FOM: the categorical approach to logic wtait at
Wed Apr 1 10:54:38 EST 1998

I do not want to be involved in a discussion of category thoeretical vs 
set theoretical foundations. I indicated earlier that no one has yet 
convinced me that the issue is more than one essentially of which among 
possible languages to use. But Steve's reply to Walter Felsher contains 
an example of precisely the kind of thing that is driving many of us up 
the wall:

>Much to my surprise, even with this simple example, I ran into
>difficulty because one of the category theorists denied the underlying
>algebraic facts, e.g. the well known fact that Boolean algebras and
>Boolean rings are not "the same", because they have different
>signatures.  Perhaps we should learn to expect this kind of difficulty
>whenever we attempt to communicate with category theorists.
>Nevertheless, I still hold out hope that the attempt to communicate
>with them will be worth while.

I would agree that I would not say that a BA and the corresponding BR are 
the ``same''. But rather than argue that terminological point, I would 
consider what it is that is being expressed by calling them the same. 
That is what Walter did in his posting and it is what other people have 
tried to do, although in some cases using the same contentious sort of 
rhetoric that Steve is using---as though one side has the `right' meaning 
of `same' and the other lives in sin. 

I must say: thank god for email. If this utterly pointless debate were 
conducted on paper, we would have lost the remainder of Earth's forests.

Bill Tait

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