Logic/syntax versus arithmetic

[Timothy Y. Chow]

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.

Tim