Jerry, list,
You wrote,
Consequently, I associated 'ampliative' with ratiocination and the
notion of proof theory of going from the known to the unknown.
[End quote]
I think you weren't far off. Strictly speaking, an ampliative inference
does go from the known (or given) in the premisses to the unknown (or
not given) in the premisses. It's just that there's also a question (not
always urgent) of whether the conclusion says or entails all that was
known (or given) in the premisses.
Your remarks on chemistry reminded me of a further issue that's bounced
around in my mind. It has to do with statements that are standing givens
(something like 'axiomatic' in the ancient sense discussed by Peirce in
"Kaina Stoicheia"). Pardon my long-windedness in the following example.
(Also readers generally deserve to know that I'm no mathematician.)
Now, in mathematical induction, the conjunction of the ancestral case
with the heredity is equivalent to the conclusion. In that sense, the
mathematical induction is a deduction through an equivalence (it is
deductive and repletive, not deductive and attenuative). Moreover, it is
much in the spirit of mathematical reasoning, which is so often through
equivalences (Aristotle spoke of mathematical premisses and conclusions
as tending to "reciprocate"). This reflects that mathematical reasoning
tends to be elucidative and, for lack of a better word, translative,
from one proposition (or compound) to another proposition equivalent to
it but easier to work with for the purpose at hand. In mathematical
induction, one takes a thesis that is to be proved, and 'translates' it
into the ancestral case and the heredity, conjoined. Once they've been
separately proved, then the mathematical induction itself, the induction
step, consists in 'translating' the conjunction of ancestral case with
heredity back into the thesis, proving the thesis.
But a mathematical induction is for a well-ordered set. Its conclusion,
by itself, does not entail that the given set in question is
well-ordered. If the well-orderedness of the set is considered a premiss
on a par with the ancestral case and the heredity, then the mathematical
induction is an 'attenuative' deduction, and is deductive 'forward-only'.
Classifying inferences by their entailment properties does not tell one
the fairest ways to frame an inference. If we allow a distinction
between 'standing givens' and 'new premisses' so as to help classify
some mathematical inferences as equivalentially "translating" from new
premisses to conclusion under the general assumption of some standing
givens, then why couldn't this way of looking at it be applicable in
other modes of inference? It seems at this point to start offering too
much wiggle room for framing an inference as, say, inductive or instead
deductive. Such thoughts come to me as I think about whether some
chemical conclusions of the kind that you describe (and of which I have
only the haziest idea) should be classified as deductive, inductive,
attenuative, and so on. Maybe anti-climactically, my general sense of
it is that consideration of fair ways to frame an inference needs to
encompass consideration of the purpose embodied in the given inference
(e.g., elucidation? explanation? etc.).
Best, Ben
On 4/8/2015 1:12 AM, Jerry LR Chandler 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:
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