Dear Ben, lists - Thanks for good comments. We certainly agree about the centrality of theorematical reasoning. An important reason for its prominence in Peirce is his extension of logic to embrace both contexts of discovery and contexts of justification, to repeat Reichenbach's famous distinction. If you confine yourself to justification, which has often been recommended in 20 C philosophy, it is understandable that deduction will appear trivial, for justification is post hoc, after discovery, and just runs through and controls established evidence. Moreover, it is often concluded that the context of discovery is only open to psychological study, not logical investigation. Otherwise, of course, if you include the context of discovery in logic - here the selection of the right steps to conduct your deductive proof comes to the forefront, and in any proof, of course, there is a wide selection of possible ways to proceed. Only after having found the right sequence of steps - which may take years or centuries - the air of triviality may appear. This is the same reason why the issue of novelty or creativity can only be posed in the context of discovery. A bit of the same goes for the introduction of abduction in logic. Seen from a justification p-o-v only, it may seem external to logic how you manage to make good guesses. If you include discovery, it immediatly becomes a logical issue how the relation is between ab-de-induction in the investigation process.
PS - Tomorrow, I shall travel to the International Semiotics Conf. in Sofia, Bulgaria. I do not know when I shall be back online, but I hope to be on the list again at least by Tuesday - Best Frederik Den 14/09/2014 kl. 22.21 skrev Benjamin Udell <bud...@nyc.rr.com<mailto:bud...@nyc.rr.com>> : Dear Frederik, lists, I don't see that we disagree on any fundamental points as to, for examples, the difference between philosophical logic and idioscopic psychology, or the pertinence of the theorematic-corollarial distinction (which I've brought up on peirce-l at various times; I also did the all too brief paragraph on it in "Corollary" at Wikipedia, with footnotes containing links to primary texts). I certainly don't think in some Kantian-shadowed way that all deduction is trivial or repetitive. The point of theorematic reasoning is to get far beyond the truisms, the triviality and repetitiousness, to which, as the reasoner recognizes, deduction is vulnerable - not destined but vulnerable - by its formally definitive character of claiming in the conclusion nothing unclaimed in the premisses. The tautologous 'A is A' is a most important truism, so people should appreciate it. But usually we want to reach stronger conclusions than "A horse is a horse". Hence, even the corollarial reasoning that we do use in practice, for example in the form of a categorical syllogism, ensures a modicum of novelty in a deduction. To like to learn in deduction is to like to find in deduction the nontrivial or deep, the surprising and counterintuitive, etc., even though (oppositely to natural simplicity and Peircean versimilitude) they contribute initially to doubt of a conclusion and incline us to check our premisses and reasoning. The premisses 'know' the deductive conclusions but often we don't, and almost tautologous to that is the most basic reason for it: Often we don't understand the premisses as well as we think we do. In a mathematical context, knowing or understanding something involves cognizing it not mainly as a descript or resistant chunk but instead in its diagrammatic transformabilities. I'm pretty firmly convinced, that novelty and nontriviality in a deduction are not merely psychological even though such aspects of inference seem to resist being quantified or otherwise mathematized despite varying in seeming degree and despite echoing some mathematical ideas. The nontriviality (in the sense of requiring creativity as you said of theorematic reasoning, and not mere tiresome difficult complication) is not usefully mathematized as relational properties such as arity, transitivity, etc. in whatever complexity - at least, not that I've heard of. The novelty is not usefully quantified as information in the information-theoretic sense. Peirce insisted that an induction's verisimilitude in his sense is not a quantifiable probability, and I haven't heard of any attempt to generally equate plausibility (natural simplicity) of a hypothesis with optimality or feasibility in the sense of maths of optimization. (The prizing of verisimilar inductions and plausible abductions suggests - and I have not thought about it much - a prizing of the more corollarial over the more theorematic in induction and abduction - or a prizing of something like that, insofar as corollarial and theorematic are defined as classes of deduction, not of other modes of inference.) Thus, much of the quasi- or semi-subjective element seems to come down to this, that although the prized aspects of nontriviality, novelty, verisimilitude, and plausibility are associated with specific cenoscopically defined modes of inference in seeming counterbalance to those modes' 'chalkboard' formal characters, and although the prized aspects have mathematical echoes, they seem to lack useful mathematical bases, yet seem variable in degree; and the degree of a given one of those aspects that one instinctively or, as we often say, intuitively, attributes to a conclusion seems relative to one's intelligence and training. '3 x 5 = 15, ergo 15/5 = 3' seems a less trivial deduction to a schoolchild than to an average educated adult. Maybe the prized aspects really are 'semi'-something, insofar as they involve relations between, on one hand, actual reasoners at varying levels of intelligence, training, etc., and, on the other hand, philosophical logical forms. In the case of abductive inference about idioscopic nature, lines should be drawn, like you say about theorematic deduction, between the psychological process adapting itself to reason, and the logical structure of reasoning. Now, Peirce calls the most general idioscopic sciences 'nomological' - pertaining to universal laws and elements that seem simply to hold, we don't yet know why, in our actual universe. We have not derived them from purely mathematical, logical, or cenoscopic considerations; for all their universality, there's still something idiosyncratic about them, they're still idioscopic. And in idioscopy, there is much detective work to be done about further idiosyncratic phenomena governed by those laws but not fully understood through them. Idioscopy is where some evolved attunement comes in particularly handy for abductive inference's quick leaps, its expeditiousness which is much of its purpose. Much can be conscious and deliberate in the "larger" abductive process, but the general formal character of the abductive generation of a hypothesis is for quick leaps, as opposed to slow, conscious, deliberate reasoning, and we can note these things at a cenoscopic level of generality, I think. Peirce said of abduction, that there's no point in specifying more inference rules than necessary. It's a long-time issue. Some people think, I believe wrongly, that abductive inference isn't really logical at all, and shouldn't be studied in logic. Still, in abductive generation of a hypothesis, particularly about idioscopic nature, there is so much that is vague, dependent on idioscopic context, etc., that the lines to be drawn may leave cenoscopy with less to say about abductive inference than it has to say about inductive inference, especially if we place inferential statistics in cenoscopy. Best, Ben On 9/13/2014 8:16 AM, Frederik Stjernfelt wrote: Dear Ben, list - Dear Frederik, lists, You wrote, >> [BU] The 'novel' aspect has sometimes been called psychological. > [FS] Why? - and by whom? I think de Wulf or some other (neo-)scholastic did. I think it's been said by others too, but I admit that I've forgotten, it's been so many years. I guess they just didn't know what else to call it. The deductive conclusion doesn't really say something new, instead it merely elucidates what's already in the premisses. That was Kant's idea, giving rise to the idea of deduciton as tautological, almost trivial - to some degree inherited by the positivists. But Peirce's distinction corollarial/theorematic deductions goes against this - I discuss this in ch. 11 of the book. But, if it's worth deducing, then it seems to say something new. Categorical syllogisms are ways to ensure a modicum of such novelty. As Peirce put it, deduction "merely gives a new aspect to the premisses." I don't want to call that new aspect entirely psychological, or entirely subjective, or whatever, but it seems partly subjective in some sense, likewise as nontriviality, verisimilitude, and natural simplicity seem. The general character of these semi- or quasi-subjective aspects seems a philosophical subject to me. But I can't see how to rule out that psychology may have something to say about them too. I think that they matter because it's hard to see why a mind would reason if there were no hope of its conclusions having any of those aspects. I think by now you know my p-o-v: the study of the psychological processes supporting theorematic reasoning is important - but it must be kept apart from the logical structure of such reasoning itself. Let me give a bit goofy analogy. We do not say that motion is something which results only form the machinery of cars, just because cars form an empirical class of objects providing a widespread and central example of movement. Quite on the contrary, movement is found in astronomical objects, bacteria swimming, birds flying, persons walking etc. - and it may be studied in itself, apart from any of the objects realizing it. This does not imply the study and development of car engines is superfluous - but we should not imagine that the very nature and structure of movement is somehow created by car engines and that the deep study of them will reveal the deepest truths about movement as such. Best F I'm feeling a hankering to let you get back to discussing your book! Best, Ben
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