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Thought-objects

17/11/2015 - 17:43 von WM | Report spam
David Hilbert in 1904 [...] wrote that sets are thought-objects which can be imagined prior to their elements. At request of the referee who asked what is a thought-object let me add: I understand it to be a thought about an object which may exist or not. Thus it is an electrochemical event in the brain or/and its record in the memory. In particular it is a physical thing in space time. Of course it is difficult to characterise any physical phenomena. But we have the ability to recognize thoughts as identical or different, just as we have the ability to recognize a silent lightning from a thunderous one. Hence I understand Hilbert's words as follows: mathematicians imagine sets which do not exist, but their thoughts about sets do exist and they can arise prior to the thoughts of most elements in those sets. {{And all thoughts can be enumerated by one of the covered rational spatio-temporal coordinates.}}
[J. Mycielski: "Russell's paradox and Hilbert's (much forgotten) view of set theory" in "One hundred years of Russell's paradox: mathematics, logic, philosophy" G. Link (ed.), de Gruyter (2004) p. 534]

Gruß, WM
 

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#1 Rudolf Sponsel
18/11/2015 - 11:12 | Warnen spam
Am 17.11.2015 um 17:43 schrieb WM:
mathematicians imagine sets which do not exist, but their thoughts about sets do exist and they can arise prior to the thoughts of most elements in those sets.



Schon wieder dieser dubios schillerende Begriff der "Existenz".
Wie siehst Du übrigens die "Existenz" der leeren Menge?

Gruß: RS

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