Thread: CL:http://permalink.gmane.org/gmane.science.philosophy.peirce/15739 CL:http://permalink.gmane.org/gmane.science.philosophy.peirce/15776
Cathy, List, Frederik's thesis went off the track for me in one of the early chapters -- I've been meaning to do the good scholarly thing and articulate exactly where and why, but other business pre-occupies, so let me just say what I have come to opine from my own study of Peirce's information theory in relation to his theory of inquiry. Peirce's concept of information generalizes Shannon's to the degree that triadic sign relations generalize dyadic cause-effect notions of information transmission, but Peircean information is not substantially different in that it makes sense only in a context of prior uncertainty, the "irritation of doubt" that drives inquiry, and its measure is based on the power of signs in a given sign relation to reduce the uncertainty of an interpreter about an object, if we may use the sop of agent-talk. In that view, signs bear information on account of their place in a specified sign relation, and it is a matter of secondary concern whether the sign is a picture, proposition, term, or something else entirely, like the state of a computer system. Regards, Jon 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 <cl...@waikato.ac.nz> 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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