Chemistry and biology are not my concern here. I speak only of deduction in a purely mathematical sense.
Steven On Wed, Apr 8, 2015 at 9:13 AM, Jerry LR Chandler <[email protected]> wrote: > Steven: > > I am not aware of any formalized deductive system for the pan-chemical > sciences. > So, the underlying issue is, what is the formal logic for biophysics? > biochemistry? biology? > Alternatively, what copulates the logic of biophysics to the logic of > biochemistry? > > Cheers > > Jerry > > On Apr 8, 2015, at 11:03 AM, Steven Ericsson-Zenith wrote: > > > 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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