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
