Logic/syntax versus arithmetic
Timothy Y. Chow
tchow at math.princeton.edu
Fri Feb 14 11:01:16 EST 2020
On Fri, 14 Feb 2020, Mikhail Katz wrote:
> I read Leng's piece and it left me a bit puzzled, as well. Possibly
> Leng's problem is with viewing 2+3=5 not as a metalanguage statement but
> rather as a statement in the object language, with an apparent
> implication of infinitary ontology behind it. Perhaps logical rules of
> inference are more defensible (according to Leng) because they are
> surveyable at the metalanguage level. Perhaps what Leng finds
> objectionable is the mathematician's facile identification of
> metalanguage counting numbers with "the" natural numbers (at the level
> of the object language).
This could be, but Leng's emphasis on nominalism (rather than, say,
anti-infinity arguments) makes me doubt that this is what she means.
I did try to email Leng directly, but have not received a response. (It
may be that I got the email address wrong or that my message was trapped
by a spam filter.)
By the way, the full title of Leng's article is, "Does 2+3=5? In Defence
of a Near Absurdity" and it first appeared in the Mathematical
Intelligencer, Volume 40, Number 1, 2018, pages 14-17.
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