERS MAC LANE has drawn attention many times, particularly in his book Mathematics: Form and Function, to the system ZBQC of set theory of which the axioms are Extensionality, Null Set, Pairing,
Debreu’s apologies for mathematical economics after 1983
"... Abstract: When reassessing the role of Debreu’s axiomatic method in economics, one has to explain both its success and unpopularity; one has to explain the “bright shadow ” Debreu cast on the discipline: sheltering, threatening, and difficult to pin down. Debreu himself did not expect to have such a ..."
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Abstract: When reassessing the role of Debreu’s axiomatic method in economics, one has to explain both its success and unpopularity; one has to explain the “bright shadow ” Debreu cast on the discipline: sheltering, threatening, and difficult to pin down. Debreu himself did not expect to have such an influence. Before he received the Bank of Sweden Prize in 1983 he had never openly engaged with the methodology or politics of mathematical economics. When in several speeches he later rigorously distinguished mathematical form from economic content and claimed this as the virtue of mathematical economics, he did both: he defended mathematical reasoning against the theoretical innovations since the 1970s and expressed remorse for having promised too much because it cannot support claims about economic content. The analysis of this twofold role of Debreu’s axiomatic method raises issues of the social and political responsibility of economists over and above standard epistemic issues.
ARISTOTELIAN REALISM
"... Aristotelian, or nonPlatonist, realism holds that mathematics is a science of the real world, just as much as biology or sociology are. Where biology studies living things and sociology studies human social relations, mathematics studies the quantitative or structural aspects of things, such as rat ..."
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Aristotelian, or nonPlatonist, realism holds that mathematics is a science of the real world, just as much as biology or sociology are. Where biology studies living things and sociology studies human social relations, mathematics studies the quantitative or structural aspects of things, such as ratios, or patterns, or complexity,