{(Extract, & Comment:) The Nature of Mathematics}[7th July 1988]

[Redbook5:207][19880704:0000]{(Extract, & Comment:) The Nature of Mathematics}[7th July 1988]

198807(04)

'The theory of computability prompts many philosophical questions, most of which have so far not been answered satisfactorily. It poses the question, for example, of the extent to which all thinking can be carried out mechanically. Since it quickly turns out that many functions employed in mathematics – including many in elementary number theory – are nonrecursive,* one may wonder whether it follows that a mathematician's mind in thinking of such functions cannot be a mechanism and whether the possibly non-mechanical character of mathematical thinking may have consequences for the problems of determinism and free will. Further work is needed before definitive answers can be given to these important questions.'**

This is probably the most important thing I have read so far – and confirms my tentative feelings about the nature of mathematics***,**** up to a point, anyway (leaving the way open for the rest).

*(Recursive functions are functions ('laws governing numerical or other precise one-to-one or many-to-one relationships') which can be computed: that is, mechanically (which may equal effectively) calculated.)

**E[ncyclopedia ]Britannica ]XXV.720-1[, ]Philosophy of Logic]

cf [[Redbook5:167][19880617:1949f]{Inner Truth: Love [continued (5)]}[17^th June 1988]&ant?,] 167,

[[Redbook5:185-186][19880620:1040b]{Revival?}[20^th June 1988],] 186 [Presumably an incorrect ref?]

[It is possible that this fn refers not to this Vol, Vol V, but to Vol II, ie:

[Redbook2:168-169][19800805:2325]{'[0]'}[5th August 1980], &
[Redbook2:185-186][19810628:2240]{A Tarot Reading}[28th June 1981],ff]

***(& its position on the Circles at ?C~-S~?)

****not to mention the Materialist v Idealist controversy over the nature of Mind

(ref [[Redbook5:178-179][19880619:1707h]{Materialism and Idealism: The Nature of Mind}[19^th June 1988],] 178

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