Hi Ben, List,
Thanks for your helpful remarks. First off, I agree with the worry you've expressed--to
the effect that the way the question is phrased may involve some kind of "wrong
turn." I stated it that way because I was trying to express the question in a
manner was neutral between a more descriptive and psychological explanation of validity
and a more normative and logical explanation. That is the kind of debate he starts with
when he considers the psychological explanation of déjà vu and then works his way to a
logical account of the comparison of qualities of feelings.
Having said that, I would like to point out that many of the passages you've
cited are meant to explain the validity of an argument that is written on a
chalk board. From this point of view, we are trying to account for the
validity of the argument itself--and that is largely a matter of the truth of
the underlying principle that is governing the inference (however it is
embodied).
On the top of page 320 in EP, however, he is considering questions about how
we--as human cognizers--are able to *recognize* that two things are similar or
dissimilar. My hunch is that he is focusing on these points about what is
needed to recognize similarity of two feelings because he is interested in the
question of what is necessary to recognize that a comparison of similarity is
apt, or recognize that an abdutive inference to a hypothesis is valid, or what
have you. My sense is that these are related questions.
On the same page, he makes the following claim: "it must be remarked that the only
effect of a quality of feeling is to produce a memory, itself a quality of feeling; and
that to say that two of those are similar is, after all only to say that the feeling
which is the symbol of similarity will attach to them. Thus the feeling of recognition of
a present idea as having been experienced has for its signification the applicability of
a part of itself. The general occurrences of the feeling of similarity are recognized as
themselves similar, by the application to them of the same symbol of similarity."
My hunch is that this remark is part of the larger explanation he wants to
offer of how we can recognize that an abductive inference is valid.
He goes on to say: "It is Kant's "I think," which he considers to be an act of
thought, that is, to be of the nature of a symbol. But his introduction of the ego into it was due
to his confusion of this with another element." I'd like to figure out what Peirce thinks the
confusion amounts to. On the Kantian account, the recognition of the validity of an act is a key
idea.
--Jeff
Jeff Downard
Associate Professor
Department of Philosophy
NAU
(o) 523-8354
________________________________________
From: Benjamin Udell [[email protected]]
Sent: Sunday, August 24, 2014 4:21 PM
To: [email protected]
Subject: Re: [PEIRCE-L] Phaneroscopy, iconoscopy, and trichotomic category
theory
Jeffrey, list,
My turn to write a long one. I think you take a bit of a wrong turn regarding
Peirce's views when you ask
[Quote]
What is the standard that we can use when comparing the feeling that an
argument is a good inference to the feeling that an argument is an invalid
inference?
[End quote]
Peirce insisted that an argument's validity has nothing to do with a feeling of its being a good
inference, a feeling of logicality. See for example "What Makes a Reasoning Sound?" in EP
2. For example, in "The Doctrine of Chances"
http://en.wikisource.org/wiki/Popular_Science_Monthly/Volume_12/March_1878/Illustrations_of_the_Logic_of_Science_III
, Section III, he writes,
According to this, that real and sensible difference between one degree of
probability and another, in which the meaning of the distinction lies, is that
in the frequent employment of two different modes of inference, one will carry
truth with it oftener than the other. It is evident that this is the only
difference there is in the existing fact.
In "The Probability of Induction," he sharply criticizes Bayesian or subjective
probabilities, and discusses confidence intervals (without calling them that) in
statistics. Statisticians have labored long to come up with measures of goodness of an
induction. But the confidence can be quite deceiving, because it can't take systematic
error (sample bias) into account, much less other kinds of error (the botch in the
equipment that made it seem that neutrinos sometimes travel faster than light - note that
the statistical confidence level of the result was very high).
At the same time, there are characters, namely verisimilitude and plausibility
(natural simplicity) that he associates with good inductions and good
abductions, respectively, characters that one might think of as feelings.
Verisimilitude (sometimes he calls it 'likelihood') in Peirce's sense consists
in that, if pertinent further data were to continue, until complete, to have
the same character as the data supporting the conclusion, the conclusion would
be proven true.
[From CP 8.224, draft letter to Paul Carus, circa 1910. Quote]
By verisimilitude I mean that kind of recommendation of a proposition which
consists in evidence which is insufficient because there is not enough of it,
but which will amount to proof if that evidence which is not yet examined
continues to be of the same virtue as that already examined, or if the evidence
not at hand and that never will be complete, should be like that which is at
hand.
[End quote]
[From CP 2.663, "Notes on the Doctrine of Chances," 1910. Quote]
I will now give an idea of what I mean by _likely_ or _verisimilar_. It is to be understood that I
am only endeavouring so far to explain the meanings I attach to "plausible" and to
"likely," as this may be an assistance to the reader in understanding the meaning I
attach to _probable_. I call that theory _likely_ which is not yet proved but is supported by such
evidence that if the rest of the conceivably possible evidence should turn out upon examination to
be of a _similar_ character, the theory would be conclusively proved.
[End quote]
It is a likeness that the inductive conclusion bears to the data in the sample. This
really doesn't sound like a confidence interval. It sounds like that in virtue of which
one calls an induction an inductive 'generalization'. In his "Notes on The Doctrine
of Chances," (1910) CP 2.664, he wrote:
[Quote]
this history [...] shows only too grievously how great a boon would be any way
[of] determining and expressing by numbers the degree of likelihood that a
theory had attained—any general recognition, even among leading men of science,
of the true degree of significance of a given fact, and of the proper method of
determining it. I hope my writings may, at any rate, awaken a few to the
enormous waste of effort it would save. But any numerical determination of
likelihood is more than I can expect.
[End quote]
But this verisimilitude, even if it is a feeling, is a starting point, until one can expand and
improve one's sampling and analysis to the point where more than sheer verisimilitude is involved.
Once that happens, we don't regard an inductive conclusion as merely 'likely'. In the case of
abduction, plausibility may vary, but any inference that explains the phenomenon is justified at
the level of critique of arguments. But as a result of further research, a hypothesis may be so
strongly supported that we no longer regard it as merely 'plausible,' merely 'appealing to
instinct', etc. The validity of abduction and induction both depend ultimately on the idea of an
indefinite community that, by followup, self-correction, etc., can bring about definite increase of
knowledge. I've argued that, since deduction can get tricky and complex, even the validity of
deduction, in our actual use of it, depends on the idea of that indefinite community. The
definition of deductive validity is such that any deduction is valid on inconsistent premisses, but
we care about deductions from consistent premisses, deductions whose prospects of soundness are not
doomed from the start by the formal character of the premiss set. Many systems of math are proven
consistent-if-arithmetic-is-consistent. But it is not a feeling, or more precisely, a quality of
feeling, but rather the experience of not collapsing in contradictions, that leads mathematicians
to regard those systems as flat-out consistent for their purposes, and the experience that
contradictions can be cordoned off, if, for example, division by zero in the real number system is
considered a source of inconsistency. The probability of a deductive conclusion can be quantified
in Peirce's sense, but there's little feeling in that. There are other characters that deductive
conclusions can have, which make them valuable, but which incline the reasoner more, or less, to
doubt rather than to acceptance - novelty (an opposite to verisimilitude) and nontriviality (an
opposite to natural simplicity), even when we distinguish the nontriviality of a conclusion (such
as the Pythagorean theorem) from the complexity (or lack thereof) of its proof. Peirce references
deductive novelty just once that I know of (he says deduction "merely gives a new aspect to
the premisses"), but it's a topic with some history; Peirce's student Gilman published a paper
on deductive novelty "The Paradox of the Syllogism Solved by Spatial Construction" in
1923 that I hope to read at some point.
Anyway, verisimilitude seems not usefully quantifiable, least of all quantifiable like probability; the
novelty or new aspect of a deductive conclusion seems not usefully quantifiable like information in the
information-theoretic sense; and the history of complexity theory shows the difficulty of trying to quantify
or otherwise mathematicize usefully the nontriviality or 'depth' of a deductive conclusion - it's certainly
not merely mathematical arity, adicity, valence. I'm not aware of attempts to quantify or graph or
mathematicize naturalness or simplicity in terms of optimization, but again the challenge seems to be to do
so in a useful way. And, again, the problem is that even if it is shown that people with sufficient
experience and discipline in the given subject matter tend to agree about degrees of verisimilitude,
plausibility, nontriviality, etc., still in the build-up of knowledge, the logic must rest come to rest on
facts, not on feelings, they should rest on some sort of externality, some sort of compulsion by the facts,
as he discussed back in "The Fixation of Belief," even if, as in mathematics, one's being compelled
to truth happens internally in some sense, that is, in one's imagination. In one of his last words on
plausibility, in the letter to Carus, Peirce gave plausibility an explicitly normative turn with the word
"ought": "By plausibility, I mean the degree to which a theory ought to recommend itself to
our belief independently of any kind of evidence other than our instinct urging us to regard it
favorably." (CP 8.223).
If Peirce was interested, as you suggest, in phaneroscopy in part because of
issues of evaluating our reasonings, then it would be in terms of how such
'feelings', or whatever they are, as plausibility and verisimilitude facilitate
and expedite investigation, - I guess I'd call that the 'right turn' - not
because of how they ultimately justify our reasonings and investigative methods
(what I meant by the 'wrong turn')1.
Best, Ben
On 8/23/2014 9:26 PM, Jeffrey Brian Downard wrote:
1) What is the standard that we can use when comparing the feeling that an
argument is a good inference to the feeling that an argument is an invalid
inference? Isn’t this similar in some respects to comparing the intensity of a
one experience of a feeling of blue to another feeling of blue? Isn’t it
different in other respects?
2) Once we have formed a class of sample arguments that we take to be good
and a class that we take to be bad, what kind of measurements can be made when
comparing these classes? At the very least, we can apply a nominal scale in
saying that they are labeled as different classes. For the sake of the logical
theory, however, we need a stronger standard of measurement, don’t we?
3) What is the standard for making the comparison of the goodness or
badness of an argument? Should we take it to be a prototypical argument that
appears to be beyond criticism? Perhaps we should take an argument, such as a
cogito argument, or an ontological argument for God’s reality, or an argument
for the indubitability of the axioms of logic as a prototype, and then place
one or another of these arguments in a glass case in Westminster. I suspect
that this would fail to serve the purpose we have in removing possible errors
from our measurements of the goodness or badness of any given argument.
How can the examples of measuring silk against a yardstick, comparing
biological specimens to a “type-specimen”, and comparing the weight of carbon
and gold to hydrogen help us think more clearly about the grounds we having for
comparing arguments and saying that one class contains a sample of good
inferences and that another class contains a sample of bad inferences. In
making such comparisons, we need something more than just a nominal assignment
of the term ‘good’ to one class and ‘bad’ to another. Having said that, don’t
we need more than an ordinal scale that enables us to make relative comparisons
of goodness and badness? How might we arrive in our theory of logic at a
standard of measuring the validity of inferences that is richer than a nominal
or ordinal scale? After all, we are relying on our standards for comparing
arguments for the sake of arriving at conclusions about what, really, is true
and false.
