Re: Category without objects

[Tadeusz Litak <tadeusz.litak@gmail.com>]

On 11/03/15 05:20, Vaughan Pratt wrote:
>
>
> Quine wrote "Word and Object".  Reasoning analogously as above, what a
> category theorist would call an object, Quine would call a word.


There is actually a (perhaps) more direct reference to Quine in the context of this discussion.

In the entry "Mathematosis" of his "Quiddities: An Intermittently Philosophical Dictionary", he wrote:

> There has been a tendency of late to sacrifice simplicity at the
> altar of model theory. For instance we find a group defined as
> an ordered pair (A, f) where A is a class and f is a FUNCTION,
> q.v., whose arguments and values comprise A and fulfill certain
> axioms that I shall not pause over. This dragging in of a class
> A, and therewith of an ordered pair, is a gratuitous conformity
> to model-theoretic fashion; the function f is enough by itself,
> since A is definable in terms of f as the class of its arguments
> and values.

One can see here an analogy to the redundancy of objects in category theory.

However, the entry "Function" in the same book makes it clear that Quine thinks of functions in entirely set-theoretic
terms: as collections of ordered pairs.

t.


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