Mathematics, Form and Function: Difference between revisions

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'''''Mathematics, Form and Function''''', a book published in 1986 by [[Springer-Verlag]], is a survey of the whole of [[mathematics]], including its origins and deep structure, by the [[United States|American]] mathematician [[Saunders Mac Lane]].

== Mac Lane's relevance to the philosophy of mathematics ==

Mac Lane cofounded [[category theory]] with [[Samuel Eilenberg]], which enables a [[unifying theories in mathematics|unified treatment]] of mathematical structures and of the relations among them, at the cost of [[abstract nonsense|breaking away from their cognitive grounding]]. Nevertheless, his views&mdash;however informal&mdash;are a valuable contribution to the [[philosophy of mathematics|philosophy]] and [[anthropology]] of mathematics.<ref>On the anthropological grounding of mathematics, see White (1947) and Hersh (1997).</ref> His views anticipate, in some respects, the more detailed account of the [[cognitive science of mathematics|cognitive basis of mathematics]] given by [[George Lakoff]] and [[Rafael E. Núñez]] in their ''[[Where Mathematics Comes From]]''. Lakoff and Núñez argue that mathematics emerges via [[conceptual metaphor]]s grounded in the [[embodied philosophy|human body]], its motion through [[space]] and [[time]], and in human sense perceptions.

== Mathematics and human activities==

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|-

|Collecting

|[[CollectionObject (mathematics)|Collection]]

|[[Set (mathematics)|Set]]; [[class (set theory)|class]]; [[multiset]]; [[list (computing)|list]]; [[Familyindexed (disambiguation)#Mathematicsfamily|family]]

|-

|Connecting

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|-

| "

|[[Proximity space|Proximity]]; [[connectedness|connection]]

|[[Topological space]]; [[mereotopology]]

|-

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|-

|[[Counting]]

|[[Successor ordinal|Successor]]

|[[Successor function]]; [[ordinal number]]

|-

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|Estimating

|[[Approximation]]

|[[Real number]]; [[real closed field|real field]]

|-

|Moving through [[space]] & [[time]]:

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Mac Lane (1986) cites a related monograph by [[Lars Gårding]] (1977).

== Mac Lane's relevance to the philosophy of mathematics ==

Mac Lane cofounded [[category theory]] with [[Samuel Eilenberg]], which enables a [[unifying theories in mathematics|unified treatment]] of mathematical structures and of the relations among them, at the cost of [[abstract nonsense|breaking away from their cognitive grounding]]. Nevertheless, his views&mdash;however informal&mdash;are a valuable contribution to the [[philosophy of mathematics|philosophy]] and [[anthropology]] of mathematics.<ref>On the anthropological grounding of mathematics, see White (1947) and Hersh (1997).</ref> His views anticipate, in some respects, the more detailed account of the [[cognitive science of mathematics|cognitive basis of mathematics]] given by [[George Lakoff]] and [[Rafael E. Núñez]] in their ''[[Where Mathematics Comes From]]''. Lakoff and Núñez argue that mathematics emerges via [[conceptual metaphor]]s grounded in the [[embodied philosophy|human body]], its motion through [[space]] and [[time]], and in human sense perceptions.

== See also ==

* [[1986 in philosophy]]

==Notes==

<references />

==References==

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* [[Leslie White]], 1947, "The Locus of Mathematical Reality: An Anthropological Footnote," ''Philosophy of Science 14'': 289-303. Reprinted in Hersh, R., ed., 2006. ''18 Unconventional Essays on the Nature of Mathematics''. Springer: 304–19.

[[Category:1986 non-fiction books]]

[[Category:Mathematics books]]

[[Category:Philosophy of mathematics literature]]

[[Category:Cognitive science literature]]