Jerry, list, Well, this turned out longer than I anticipated.
You wrote: BTW, this is just another example of CSP's usage of his chemical knowledge > to ground his logical explorations. Yes, I was surprised some such reference to chemistry and its importance in influencing Peirce's work wasn't in your first post; I suppose you were winding up for the pitch. There is a very decidedly chemistry-centric direction that your posts take here on Peirce-L. I think it's important to notice that I'm not a chemistry whiz, but that I will do my best to keep up. For what it's worth, I would like to point out that I see no reason to deny your claims about the important influence of developments in chemistry on Peirce's work in logic. I just don't always see the relevance in a given discourse. What is the information content of a symbol (as a diagram, icon, index or > any term) if the change of the sign does not indicate a change in > information? > > Recent extension of the discussion point out that both "breadth" and > "depth" can be viewed as changes in the distinctiveness of the sign (or > information content.) This question needs some clarification before it can be answered. When you say "What is the information content of a symbol (as a diagram, icon, index, or any term)," it is unclear whether you mean for diagrams, icons, indices, and any term to be understood as a symbol. Strictly speaking, icons and indices cannot be symbols, a diagram is a type of icon, and terms, well, that depends on how one means term; in particular, it matters if one envisions dicisigns as involving terms (rhemes?), or whether one restricts terms to propositions proper, and then specifically the predicate term. My guess is that you understand all of this, but your wording was vague, and I wanted to be clear that we are specifically talking about symbols. If you want to include diagrams, icons, indices, and any term, then it is important to note that icons only serve content for information; indices also serve content for information, and some types of indices also convey information--i.e., dicent indices. But they do not possess information in the sense that a symbol does. Information is the ongoing relating of informed breadth and informed depth relative to one another, which is possible only in a symbol. I would also like to point out that "Upon Logical Comprehension and Extension" (ULCE) only deals with terms, not propositions or arguments. I seem to recall that in his later years Peirce had specified what information would be like for propositions and arguments, but after looking around a bit, I can't find a text to cite and I don't exactly recall how it worked, only that it didn't work the same way for them as for terms. (At least in the case of propositions, I think it had to do with the possible cases in which a given proposition was applied or true, or followed validly, or some such thing.) So if we talk about the information content of a symbol, we must limit ourselves to terms. Moreover, it's not clear that the term in some sense contains anything, but rather the term's information relates to the synthetic propositions, or facts, in which it participates as either subject or predicate. So the information of a term-symbol is something that the term has relative to other terms given in synthetic propositions that collectively inform what Peirce referred to as the state of information. This idea of the state of information is important to keep in mind. Consider how in ULEC Peirce treats of the idea of distinctness (in a footnote following the quote he references the introduction of the idea of distinctness to the work of Scotus): If *T* be a term which is predicable only of *S'*, *S''*, and *S'''*, then > the *S'*'s, the *S''*'s, and the *S'''*'s will constitute the informed > breadth of *T.* If at the same time, *S'* and *S''* are the subjects of > which alone another term *T'* can be predicated, and if it is not known > that all *S'''*'s are either *S'* or *S''*, then *T *is said to have a > greater informed breadth than *T'*. If the *S'''*'s are known not to be > all among the *S'*'s and *S''*'s, this excess of breadth may be termed > *certain,* and, if this is not known, it may be termed *doubtful.* If > there are known to be *S'''*'s, not known to be *S'*'s or *S''*'s, *T* is > said to have a greater *actual* breadth than *T'*;but if no *S'''*'s are > known except such are known to be *S'*'s, and *S''*'s (though there may > be others), *T* is said to have a greater *potential* breadth than *T'*. > If *T* and *T'* are conceptions in different minds, or in different > states of the same mind, and it is known to the mind which conceives *T* that > every *S'''* is either *S''* or *S'*, then *T* is said to be more *extensively > distinct* than *T'.* > And then The depth, like the breadth, may be certain or doubtful, actual or > potential, and there is a comprehensive distinctness corresponding to > extensive distinctness. > So extensive distinctness (distinctness in breadth) and comprehensive distinctness (distinctness in depth) have to do with there being two terms, say T and T', in a given state of information. The term T, identifying every S''' as either S'' or S', is more extensively distinct than T', because T' applies to S' and S'' like T, but does not identify S''' in its breadth as T does; T' simply doesn't account for any S''', because it is not predicated of any S'''. But if it did, it would be the term T, which is already understood by the mind. Even if T' came to be predicated of every S''', it would not add information. Instead, it would show itself as really being the term T, which is already known. So by comparison, we can see that one term would be more distinct than another. Peirce avers that all deductive inference is simply a matter of increasing distinctness of terms, in which there is an exchange between two terms, a sort of sharing of information already known. I submit that I think Peirce could have been clearer about this. He says in ULCE that deduction is easily understood in terms of the increase of distinctness in terms, and so does not need explanation, and simply moves on to induction and hypothesis. Personally, I wish he had explained deduction anyway. I might guess that somewhere along the way it is possible for two terms to be understood as turning out to be identical, and this might be what deduction ultimately aims at as a form of reasoning. But more likely, T and T' don't typically meet in deduction, and so won't become identified with each other, but we might compare T participating in a deduction that makes it more distinct, while T' remains less distinct because it is not involved in the deduction. Say, for example, that we have the term human being, and the term featherless biped. We know that both human being (T) and featherless biped (T') involve all cases of men (S') and all cases of women (S"). But human being also is predicated of all cases of animals that can learn to reason (S'"). It turns out that all the animals that can learn to reason (S'") are either men (S') or women (S"), so human being (T) now is more extensively distinct than featherless biped (T'), though it does not have greater actual breadth; but it does have a greater potential breadth, because it may turn out that some animals that can learn to reason may turn out to be neither man nor woman. For example, someone who is transgender. Now, moving on, you wrote: Thus, CSP used these advances in chemical abstractions to ground his > extension of information from "breadth and depth" to graphs, then alpha, > beta and gamma graphs. see: CP 4.510-511 for specific claims about the > rhetorical meaning of graph extensions and to compare with his work in the > 1860's. Is this what CSP is referring to when he writes, "dispatch > reasoning of a very intricate kind" and "utmost clarity and precision"? > Such terms as "depth" and "breadth" are crude by comparison. I looked at the paragraphs you referenced, but I'm not sure where the connection is to be found to which you are pointing. My guess is that you are suggesting, as you say, that "Such terms as 'depth' and 'breadth' are crude by comparison." I'm not sure they are quite so crude as you represent them to be. Peirce is in fact pointing out in the second paragraph that not only the alpha, but also the beta graphs are incapable of treating of qualities or relations treated as subjects. Not being able to reason about qualities, nor about relations treated as subjects, means that the alpha and beta graphs are deficient insofar as they cannot fully account for logical depth and logical breadth, because they fall short in the analysis of predicates and subjects. Supposing they were to become accurately represented in the gamma graphs, the motivation for continuing to develop the gamma graphs is just because of these noted deficiencies, which could only be observed as deficiencies because we have a theory of logical quantity and information that says that such things need to be given an accurate account in the theory of inference and reasoning. The way I see it, the conceptions of breadth and depth are not so much crude as they are basic, forming as they do the basic elements from which classes of terms are formed and differentiated from one another, and in some cases eventually identified with one another, in part or in whole. My own thought is that as Peirce continued to develop his theory of signs and sign classes, the conceptions of breadth and depth took on nuances that Peirce didn't typically notice in an explicit way. So for instance we know from ULCE that not only is there a distinction between depth and breadth, but that there is actual and potential, certain and doubtful, etc. as distinctions that can modify the significance of some received breadth or depth. With more refined sign classification, it may very well be the case that more modifiers can be applied to differentiate between kinds of breadth and depth. Now what I have said about information above does not, I think, lessen at all the significance of graphical logic. I would certainly consider myself among those who believe that Peirce's graphical logic reaches the height of representation of logical inference and reasoning. I simply wish to point out that, rather than replace or supplant the importance of breadth and depth in the theory of information, graphical logic can be seen to incorporate the conceptions of breadth and depth in their construction. Well, at least potentially so in the gamma graphs. I remain optimistic about the project. Finally, a word on this: The assertions of CSP are primitive relative to the modern state of > information theory, chemical notation and mathematics and hence I could not > accept them as meaningful in modern terminology of the natural sciences. I'm not entirely sure there is a correspondence between what Peirce's theory of information aims to explain and what 'modern' information theory aims to explain; seems to me that there could be a case of two ships sailing different seas. But maybe Jon Awbrey will prove me wrong. As for chemical notation, I'm not even sure how to compare. But as to mathematics, I don't know how you could imagine this to be the case. Set theory, as far as I know, is still used and studied. But set theory is simply a theory of elements, and what Peirce offers is a competing account, and I'm given to understand a viable one. See John Sowa's book Knowledge Representation, ch.2 on Ontology, for a clear account of the differences between set theory, mereology, and Peirce's theory of collections. Franklin On Sat, Nov 7, 2015 at 2:42 PM, Jerry LR Chandler <[email protected]> wrote: > Franklin: > > I fear that you missed the essential element of my post. > Let's go back to the assertion that motivated it: > > In any case, change in distinctness is not change in information. >> >> > Your response fails to address the substantial notion of the meaning of > the symbol "distinctness". > > So, allow me to ask a question: > > What is the information content of a symbol (as a diagram, icon, index or > any term) if the change of the sign does not indicate a change in > information? > > Recent extension of the discussion point out that both "breadth" and > "depth" can be viewed as changes in the distinctiveness of the sign (or > information content.) > > I recall clearly my own puzzlement at reading this paper in the first > decade of this century. The assertions of CSP are primitive relative to > the modern state of information theory, chemical notation and mathematics > and hence I could not accept them as meaningful in modern terminology of > the natural sciences. > > More recently, I have accepted the fact that I must follow CSP's mental > development from period to period is within the texts I have available to > me. A difficult but necessary chore. In this case, CSP extends these very > simple notions of information to his constructions of logical diagrams in > the 1890's and later, after he developed his remarkable views on relational > logics. > > Historically, the parallelism between his texts on logic and logic of > relations overlap with the corresponding development of chemical diagrams. > The deep changes in chemical notation that occurred in this period were a > consequence of Pasteur's separation of the optical isomers of the tartaric > acid and the explanation for these isomers in terms of three-dimension > spatial diagrams with different arrangements of the SAME parts into > different wholes (van't Hoff and LaBel, ca 1880.) (These two advancements > in chemical inquiry dramatically changed the symbolization and signage for > chemistry and propelled it toward its modern form. The morphism of chemical > notation from one based on mass to its current form which is dominated by > electrical particles in space is continuing even today in molecular > biology, eg, DNA as a double helix) > > Thus, CSP used these advances in chemical abstractions to ground his > extension of information from "breadth and depth" to graphs, then alpha, > beta and gamma graphs. see: CP 4.510-511 for specific claims about the > rhetorical meaning of graph extensions and to compare with his work in the > 1860's. Is this what CSP is referring to when he writes, "dispatch > reasoning of a very intricate kind" and "utmost clarity and precision"? > Such terms as "depth" and "breadth" are crude by comparison. > > See:The Philosophical Status of Diagrams (Mark Greaves), CSLI, 2002 for a > lucid and compelling argument on the nature of CSP's argument and it's > relation to modern logic. > > BTW, this is just another example of CSP's usage of his chemical knowledge > to ground his logical explorations. > > > Cheers > > Jerry > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to > [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L > but to [email protected] with the line "UNSubscribe PEIRCE-L" in the > BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm > . > > > > > >
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