I am only thinking of the formalization of deduction. What problem do you see, exactly?
My point to Ben is only that you cannot put a smattering of "some" around such definitions. Regards, Steven On Wed, Apr 8, 2015 at 8:19 AM, Jerry LR Chandler <[email protected]> wrote: > Steven: > > I was slightly stunned by your response. > > When you write: > > I am thinking only of Babara as the starting point. > > > I wondered if this broad assertion refers to your views on biophysics as > well (either inferring FOL or not)? > > Cheers > > Jerry > > > > On Apr 8, 2015, at 10:03 AM, Steven Ericsson-Zenith wrote: > > I am thinking only of Babara as the starting point. > > > Steven > > > > > > > On Tue, Apr 7, 2015 at 10:12 PM, Jerry LR Chandler < > [email protected]> wrote: > >> Ben, Steven, List: >> >> Ben: Thanks for the update on your views. >> >> I will think about your categorization for a bit and respond if anything >> trivial or better comes to mind. >> >> Thanks for the reference to Kant. I have been digging a bit further >> myself, but got side-tracked by the more general problem of the semantics >> of logic itself. >> >> Although my knowledge of German is scant, my recall suggests that CSP did >> not choose the best term for translation. >> But, see 4.43. where CSP states rather clearly the basis for his >> disagreement with Kant's terminology, that is Kant's notion of 'synthetic' >> reasoning. What is important in this passage is that CSP asserts the >> classification of propositions is by "per se" or "per accidens", drawing >> upon the Isagoge of Porphyry! So that gives us one historical path from >> Aristotle's view to the present day. The meaning of "ampliative" (as I was >> using it) was in the sense of "per accidens'. >> >> My thinking about the term "ampliative" was by assuming that the term was >> a sibling to the term 'amplification' and its well defined technical >> meaning in both mathematics and wave mechanics. >> >> Consequently, I associated 'ampliative' with ratiocination and the notion >> of proof theory of going from the known to the unknown. >> >> It is in this sense that I concluded that >> >> > the ampliative conclusion deductively implies the premisses. >> >> because this is true for the proof theory of chemical relations. In this >> form of proof theory for chemical structures, the validity of the >> assertion lies in the conservation laws of physics and concurrence of >> measurements of mass and charge in atoms and the molecules composed from >> them. >> >> The "abductive logic" is in the postulation of a particular structure >> from a set of atoms. This ampliative wrt to size of the molecule. >> >> Steven: >> >> Your assertion that: >> >> "Deduction has been formalized since Aristotle." >> >> is a bit strong, isn't it? >> >> The hybrid logics of T. Brauner offer relations between deductions and >> proof theories as being term dependent in the sense of Kripke semantics. >> >> BTW, at the moment at least, I really like the approaches of Brauner, >> which bases the method of proof on the meaning of the terms. And, rather >> remote from Aristotle's sorites. >> >> The gaps between Danko's cybernetics and "Natural Propositions" and >> Brauner's hybrid logic are obvious. But, as of now, I have not found any >> obvious conceptual gaps between Brauner's Hybrids and chemical proof >> structures. VERY exciting to me! >> >> Cheers >> >> Jerry >> >> >> >> >> >> On Apr 7, 2015, at 12:51 PM, Benjamin Udell wrote: >> >> Jerry, list, >> >> I felt somewhat hampered in the discussion below by a lack of >> terminology. We have the words 'deductive' and 'ampliative' for inferences >> where the conclusions don't or do, respectively, add something beyond the >> premisses. But I can't find a generic word for an inference where the >> conclusion says _*at least as much as*_ the premisses say, nor a generic >> word for an inference where the conclusion _*omits*_ something that the >> premisses say. >> >> So I've come up with a couple of words - _*repletive*_ and _*attenuative*_ >> - that will come in handy if such discussion arises again, though such >> discussion doesn't arise often. >> >> ('Entail' = 'deductively imply'.) >> >> >> *Inferences: Deductive = Everything* (explicit or entailed) *in the >> conclusion is* (explicit or entailed) *in the premisses.* >> *Ampliative = Something* (explicit or entailed) *in the conclusion is >> not* (explicit or entailed) *in the premisses.* >> *Repletive = Everything* (explicit or entailed) *in the premisses is* >> (explicit or entailed) *in the conclusion.* >> *Attenuative = Something* (explicit or entailed) *in the premisses is >> not* (explicit or entailed) *in the conclusion. * >> Inferences >> *Deductive:* *Ampliative:* *Repletive:* *'Reversible' deduction. * *Some >> induction. * *Attenuative:* *'Forward-only' deduction. * *Abduction, >> much induction*. * >> >> *E.g., "3/5 of the sample is blue, so (likely) 3/5 of the total is blue" >> is usually considered inductive. Still, it's not only ampliative, it's also >> attenuative. >> Summary of properties from perspectives of proof theory and model >> theory >> (not that I know much about them) . Inferences ⇓ *Proof-theoretic >> perspective:* >> *Model-theoretic perspective: * *Deductive:* Premisses *entail* >> conclusions. Automatically *preserves truth*. >> *Ampliative (i.e., non-deductive):* Premisses *do not entail* >> conclusions. *Does not* automatically *preserve truth*. *Repletive:* >> Premisses >> *are entailed by* conclusions. Automatically *preserves falsity*. >> *Attenuative (i.e., non-repletive):* Premisses *are not entailed by* >> conclusions. *Does not* automatically *preserve falsity*. >> >> Best, Ben >> >> *Subject:* Re: [PEIRCE-L] Bayes and abduction - from the perspective of >> organic mathematics / the unity of the sciences >> *Date:* Mon, 06 Apr 2015 14:00:32 -0400 >> *From:* Benjamin Udell >> *To:* [email protected] >> >> Jerry, all, >> >> Jerry, I can't address the things you say about chemistry, I don't have >> the background. But I can say some things about Peirce's examples of >> abductive and inductive inferences. >> >> Jerry, you wrote, >> >> CSP's usage of the term ampliative infers that: >> > the ampliative conclusion deductively implies the premisses. >> >> In most of Peirce's examples (e.g., 1867, 1878, 1883) that I've seen, >> neither the inductive conclusion usually nor the abductive conclusion ever >> deductively implies its premisses. So it seems unlikely that he thought the >> term "ampliative", as applied to inference, meant that the conclusion >> deductively implies the premisses. Anyway he says that non-deductive >> inferences are ampliative and that this means that "they conclude something >> not implied in the premisses" in "The Doctrine of Necessity Examined" >> (1892, see CP 6.40 >> http://www.iupui.edu/~arisbe/menu/library/bycsp/necessity/necessity.htm >> ). Obviously, just in order to be non-deductive, a non-deductive inference >> does not have to have a conclusion that deductively implies its premisses. >> It just needs to have a conclusion that its premisses don't deductively >> imply. >> >> The inductive conclusion that all the beans from the bag are white does >> not deductively imply the premisses that these beans here are from the bag >> and that they are white. >> >> A rare exception is the crude induction of the kind (not Peirce's actual >> example), 'all swans in England are white, ergo all swans in the world are >> white' (except insofar as the conclusion fails to imply that there is an >> England; but one might get around that somehow). But if one says, 3/5 among >> all swans in England are white, ergo 3/5 among all swans in the world are >> white, then the conclusion does not deductively imply the premiss, yet the >> inference would usually be regarded as inductive (and hardly less crude >> than the first one). Can we get the deductiveness by adding qualifiers? If >> the conclusion is that it is _*likely* _ that 3/5 among all swans in the >> world are white, that deductively implies at most that it is _*likely, >> but somewhat less likely,* _ that 3/5 among all swans in England are >> white. And that was not the inductive premiss. >> >> A finding (predating the fame of black swans as in the above examples) >> might be stated carefully, "All swans in Europe are white, ergo all swans >> in Europe and very likely all swans elsewhere, are white." There the >> conclusion deductively implies the premiss, by repeating it somewhat >> crudely. Still (and I don't know what Peirce would think of this), maybe >> that's more in the spirit of an inductive conclusion, painting a fuller >> picture of a total population, showing observations and predictively >> extended trend line together; the extended trend line all by itself might >> be taken as a weakly abductive (non-explanatory and involving no new or >> outside idea) statistical hypothesis of some sort, the interest in it >> remaining grounded in interest in the particular population under >> observation; so maybe the "really" inductive conclusion is observations >> plus extended trend line. On the other hand, the inquirial interest of an >> abductively conceived theory like general relativity goes beyond the >> inquirial interest of the Sun and any actual stars around which >> gravitation's bending of light is observed; the theory's conclusions are >> stated in general forms without mention of the Sun etc. But I admit that >> I'm trying to get at things here that I'm not quite clear on. >> >> As to abducing particulars, one sees the lawn wet one morning, considers >> that, as a matter of course, if it rains at night, the lawn is wet the next >> morning, and concludes that very plausibly it rained last night - which >> conclusion does not deductively imply its premisses. To check the >> conclusion, one might check neighboring lawns. The interest has become >> whether it rained last night, not the total set of nights and mornings at >> the lawn, nor just the condition of one's own lawn. A rainfall last night >> might explain many things. So it doesn't make sense to recast the >> conclusion in some premisses-implying form like "it rained last night and >> my lawn is wet, and that happens as a matter of course, with night rain >> never failing to leave my lawn wet." >> >> Best, Ben >> On 4/6/2015 12:39 AM, Jerry LR Chandler wrote: >> >> List, Ben, Clark, Danko: >> >> On Apr 3, 2015, at 1:04 PM, Benjamin Udell wrote: >> >> Peirce also characterizes non-deductive inference as _*ampliative* _, >> that is, having conclusions not deductively implied by the premisses, and I >> still like the idea, that I had before reading Peirce, of distinguishing >> induction from more 'leapy' or conjectural inference, by whether the >> ampliative conclusion deductively implies the premisses or not (I've tended >> in the past to speak of 'surmise' when I've had in mind conjectural >> inference so defined, because I've doubted that people would agree to >> define abduction as inference that lacks deductive implication whether by >> premisses of conclusions or vice versa). Now, it's easy enough to come up >> with an ampliative conclusion; such a conclusion doesn't need abductive >> plausibility or Peirce's inductive verisimilitude (the likeness of the >> conclusion to the premissual samples) in order to be ampliative; but, >> without them, it just isn't intrinsically fruitful or promising in inquiry. >> Likewise a deductive conclusion can simply repeat a premiss word for word >> and still be deductive, but such a deduction, lacking any new or nontrivial >> aspect, just isn't intrinsically fruitful or promising in inquiry. >> >> First, thanks to you, Ben, I have studied the potential meaning of the >> logical term, ampliative, for nigh unto a decade now, perhaps longer. >> >> At this point in time, one firm conclusion about CSP's usage of this term >> is clear, at least in my mind, with respect to the life sciences. >> >> Within the framework of the explicit sortal logic of chemistry, molecular >> biology, and the pan-chemical sciences, CSP's usage of the term ampliative >> infers that: >> >> the ampliative conclusion deductively implies the premisses. >> >> Within the Peircian mathematical / philosophical context, this >> conclusion is a central component of the trichotomy components, sin-sign, >> index, icon, Rheme and Dicisign *with respect to* the legisign as well >> as organic mathematics >> >> As I have asserted before, the trichotomy is an example of chemical >> reasoning that is extensible. Within the sortal logic of organic >> mathematics, the legisign (natural law in the sense of Kant?) includes the >> concepts of atomic masses and valence. >> >> In this case, I simply assert that sin-sign of a molecule, as >> representations of the forms of atomic weights, is a basis of CSP's central >> term "index." This basic logical chemical operation of addition of atomic >> weights is physically measured as a quali-sign of a molecular sin-sign. >> *Both >> the qualisign and index are quantitative predicates of logical propositions >> of a molecular sin-sign. * >> >> In the modern chemical icon (structure), these physically measured >> quantities, take on the form of a diagram, a graph, and, yet, more >> specifically, a labelled bipartite graph, a connected lattice of electrical >> relations that serves as the initial conditions for quantum mechanical >> calculations. In this context, these terms all describe mathematical terms >> relatable to the the index. >> >> *Thus, I conclude that the Peircian term, ampliative, adroitly coheres >> with the logical unity of the natural sciences because of the physical >> logical connection between the sin-sign and it's index.* >> [.....] >> >> Cheers >> >> Jerry >> >> >> ----------------------------- >> 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] . 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