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 - twitter.com/JonAlanSchmidt >
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