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Russell's and Frege's Definition of Number 
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#19
Feb211, 05:05 PM

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#20
Feb211, 05:10 PM

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#21
Feb211, 05:16 PM

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Sure it is rigorous insofar his system of axioms is, but it is not a definition of what a number is. It is a definition of what he calls "numbers" with respect to his axiomatic system of classes, but it does not encapsulate the general concept of a number. It was proposed, as I understood OP, as a universal definition of what it means to be a number. That simply cannot be done. Compare with the concept of a function. It has many definitions in different axiomatic settings, but they don't contradict each other, nor are they battling for the status as the "correct" definition of a function. They simply reflect how a function can be treated in the particular setting one find oneself. The concept of a number, and a function, remains a part of language, not logic. 


#22
Feb211, 05:24 PM

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#23
Feb311, 02:05 AM

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#24
Feb311, 02:14 AM

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#25
Feb311, 09:20 AM

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Of course, the name was chosen to be suggestive  the technical term is meant to be logically equivalent to something we might mean by the English phrase. The technical term doesn't define "set with ____ element(s)" where ___ is replaced by some sort of number. It only defines "set with one element". English dictionaries are not mathematical reference books. (moderator's hat on) Anyways, this discussion had been dead for 5 years, is in the wrong section, and the necromancer seems to just want to be contrary, so I don't see any reason to leave the thread open. 


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