FOM: defining ``mathematics''

Vaughan Pratt pratt at CS.Stanford.EDU
Wed Dec 22 00:03:43 EST 1999

Simpson Tue, 21 Dec 1999 19:07:24 -0500
(On Buss Tue Dec 07 00:51:16 1999)
>Thus mathematics, like every other science, is to be defined as the
>study of a specific subject matter.  To delimit that subject matter
>may be difficult, but as a first attempt let's call it ``quantity''.
>In other words, I am suggesting to define mathematics as the science
>of quantity.

"Theory" might work even better here than "quantity."  And rather than
being a science I would say that it was a limit: mathematics is the
limit of theory.  The more theoretical a scientist becomes, the more
mathematical the subject matter.

Logic is the glue that binds propositions coherently, whether they be
facts, opinions, beliefs, judgments, misunderstandings, propaganda,
or statistics.

Logic and mathematics are two sides of the same coin.  Logic does for
propositions and inferences what mathematics does dually for objects
and constructions.

I take Sam's position to be entirely consistent with this, at least for
logic and mathematics individually if not as a complementary couple.

Vaughan Pratt

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