[FOM] FOM: Neo-classical theories of number

Dean Buckner Dean.Buckner at btopenworld.com
Tue Mar 4 13:47:40 EST 2003

Ron Pisaturo is now just one of a growing number of people working with
"neo-classical" ideas about number.  I mean theories which tend to reject
Frege's idea that number is a property of concepts, in favour of the
classical idea that "number" - the Greek arithmos - is just a term for a
plurality, composed of "units".

Jonathan (E.J.) Lowe recently wrote to me mentioning a paper of his
defending Locke's theory of number (which is similar to Mill's) against
criticisms levelled by Frege in the Grundlagen.  (I hope Jonathan doesn't
mind my advertising this).  Hartley Slater has written a paper on similar
lines (hope he won't mind either).

Finally, I found today an old but excellent paper by Gyula Klima,
medievalist extraordinaire, defending Ockham's theory of number and
numerical quantification.  I won't summarise this, however, as discussion of
Ockham's theory is outside the scope F.O.M., and is not encouraged by the
editorial board.  You can find the paper anyway here


Ockham's theory is much more subtle than I had supposed, and contains a
powerful explanation of constructions like "John wants to buy six horses",
difficult to explain in modern logic.

May all of this work flourish forever.

Dean Buckner

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