On Jan 30, 2009, at 3:56 PM, Len Yabloko wrote: (01)
> Mitch,
>
>> 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.
>
> Reasoning and transformations are closely related to each other,
> even in strict mathematical sense- I believe. (02)
Its hard to say whether this is true or not until you say what you
mean more precisely what you mean. There are certainly connections
between logics and CT, which is hardly surprising given that CT is
such a very general theory. One connection is that formal reasoning
systems - more exactly, formal proof systems - form a natural category
in which the sentences are the objects and the proofs are the
morphisms: a proof with A as premis and B as conclusion is the
'mapping' from A to B. (Exercise for the reader: show that this is a
category. You have to show that the morphism composition is
associative and that there is an identity morphism. Hint: its so
simple you might find it hard to see that there is anything to do.)
So that is one relationship between reasoning and transformations,
yes. Is that the one you had in mind?
>
>
>>
>> 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.
>>
>
> It is not that difficult to extract since 'morphisms' are at the
> very definition of Category. What is difficult is to understand what
> it is 'appropriate direction' for each. I dawned on me long time ago
> that both complement each other (03)
Can you elaborate on this insight? In what sense do they complement
each other? (04)
> , but I still can't figure out why everybody insists on keeping them
> separate (and seemingly as far from each other as possible). (05)
They clearly are separate. They are different topics, with different
motivations and different methods and topics of interest. It isn't at
all remarkable that they are separate. They do have connections, cf.
the above, which have of course been thoroughly explored. (06)
> What am I missing?
>
>>
>>> 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 business transactions.
>>
>> 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.
>>
>
> I always thought that you don't need to be a specialist to apply
> someone else specialty to your work. Isn't it the job of specialist
> to make it possible? (07)
No. The job of the specialist is to specialize. :-) (08)
Pat (09)
> (010)
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