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
<http://www.iupui.edu/%7Earisbe/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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