Jon, List: Some comments from the perspective of modern science are offered. While technical language is remote from the languaging of CSP, there is a remote possibility that it may be useful since the notion that atoms beget molecules has not changed.
It is well known that abductive logic is essential to constructing the alignments of atoms of chemical graphs, locative logic among pairs of the indices. These abductive propositions are later verified by physical methods that became available after 1913, such as X-ray crystallography. Given that the composition of terms is necessary to construct molecular graphs from atomic names of elements (the index), the challenge of “proof of structure” is to construct such existential graphs that are consistent the attributes (predicates) of matter. Scientific locative logic uses the algebra of atomic numbers and their valence to draw objective truth functions from the thematic and dicisigns to generate the symbol that corresponds with the legisign. These factors are necessary in chemistry to differentiate isomers (such as handedness). These occasions arise when the analysis of the two different sin-signs generates identical atomic indices but with two different sets of quali-signs. Existential graphs can be used to show why / how the patterns of the two natural objects (sin-signs) differ and hence are nominated as two different legisigns with names that specify the sameness of the indices but also specify the difference in the relative locations of the same parts in the two different wholes. (This is a crude statement of the concept of isomerism.) While I find your explications of your beliefs to be unrefined, it appears possible that a semantic path between your beliefs and CSP’s assertion that chemistry is the bedrock of his logic is conceivable. Reasoning “backwards" from molecules to atomic constituents and alignments within a locative logic is essential to the pragmatism of the chemical sciences. Also, modern work (21 st Century) in artificial intelligence often crow about the power of back-chaining propositions and many papers assert positions about various meanings of “abductive” reasoning. Avoiding narratives about “lattices” will probably serve you well. Cheers Jerry > On Dec 13, 2020, at 5:46 PM, Jon Alan Schmidt <jonalanschm...@gmail.com> > wrote: > > List: > > I have been thinking about existential graphs again lately and wondering how > they might be employed to represent abduction, rather than deduction. Peirce > describes the form of abductive inference as follows. > > CSP: The surprising fact, C, is observed; > But if A were true, C would be a matter of course. > Hence, there is reason to suspect that A is true. (CP 5.189, EP 2:341, 1903) > > He elaborates on this a few years later. > > CSP: Every inquiry whatsoever takes its rise in the observation, in one or > another of the three Universes, of some surprising phenomenon, some > experience which either disappoints an expectation, or breaks in upon some > habit of expectation ... . The inquiry begins with pondering these phenomena > in all their aspects, in the search of some point of view whence the wonder > shall be resolved. At length a conjecture arises that furnishes a possible > Explanation,--by which I mean a syllogism exhibiting the surprising fact as > necessarily consequent upon the circumstances of its occurrence together with > the truth of the credible conjecture, as premisses. On account of this > Explanation, the inquirer is led to regard his conjecture, or hypothesis, > with favor. As I phrase it, he provisionally holds it to be "Plausible" ... > (CP 6.469, EP 2:441, 1908) > > Hence abduction is "reasoning from consequent to antecedent" (ibid) or > reasoning from conclusion to premisses--i.e., reasoning backwards, which is > why Peirce ultimately prefers to call it retroduction. Accordingly, in EGs we > can scribe any true proposition on the sheet of assertion--such as a > surprising fact (C)--and "scroll" it so that it becomes the consequent of a > conditional (in the inner close), then insert any proposition whatsoever (A) > as the hypothetical antecedent (in the outer close). Since C is true and we > have complied with the transformation rules, the resulting consequence (if A > then C) cannot be false no matter what we choose for A. But does this entail > that it is true? > > On the contrary, as with intuitionistic logic, excluded middle does not hold > in such a case. Given that C is true, we only have reason to suspect that A > is true if C follows from A as a matter of course. In other words, the > plausibility of A as an explanation of C relies on there being a rational > sequence from A to C. This requirement is obscured in classical deductive > logic, "completely hidden behind the superfluous machinery which is > introduced in order to give an appearance of symmetry to logical law" (R > 490:29, CP 4.581, 1906), by treating "if A then C" as equivalent to "not-(A > and not-C)" or "not-A or C"--i.e., a scroll as equivalent to nested cuts or a > shaded area enclosing an unshaded area--because the latter formulations are > always true as long as C is true. > > CSP: The second failure of Selectives to be as analytical as possible lies in > their encouraging the idea that negation, or denial, is a relatively simple > concept, and that the concept of Consequence, is a special composite of two > negations, so that to say, “If in the actual state of things A is true, then > B is true,” is correctly analyzed as the assertion, “It is false to say that > A is true while B is false.” I fully acknowledge that, for most purposes and > in a preliminary explanation, the error of this analysis is altogether > insignificant. But when we come to the first analysis the inaccuracy must not > be passed over. (R 300:48-49[47-48], 1908) > > Even in deductive reasoning, there is "a real movement of thought" from > antecedent to consequent, from premisses to conclusion. The continuous scroll > preserves this aspect, while discrete nested cuts or shaded/unshaded areas do > not. > > CSP: All my own writings upon formal logic have been based on the belief that > the concept of Sequence, alike in reasonings and in judgments, whether the > latter be conditional or categorical, could in no wise be replaced by any > composition of ideas. For in reasoning, at least, when we first affirm, or > affirmatively judge, the conjugate of premisses, the judgment of the > conclusion has not yet been performed. There then follows a real movement of > thought in the mind, in which that judgment of the conclusion comes to pass. > Now surely, speaking of the same A and B as above, it were absurd to say that > a real change of A into a sequent B consists in a state of things that should > consist in there not being an A without a B. For in such a state of things > there would be no change at all. (R 300:49[48]) > > There is likewise "a real movement of thought" in abductive/retroductive > reasoning, but in the opposite direction. That is why it is ampliative rather > than merely explicative, with the tradeoff that its inferences are merely > plausible rather than certain. > > Regards, > > Jon Alan Schmidt - Olathe, Kansas, USA > Structural Engineer, Synechist Philosopher, Lutheran Christian > www.LinkedIn.com/in/JonAlanSchmidt > <http://www.linkedin.com/in/JonAlanSchmidt> - twitter.com/JonAlanSchmidt > <http://twitter.com/JonAlanSchmidt> > _ _ _ _ _ _ _ _ _ _ > ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu > . > ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu > with no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of > the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . > ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and > co-managed by him and Ben Udell.
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