One take on category theory contrasted with set theory that I read
somewhere was that set theory lets you enumerate members, while category
theory lets you talk about the social lives of those members. Don't
recall where I read that. (01)
Mitch Harris wrote:
> On Fri, Jan 30, 2009 at 12:36 PM, Len Yabloko <lenya@xxxxxxxxxxxxx> wrote:
>> my impression of CT remains to be as of an attempt to make abstract
>reasoning in general (not only mathematical form of it) more precise.
> If anything, the executive summaries of logic and category theory are:
> logic is the study of reasoning.
> category theory is the study of transformations.
> Sure a gross oversimplification, but I think in the appropriate
> direction for each, and it allows meaningful distinction and
> comparison. It might be difficult to extract the above from wikipedia
> or other easy online sources, but still it's a start.
>> I believe this objective to be a paramount to making it useful beyond
>calculation and in the real of reasoning. If I am wrong and CT is not
>attempting to do that, then some other theory should. And my observation is
>that neither classical Logic nor Ontology as discipline are adequate to this
>goal if they can't "nail down' the identity.
> There's all sorts of discussion within the ontology community about
> identity. Whether the unique name assumption (UNA) holds, inferring
> subsumption of one concept by another.
>> Again, I not talking about absolute and universal identity (I don't know
>what it is), but about sufficient level of identification required for
> If you're concerned that a particular formalism might be inappropriate
> for business transactions, then CT is definitely it. Even
> well-educated and, separately, intelligent people have difficulties
> with even boolean logic.
>>> No mathematical theory, category theory or anything else, is magic.
>>> You have to decide which aspects of the world to represent in the
>>> mathematics: your size and weight or your DNA and fingerprints.
>> I don't see a big difference between what mathematicians and magicians do -
>it is all matter of talent and imagination.
> There's what magicians do and then there's magic. There's no magic.
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