FOM: Re: three challenges for McLarty

Kanovei kanovei at
Mon Jan 26 12:18:55 EST 1998

[especially for Harvey and Steve]

>Challenge 1. McLarty needs to explicitly state fully formal axioms of
>topos theory plus natural number object etc.  These axioms are to be[...]

Steve Awodey:
>There's an obvious question of what is meant by "simple" here - perhaps
>"familiar-looking to set theorists"?  Moreover, there is the question, what
>the point of such a comparison is supposed to be.  That is, what is shown
>by determining certain axioms to be more "simple", in one sense or another?
>For example, the topos axioms are essentially algebraic, a condition that
>can arguably be interpreted as a kind of logical simplicity (and is so
>regarded by category theorists).  By contrast, ZFC does not have this
>property (not even close).  Now what is this supposed to show?

Look how smartly S. A. escapes answering the main point: 
to explicitly state ... . 

A Middle - East colleague of myself once told me some  
main principles of negotiations at Eastern bazaar, 
which amount to the following 
never hurry to say yes never hurry to say no 
never say something that can be an immoveble target 
in general try to get the opposite side nervous 

Doesn't it seem that the discussion goes this way ? 

Vladimir Kanovei

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