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
>>>
>
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