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.
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