Gary R., Thanks for the reply. I don't have any brilliant answers at this point, but there seems to be an immense amount of confusion surrounding Peirce's theory of the modes of inference and the order of inquiry. I learned at the Centennial Conference that Professor Stjernfelt associates the two forms of deduction with secondness, and the three forms of induction with thirdness. For now, I will await his reply before offering any of my half-baked ideas on the relationship between these irreducible types of reasoning/stages of inquiry.
List, Please note that among other typos in my last posting, I misspelled the name of Irving Anellis, and I meant to say that the model-theoretic tradition's approach to language does **not** run up against prison-house of language problems (ineffability claims) given the possibilities of meta-languages. Yours, DH On Tue, Dec 16, 2014 at 7:19 PM, Gary Richmond <[email protected]> wrote: > > Douglas, lists, > > Thank you for this insightful post--you've clearly given considerable > thought to these matters. Because of time constraints, for now I'd like > only to respond to your question to Frederik at the conclusion of your post. > > DH: I would like to close by asking Professor Stjernfelt if he agrees with > Francesco Bellucci that the late Peirce saw diagrammatic reasoning > containing its own abductive and inductive phases. I look forward to any > questions or comments before we begin Chapter 8. > > > I too would be interested in Frederik's answer to this question. > Meanwhile, your question did make me think of a comment Peirce made in one > of the drafts of the 1903 Harvard *Lectures on Pragmatism* which may have > some, even if small, bearing on the answer to your question. > > I have occasionally referred to this draft (see note 3 to Lecture 5, > 276-7, in Patricia Turrisi's edition of the lectures) to show that Peirce > had changed his mind (and then changed it back again) as to whether > deduction should be associated with categorial 2ns or 3ns. Here I would > note that at the conclusion of this section of the draft lecture that he > comments that there were some opinions upon which he had *never* changed > his mind: > > One of these is that although Abductive and Inductive reasoning are > distinctly not reducible to Deductive reasoning, nor either to the other, > yet the *rationale *of Abduction and of Induction must itself be > Deductive. All my reflections and self-criticisms have only served to > strengthen me in this opinion. But if this be so, to state wherein the > validity of mathematical reasoning consists is to state the ultimate ground > on which any reasoning must rest (Turrisi, 277). > > > Best, > > Gary R > > [image: Gary Richmond] > > *Gary Richmond* > *Philosophy and Critical Thinking* > *Communication Studies* > *LaGuardia College of the City University of New York* > *C 745* > *718 482-5690 <718%20482-5690>* > > On Tue, Dec 16, 2014 at 4:48 PM, Douglas Hare <[email protected]> > wrote: > >> 7.5 Diagrams in Linguistics >> >> In the final section of Chapter 7, language emerges from the Dicisign >> doctrine as diagrammatical tool combining “loosely coupled parts” in order >> to serve as a representing and reasoning organ with potentially “universal” >> application. Using the premiss that diagrams are responsible for all >> deductive reasoning, we can then produce an account of how ordinary >> language possesses 'diagrammaticity' at the very least in its ability to >> encode logical inferences in the form of syllogisms. But if the difference >> between language and pictorial representations is a diagrammatical matter >> of degree (measure of iconicity), not a difference of kind, then the >> Herculean tasks of reinterpreting the “levels” of natural language into >> their diagrammatic forms and figuring out how to measure gradations within >> natural language as well as with other iconic forms of signification appear >> before us. Later chapters might clarify why Peirce's Existential Graphs >> remain a valuable instrument for both ostensibly Sisyphean endeavors. But >> ignoring the Alpha and Beta Graphs for now, many recent cognitive linguists >> cited by the author seem to agree that the logical connectors of >> propositional logic, the linguistic quantifiers of first order predicate >> logic, and other more basic structures of grammar allow for possible >> topological formalization(s). >> >> Recall that for Peirce, Dicisigns are formed with icon rhemes and their >> saturation by means of index rhemes. The cognitive linguist would agree >> that sentences are formed by predicates and their saturation by means of >> subjects. To wit: “A basic tendency seems to be that the distinction >> between grammar and morphology on the one hand, and lexical semantics on >> the other roughly corresponds to diagrams pertaining to formal and material >> ontologies, respectively” (NP, 196). If iconic structures can be found in >> the form of conjunctions and sentence structures as well as the the >> multiplicity of structures of rhemes/predicates themselves, grammatical >> transformations contain logical content, and more broadly grammar and >> morphology will generally contain discoverable implicit formal-material >> ontologies while lexical semantics can fill in regional ontological >> information with particulars: adjectives, common nouns, verbs and >> combinations thereof. Based on underlying forms of diagrammatic reasoning, >> ordinary language does not remain committed to any particular ontology >> (because diagrammatic reasoning is not committed to any particular >> topological framework), even if it acquires variable ontological >> commitments to objects and relational properties of the universe of >> discourse in which we engage, which Qualities and Existents we recognize, >> and how we choose to construct our Arguments. >> >> Stjernfelt relates the blurring of the grammar/semantics distinction to >> Husserl's use of the scholastic distinction between *syncategorematica* >> (closed classes)and *categoramatica* (open classes), and makes the >> observation that, in all three accounts, formal ontologies are produced >> that contain subclasses of formal ontologies such as modal logic, temporal >> logic, higher order logic on the one hand and high-level material >> ontological concepts from epistemic logic, deontic logic, speech act logic >> on the other. The linguist might say that high-level material ontologies >> include modal verbs, tempus morphemes of verbs, in propositional stances >> verbs, in speech act verbs,” (NP, 199) but regardless of the terminological >> variation, the “doubleness of isomorphism and independence recognized >> between logic, language, and ontology” (NP, 202) is a common thread whereby >> a gluing (interdependence) between the global/local provided by the >> Dicisign structure overcomes the structuralist account the arbitrarity of >> language (usually inferred from the relationship between sounds and words), >> because “conceived from a diagrammatical point of view, language has two >> levels, one general, formal, vague, formalized in grammar and closed-class >> categorematica—and another in lexical semantics and open-class >> syncategorematic,” (NP, 199) which are open to further investigation. >> Ordinary language remains 'secular'—not committed to any topological or >> metaphysical viewpoint ahead of time because the genuine interaction >> between (what I am calling) the relatively autonomous global/local levels >> allows for language to remain an ecumenical, indefinitely-extended, >> self-critical means of information processing. >> >> The author closes the chapter with a discussion of Hintikka's >> identification of two strands of 20th century philosophy, one which >> views language as universal representation and one which sees it as a >> calculus. According to the Hintikkan geneaology, Frege, Russell, >> Wittgenstein, Quine, and even Heidegger and Derrida seem to favor the >> former approach (language as one reference domain to all reality with >> privileged semiotic access to the world) while Boole, Peirce Schroder, >> Hilbert, Husserl, and the late Carnap understand that multiple >> representational systems with differing degrees of generality, granularity, >> are quite possible if not necessary to productive inquiry as an open-system >> which does run up against, in Hintikka's words, “prisonhouse of language >> hypotheses.” I do not disagree with Stjernfelt's claim that for the >> model-theoretic tradition considers language as closer to a *calculus >> ratiocinator* than a *mathesis univseralis* but I would contend that >> Irving Annelis's *paper <http://arxiv.org/pdf/1201.0353.pdf>* ( c.f. pp. >> 25-28) offers a more nuanced assessment how these Leibnizian themes are >> re-appropriated by the late Peirce than that of Hintikka, in my humble >> opinion. >> >> For Peirce, representational pluralism does not conflict with a robust >> realism given his idea of inquiry as a distinctly communal activity, one in >> which natural language is able to engage by means of presenting various >> formalizations which “semiotically triangulate the object,” (NP, 200) and >> one in which individual inquiry itself engages in a sort of game-theoretic >> semantics. Given one representational system's ability to assess another, >> we are not left with the ineffability claims but a science of semantics. >> Indeed, a careful reading of Chapter 7 offers the reader a deeper >> understanding of how language remains capable of entertaining universes of >> discourse which lack logical consistency or logical commitment so we have >> at our disposal a tool capable of examining and experimenting with the >> ontologically inconsistent, the vague, the general, and the imaginary. >> Peirce's 'fallibilistic apriorism' (opposed to Kantian apriorism) is better >> able to account for the various *a priori* structures of different >> material ontologies. Language from the diagrammatic perspective thus >> resembles a versatile collaboration between different topological >> considerations found inside, outside, and between conjunctions, grammar, >> semantics, and their various instantiations. Along with recent developments >> in Existential Graphs, the trajectory cognitive semantics exposited by >> Stjernfelt makes a strong case for CSP's continued relevance to >> diagrammatological linguistics. >> >> I would like to close by asking Professor Stjernfelt if he agrees with >> Francesco Bellucci that the late Peirce saw diagrammatic reasoning >> containing its own abductive and inductive phases. I look forward to any >> questions or comments before we begin Chapter 8. >> >> Thankfully, >> >> Doug >> >> >> ----------------------------- >> 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 . >> >> >> >> >> >> > > ----------------------------- > 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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