SUO: Topic :> Definition Of Type Operators [<:] and [:>]
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Topic :> Type Operators. <JA, 06 Dec 2003, 09>
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Doug, Richard,
You raise some questions that nudge me over my doorstep
a bit ahead of myself, a circumstunce that is even less
graceful by way of exit than letting your door boot you
out of the house. But I will let the world take a spin
or two, as it can hardly do it without my leave, giving
Yang Zhanmin an adequate time to respond in more detail.
The labors of ground breaking and home furnishing, from
drilling down to the symbolic water table to tacking in
a plush enough carpet of syntax to begin inviting a few
semiotic and pragmatic friends over for the housewarmer,
well, all of that is taking far more time than I had in
mind initially to finish the first storey of my A-frame.
In the mean time, I'll take this as an opportune moment
to explain some things about the relational symbol [:>]
that I've been taking in passing, as letters of transit,
between supertopics and their subtopics, to put it very
roughly, as befits the transitory stage of our campaign.
Like most asymmetric signs of asymmetric relations, the
so-called 'Type Of' or 'Type Over' symbol [:>] pairs up
with the converse 'Of Type' or 'Under Type' symbol [<:].
I think of these two symbols as "Narrative Involvement"
or "Indicative Relation" symbols. In a very rough way,
to observe X :> Y is to find that a story, a narrative,
or a piece of information about X involves the similar
sorts of indications about Y.
I was just getting ready to introduce Peirce's formula
for the relation of what he called Information to what
he called Comprehension times what he called Extension:
Information = Comprehension x Extension
I call this the ICE formula. Peirce explains it here:
| We must therefore modify the law of
| the inverse proportionality of
| extension and comprehension
| and instead of writing
|
| Extension x Comprehension = Constant
|
| which crudely expresses the fact
| that the greater the extension the
| less the comprehension, we must write
|
| Extension x Comprehension = Information
|
| which means that when the information
| is increased there is an increase of
| either extension or comprehension
| without any diminution of the
| other of these quantities.
|
| Now, ladies and gentlemen, as it is true that
| every increase of our knowledge is an increase
| in the information of a term -- that is, is an
| addition to the number of terms equivalent to
| that term -- so it is also true that the first
| step in the knowledge of a thing, the first
| framing of a term, is also the origin of the
| information of that term because it gives the
| first term equivalent to that term. I here
| announce the great and fundamental secret
| of the logic of science. There is no term,
| properly so called, which is entirely destitute
| of information, of equivalent terms. The moment
| an expression acquires sufficient comprehension
| to determine its extension, it already has more
| than enough to do so.
|
| CSP, CE 1, page 465.
|
| Charles Sanders Peirce,
|"The Logic of Science, or, Induction and Hypothesis",
| Lowell Institute Lectures of 1866, pages 357-504 in:
|
|'Writings of Charles S. Peirce: A Chronological Edition',
|'Volume 1, 1857-1866', Peirce Edition Project,
| Indiana University Press, Bloomington, IN, 1982.
Let that suffice unto today ...
Jon Awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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