Cathy, list,
You wrote,
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.
[End quote]
Presumably the information to be quantified is not that of what a given
term will come to mean to us, but rather that of what it means to us now
- the difference between making our ideas true, as Peirce put it, and
making our ideas clear. What it means to us now is what we now conceive
to be its practical bearing in general on conduct.
I have to admit I have little to say about how to quantify
comprehension, denotation, information in Peirce's sense. I did find
this passage:
Writings 1:342-343, Logic Notebook Dec. 15, 1865
http://pds.lib.harvard.edu/pds/view/15255301?n=28&imagesize=600&jp2Res=0.25&printThumbnails=true
In the formula
Extension × Intension = Implication
we may have the values
(1) 0 × 0 = 0
(2) 0 × n = 0
(3) 0 × ∞ = 0
(4) 0 × ∞ = n
(5) 0 × ∞ = ∞
(6) n × 0 = 0
(7) n × n = n
(8) n × ∞ = ∞
(9) ∞ × 0 = 0
(10) ∞ × 0 = n
(11) ∞ × 0 = ∞
(12) ∞ × n = ∞
(13) ∞ × ∞ = ∞
(7) will be the case with any ordinary symbol.
(4) is the ordinary nothing.
(10) the ordinary being.
These are the cases when Implication is n. Now for those where it is 0.
(6) is the case of a sign, (2) of a copy.
(1) would be a sign of nothing or a copy of being which are
undetermined to be representations.
(9) would be being supposing it were not known to be, or being
considered abstractly of the fact that it is.
(3) would be nothing abstracting from the fact that there is
anything so that its opposition is taken away.
A being which isn't, would be a nothing which is unopposed to
anything; hence being abstracted from the fact that it is is
abstracted from all that makes it differ from nothing abstracted
from its opposition and vice versa.
We will now take up the cases where the implication = ∞. (12) is
being of which some determinate quality is supposed to be known.
(8) is a contradiction it being implied that it exists.
(13) is being which is supposed to have all attributes.
(11) would purport to be a complete list of all beings.
(5) would purport to be a complete conjunction of all attributes.
[End quote]
You wrote,
QUESTION: How does Peirce attempt to draw the distinction, in the
two cases Frederik catalogues?
[End quote]
I can't think of anything to say about this either, though the question
of natural vs. artificial kinds is quite interesting to me. Similar
question in mathematics: Are primes a natural kind? What about the class
of functions that share a certain first derivative? The class of pairs
of integers that sum to a certain integer?
You wrote,
List: if you tell me what you think then I will tell you what I think.
[End quote]
I haven't done too well, nobody else has replied, I guess you ask tough
questions, but anyway at this point I'm interested in hearing what you
think.
Best, Ben
On 3/3/2015 2:41 PM, Catherine Legg wrote:
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 wrote:
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