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 > . > > > > > >
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