Re: Fwd: SUO Quo Vadis
John, some more questions.
> > D.M.Armstrong's Theory of Universals 1978 19.VI:
> >
> > "One hand washes another; both wash the rest of the body.
> > Perhaps the trickiest sort of case is that where a person
> > loves or hates himself. But even here genuine self-relation
> > seems avoidable. If a man loves himself, then it is not
> > that self-loving state which he loves, but other aspect
> > of himself. It is possible that he should love the self-
> > loving state, but this seems to demand a new, second-
> > order, loving state which is distinct from the original one."
>
> That's an interesting solution to the apparent paradox of
> loving and hating being antonyms. You could also solve that
> problem by saying that loving and hating are not true antonyms.
> In any case, that's irrelevant to the structure of the lattice.
I can't see the connection with antonyms. You have a category
called Theory inside a hierarchy of theories. That category
cannot describe all theories, because then it would describe
itself, which causes a vicious infinite regress. What does
the category called Theory then describe in your generalization
hierarchy of theories?
> > BOT describes a contradiction, a round square.
>
> Yes. It includes all possible contradictions. So what?
The idea of TOP containing all possible truths and BOT
containing all possible contradictions is clear, but the
actual definition of an absurd BOT is impossible.
When category A has a subcategory B, then there is a certain
relation between A and B. This relation has to be specified
if we want to have a formal ontology. An example of the
specification is e.g. memberOf; a subcategory has to be a
member of its supercategory, like: {{a}} > {a} > a. What sort
of a rule do you impose on the subcategoryOf relation to reach
BOT that describes emptiness, and BOT that describes absurdity?
Please provide an example. That rule has to be totally different
from the rules that all other categories follow.
If you try to create the subcategoryOf relation, it leads to
having categories for different sorts of contradictions. There
will be a whole hierarchy of determinate contradictions. A
determinate contradiction is such that the type of a
contradiction is known. BOT would then describe the
contradictions between different determinate contradictions.
This would continue possibly indefinitely.
When we force a lattice within an actual domain ontology, then
we have to separate the three meanings of BOT: absurdity,
emptiness, and a normal category. Imagine a lattice that
currently has BOT as a normal category. Then, one category is
taken along that causes BOT to describe emptiness, but yet not
absurdity. Then another category is taken along that is not
comparable with the others. Now BOT describes only absurdity.
We have to explicitly state the meaning of BOT in these three
cases. Instead of that we can just have the normal categories.
What benefit does it give to have this sort of BOT? Why do you
want to keep it? BOT that describes absurdity is like the
vermiform appendix: totally useless, but in many cases very
harmful; slightly amusing, but mostly painful.
> > ... but in that case [a plan for something that doesn't yet
> > exist] the category would describe something that exists inside
> > the brains of a human being. And if that person dies or forgets
> > what the category describes, the category would be like a circle
> > in sand in some deserted island.
>
> So what? What's wrong anything on a deserted island? Unlike
> Bishop Berkeley, I believe that a tree that falls when nobody
> is around to hear it still makes exactly the same vibration
> in the air.
So do I, but according to the pragmatic program only those things
that have utility to the agent should be considered useful. Is
this a correct notion? Some part of the plan, like a drawing,
might be interpreted to describe totally different things to
other persons than the original planner intended. I know that
you know this. What about this formulation: when a being realizes
a category, the category describes something that exists. If
no being currently realizes a category, then the category
describes a set of things 'potentially' realizable by an agent.
A category describes different things for different persons in
different contexts. This reminds of Peirce's 123. An example:
TOP
/ \
Circle Square
When Circle=1, Square=2, and TOP=3, TOP would describe e.g. Form.
When Circle=2, Square=1, and TOP=3, TOP would describe e.g. Form.
Form
/ \
Circle Square
\ /
BOT
When Circle=1, Square=2, and BOT=3, BOT would describe contradiction
or emptiness.
When Circle=2, Square=1, and BOT=3, BOT would describe contradiction
or emptiness.
Furnitures
/ \
Circle Square
When Circle=1, Furnitures=2, 3 would describe e.g. furnitures that
have the form of a circle, i.e., the meaning of Circle in the
context of furnitures. 3 remains the same when 1 and 2 are
swapped.
What do you think about this mapping of 123 with category hierarchy?
Avril
There are two things that I disclude from ontology.
The first is that which does not exist.
The second is that about which it is impossible to talk.