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] > . 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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