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 <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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