Picking up again where I left off...
The logical tradition that Peirce was responding to with his piece "Logical
Extension and Comprehension" was basically a 'term logic', according to
which this rough formula held:
Breadth x Depth = k (where k is some constant)
This implies: the larger the extension (breadth), the smaller the intension
(depth). This formula seems to work for classic terms such as "blue", which
covers more things but is correspondingly less precise than, say, "baby
blue". Or "vehicle" which covers more things but is less precise than, say
"nuclear submarine".
However, Peirce's shift from terms to propositions as a basic analysis of
meaning allows him to question some of this framework. A proposition is now
not a simple 'multiplication' of two 'similar quantities'. A proposition
requires two separate functionalities. The part which provides the
extension (the subject) functions indexically, and the part which provides
the intension (the predicate) functions iconically.
Stjernfelt points out that, under this framework, "far from being a
constant, Breadth x Depth gives a measure of the amount of information
inherent in a proposition" (which can be higher or lower). He notes that
Peirce still retained this idea 25 years later in Kaina Stoicheia.
*QUESTIONS: In what sense, and to what degree might this 'information' be
measured? (If not in some absolute sense, then perhaps relatively, between
propositions?) Doesn't the very notion of measuring this value conflict
with Peirce's contrite fallibilism, which holds that what a given term will
come to mean to us is not something that can be decided in advance of
scientific inquiry? In other words, scientific terms can hold a great deal
of implicit information as well as the explicit information that scientists
are working with at a given time. *
Probably in the light of this kind of worry, Peirce sets himself the task
to trying to analytically define what is a 'natural class'. For natural
classes are precisely those which bear future inquiry, yielding up implicit
information to be made explicit. As Peirce says, think how much more
"electricity" means now than in the days of Dalton. Whereas an a
non-natural ("artificial") class - has nothing more to tell us apart from
the way it was already defined. Peirce gives the example of 'cow' as a
natural class and 'red cow' as artificial.
To this end, he draws two sets of mysterious diagrams, as a kind of
experiment, possibly unfinished. This seems to be an experiment in defining
"properties" or "marks" in the most minimal way possible, then varying them
in the most minimal ways possible, to try to decide what groupings our
scientific inquirer might decide are 'natural'. This is not a simple matter
of making a class for each property, as we do not have a distinction
between natural and artificial classes.
*QUESTION: How does Peirce attempt to draw the distinction, in the two
cases Frederik catalogues?*
List: if you tell me what you think then I will tell you what I think.
Cheers, Cathy
On Tue, Feb 24, 2015 at 10:12 PM, Catherine Legg <[email protected]>
wrote:
> Sincere apologies to everyone for the delay in posting. My life has
> been a bit chaotic lately.
>
> First of all I want to say how very much I have been enjoying reading
> Frederik's book. It combines mastery of the intricacies of Peirce's
> semeiotic, early and late (and we all know what a challenge that is),
> with a bold march out into contemporary mainstream philosophy of
> biology and cognitive science, flying the flag of Peircean ideas. The
> book's powerful organising idea of the dicisign's self-referential
> 'double structure' also has the capacity to blast so much cavilling,
> insufficient contemporary nominalistic philosophy of language out of
> the water! (Sorry for the somewhat drenching metaphor).
>
> Chapter 9 is a curious excursion on a very specific topic: Peirce's
> rationale for "the puzzling sheets containing 99 small
> drawings...which accompany MS 725." It seemed that Peirce was playing
> with these as a kind of experiment in breaking down the concept of a
> "natural class" to its minimal analytical components.
>
> In the background of this discussion is the topic of MS 725: Peirce's
> discussion of "Logical Extension and Comprehension" (presented as a
> talk in 1867). The tradition of logic contains a lot of discussion of
> this distinction (e.g. in Port-Royal Logic, in Mill, in William
> Hamilton), where 'extension' referred to 'things picked out', or the
> reference of a term, and 'intension' to the ideas evoked, or meaning
> of a term. So the subjects of propositions seem more suited to express
> extension and the predicates of propositions seem more suited to
> express intension. Although strictly speaking, in the proposition "The
> cat is on the mat", the phrase 'the cat' does have some intension
> insofar as certain ideas about cats pop into my mind when I hear it,
> and the phrase 'is on the mat' des have some extension insofar as we
> might think there is some (large) set of things that are on mats in
> this world of ours.
>
> The tradition was to define an inverse proportionality between
> extension and intension, such that by reducing a term's extension we
> increase its intension, and vice versa. So if I change "the cat" to
> "the brown cat" in the proposition above, I have a term that picks out
> fewer things but has a more specific meaning.
>
> But we will see Peirce challenging this simple formula.
>
> Coincidentally I published a paper on this talk of Peirce's in the
> Transaction a long time back, connecting it up with discussions of
> extensionality and intenionality in C20th philosophy. It's called
> "Extension, Intension and Dormitive Virtue". It was just when I was
> starting out as a scholar and is not a terribly elegant paper. But if
> anyone is interested:
> http://researchcommons.waikato.ac.nz/bitstream/handle/10289/2811
>
> I have been wisely advised by our esteemed Peirce-L moderators not to
> try to post too much on this chapter in a single go, so I will leave
> it there for now, and return anon!
>
> Cheers, Cathy
>
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