ONT Re: Extension x Comprehension = Information
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Note 83
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TG = Tom Gollier
TG: We do seem to be coming full circle, but let me try an example,
the legal case (I can look it up the name if you're interested)
of whether steamboat accomodations are more like hotels or trains
when it came to the provider's liability. We have this category,
"travel accomodations", containing "hotel rooms" and "train berths",
and we're adding a new element, "steamboat suites" to its extension.
It would, indeed, appear that this increase in *extension* will lead
to a corresponding decrease in *intension*. Unless: (1) what is common
to "hotel rooms" and "train berths" is already meager enough that the
addition of "steamboat suites" restricts it no further. Or: (2) the
*information* involved increases with the addition to the extension
so that the intension does not decrease or does not decrease as much.
Yikes! If this is from Peirce, then I will eventually have to look at it,
but right at the moment I have all the trouble I can handle just trying to
work through the examples from 1865-1866. Generally speaking, it has been
no help at all reading other accounts of the issue, past or present, since
they all just take the reciprocity for granted, so far as I have seen yet.
TG: On the one hand, this kind of analysis seems to commit a fallacy Peirce
himself later noted with regard to:
| Tarde, who is one of the well-known type of Frenchmen who copy
| the phraseology of mathematics, as if that possessed, in itself,
| a secret virtue of rendering vague ideas precise.
Speaking of extension and intension being *inversely proportional*
and *adding up* to information seems analogous to Tarde's assertion
that imitation increases an idea's social existence *geometrically*.
| Thus, we are told that 'impulsive social action tends to extend and
| to intensify in a geometrical progression.' Mathematicians, we are
| aware, speak of one variable increasing geometrically, while another
| increases arithmetically; but what (if anything) may be meant by
| saying that a quantity varies in geometrical progression without
| reference to any second quantity, we must confess transcends our
| powers to divine. Nor do we see that imitation can be so measured
| that it is worth while to attempt to say what the mathematical nature
| of the function is that connects it with another quantity. For the
| present, such ideas seem irrelevant. At any rate, the meaningless
| expression must excuse our suspecting that there is nothing more
| valuable beneath it than the simple remark that where there is
| a tendency to imitate, the imitation of imitations will multiply
| imitations." ["Giddings's Inductive Sociology," 1902 PW v3:69-70]
TG: On the other hand, there is the conceptual analysis by which the case
was actually settled -— the making of the new distinction within the
concept of "travel lodging" and the drawing of appropriate conclusions
in various arguments —- with which the extension of the concept's
application and the intensions of its conclusions would seem to go
hand in hand. This analysis of the example is not only less abstract,
not hinging on a rhematic system of pure possibilities; but it also
includes the rhematic (and propositional) considerations of those prior
levels within itself. And Peirce, for all his mathematical orientation,
seems to have demanded such a three-level analysis early on?
I guess I don't see what you are saying.
The early studies that I am looking at
are already deep into 3-adic analysis,
and what Peirce says there is very new,
even today.
TG: Meanwhile, I have to say I'm extremely sceptical of any attempt to
define "information" abstractly in terms of extension and intension,
as the term is so intimately intertwined these days with the attempt
to get by without any concepts at all, at least as anything different
from rhemes, as well as without any systematization of those rhemes
which amounts to more than alphabetizing a lexicon.
Granted, but what does the contemporary Information Agers'
miscomprehension of their own history have to with Peirce?
Jon Awbrey
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