Dear Gary, Douglas, lists, Thanks to Gary for the reference to the Harvard lecture draft. I went back and reread that (pretty fantastic btw) piece of prose. Gary's right about P's "waverings" (as he calls it) regarding the relation between the categories and the three argument types, ab-, in- and deduction (which is the 1-2-3 sequence followed in this text). In the deleted part added as s footnote in Turrisi's edition to which Gary also refers, P. leaves "the question undecided". I think there is no doubt in the overall perspective that Peirce stuck, despite these waverings, to the ab-, de-, in-sequence in the larger perspective of the mature version of his logic - this is supported by his stable dichotomy of deductions (corollarial vs. theorematic, to which I return in a later chapter) and his (a bit less) stable trichotomy of inductions (pooh-pooh, quantitative, and qualitative, respectively) - given P's argument that Secondnesses give rise to dichotomies, Thirdnesses to trichotomies. But despte this fact there is indeed good reason to investigate the arguments for the two different versions - the ab-in-de sequence dominated P's earlier years so it is really a case with much wavering on his part. The argument for the ab-in-de sequence in the deleted part of the Harvard lecture draft go as follows: ab-in-de function by means of icons, indices, and symbols, respectively - and induction has two subtypes (here, quantitative and qualitative) while deduction has three (here, three of the normal four types of syllogisms of which the fourth is claimed reductible). In addition to the dichotomy-trichotomy argument, the corresponding arguments for the ab-de-in sequence often relies upon taking that sequence as a typical procedural sequence in the logic of discovery: abduction first proposes a hypothesis on the basis of some facts; deduction then takes this hypothesis as an ideal model and infers some necessary consequences from it; induction finally tests those deductive results by comparing them to empircal samples. (But is there necessarily any strong link between the 1-2-3 classification and the sequence of procedure?) I think, however, that the decisive argument for finally settling on the ab-de-in sequence was Peirces double identification of deduction with diagrammatical reasoning and with mathematics (diagrams being seconds in the image-diagram-metaphor trichotomy) - instead of the identification of deduction with symbol-supported reasoning in the 5th Harvard lecture. A third sequence which P often gives in the 1900s is de-in-ab which does not seem to refer to categories nor to procedure, but rather to the falling order of degree of validity (from necessary over probable to possible) - probably also an order of importance, deduction often (also in Gary's Harvard lecture) being described as the overall argument type which the other two somehow feed into.
All this said, I think a commentary on a meta-level should be added. I am not certain that 1-2-3 sequenceing in terms of the categories should always have first priority when discussing Peircean triadic distinctions. Of course, it is easy to get this idea from the classification of sciences where categories belong to Phenomenology, being second only to Mathematics in the hierarchy. But P's own practice counts against taking this Comtean hiearchy itself as a sequence of inference from top to bottom so that lower sciences should receive dictates by higher ones. There's a traffic also in the bottom-up direction - the lower sciences receive principles from the higher ones, alright, but the higher ones articulate those principles by abstracting from the matter of the lower ones. This latter is especially the case regarding the relation between logic and categories where P follows Kant's idea that the categories should be abstracted from logic. This implies that logic is actually the source of the categories (which is also evident from many P claims already in the 1860s). So even if, in the hierarchy of the ideal, static end point of inquiry, categories give principles to logic, in the ongoing process of discovery it is rather the categories which are abstracted out of logic. So before the final doctrine of categories is consummated, we should not be able to expect them to be able to legislate over logic - also because of the simple fact that Peirce discovered a whole lot more of logic than about category phenomenology which remained ambiguous (cf. the enormous amount of very different descriptions of the categories - as compared to the far larger stability of the description of ab-de-in, irrespectively of their sequence). This is why I generally hesitate to call in the categories as final arbiters of trichotomy issues lower in the system. Finally, Doug asked about Bellucci's claim about an internal ab-de-in sequence within deduction. I perfectly agree with that suggestion - I think I also address it a bit later in the book because it becomes evident in theorematic deduction. In mathematical proofs, the case in general is that there is no given algorithm to follow, and from one proposition many different other propositions may be inferred. This immediately implies a trial-and-error procedure - which is by nature abductive. You have to check which direction of the proof proves fertile. In the other end, there undoubtedly is a phase resembling induction, namely the investigation of coherence of the result with established results of other branches of mathematics. So I am certainly with Bellucci here. Best F Den 17/12/2014 kl. 02.41 skrev Gary Richmond <gary.richm...@gmail.com<mailto:gary.richm...@gmail.com>>: Douglas, lists, You wrote: "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. In the 1903 Harvard lectures draft I pointed to, Peirce seems instead to have settled (albeit tentatively) on deduction as associated with 3ns (necessary reasoning) and induction with 2ns. I would encourage anyone interested in this categorial issue (how the categories are associated with the three inference patterns) to read that draft. It shows how Peirce assiduously applies the principle of fallibility to his own research, and just how self-critical he can be. Best, Gary R [Gary Richmond] Gary Richmond Philosophy and Critical Thinking Communication Studies LaGuardia College of the City University of New York C 745 718 482-5690 On Tue, Dec 16, 2014 at 8:08 PM, Douglas Hare <ddh...@mail.harvard.edu<mailto:ddh...@mail.harvard.edu>> wrote: 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 <gary.richm...@gmail.com<mailto:gary.richm...@gmail.com>> 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 [Gary Richmond] Gary Richmond Philosophy and Critical Thinking Communication Studies LaGuardia College of the City University of New York C 745 718 482-5690<tel:718%20482-5690> On Tue, Dec 16, 2014 at 4:48 PM, Douglas Hare <ddh...@mail.harvard.edu<mailto:ddh...@mail.harvard.edu>> 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. 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