Dear Frederick, lists,
Frederik's recent post (see below) touches again on the problematic
fact that FOL sanctions the bad argument from 1 to 2:
1. There is some married woman who will suicide if her husband fails.
2. If every married man fails then some married woman will suicide.
The Peircean diagnosis is FOL's principle according to which to say
that "there is some one individual of which one or other of two
predicates is true is no more than to say that there either is some
individual of which one is true or else there is some individual of
which the other is true." (CP 4.569, NP 224-25)
A remedy in response to this diagnosis is to suppose, contrary to the
problematic logical principle, that an individual, call it "a", can be
such that for some predicate "F" it is true that a is F or not F,
while it is false that a is F and false that a is not F. On this
remedy the universe of discourse contains such (at least partially)
indeterminate individuals.
Suppose the married woman referred to in 1 and 2 is partially
indeterminate in the following way. It is true that she will suicide
if her husband fails, but on the basis of the failure of all married
men, she has no disposition to suicide and no disposition to refrain
from suicide . In case of such large scale failure she might grow to
have one or the other disposition; perhaps she would be influenced by
what suicides occur among the other wives. But this partially
indeterminate married woman is such that, if every married man fails,
then she will or will not suicide, and yet it is false that she will
suicide and false that she will not suicide.
Given this remedy, 1 is true and 2 is false and the argument from 1 to
2 can be properly classified as invalid.
On this approach, logical theory is changed by partially suspending
the law of excluded middle. There is no change in the propositional
logic truth table interpretation of the conditional. In this way it
departs from Frederik's interpretation. (NP 225)
However it resembles Frederick's interpretation in recognizing that
the logical remedy has an "ontological correlate." (NP 225) Besides
fully determinate individuals, there must be some which are at least
partially indeterminate. There may be a closer resemblance, if
natural classes can be construed as partially indeterminate individuals.
An indeterminate individual in the sense used here may be what Peirce
finds in "the old logics" and calls an "individuum vagum." (CP
3.92-94) In this case Ben's recent posts in connection with this CP
text would be brought into more explicit connection with NP by
recognizing the connection between the individuum vagum and the
bankruptcy/suicide problem.
Reference to indeterminate individuals construed as subjects of a
disjunctive predicate, e.g. "F or not F", but where it doesn't follow
that the subject is F or that it is not F, resemble some accounts of
"merely confused supposition" which appear in medieval logic in the
13th century and thereafter. So the remedy I've sketched may add to
the story of Peirce's association with Scotus.
My characterization of indeterminate individuals is based on Richard
Smyth's work. ( _Reading Peirce Reading_, especially pp. 151-68) As
far as I know he did not explicitly apply his analysis to the bankrupt/
suicide problem, but what he does say about this problem seems to
invite the application. (RPR 95-96) So my suggested remedy may have
importance for those with an interest in his work.
There are several ways, then, in which the remedy I've sketched might
be worth consideration. Others will know where it needs correction or
whether it needs to be bypassed, having been put forward and assessed
already but in a form I haven't recognized. I would very much
appreciate any comments which bring such shortcomings to light.
Best,
Charles Murray
On Mar 9, 2015, at 8:16 PM, Frederik Stjernfelt wrote:
Dear Ben, lists,
I strongly appreciate the persistent work Ben has been doing in
tracing out, over many postings, the implications of Peirce's
problems with the "strange rule". I think Ben is quite correct in
locating the ambiguity in the quantifier "some", taken to mean
sometimes "a certain one", sometimes "some - one or several".
But I think there may lie a further reason behind this - linked to
Ben's reinterpretation in terms of modal logic where a necessity
operator distinguishes the two cases otherwise identified by the
"strange rule". When introducing his discussion of the "strange
rule" in the April 1906 note, Peirce connects it to a modal
observation: " … I soon discovered, upon a critical analysis, that
it was absolutely necessary to insist upon and bring to the front,
the truth that a mere possibility may be quite real." Why does he do
that, as the bankruptcy-suicide inference is ordinary first order
logic without any modal semantics on the surface? I think it is
because what Peirce would like to catch is the meaning of that
sentence (taken in ordinary language) that there is a causal-
tendency link between the bankruptcy of husbands and the suicides of
their wives. So that the wife-suicide is a "real possibility"
actualized by the husband-bankruptcy. This is obviously indicated by
saying that a "certain one" wife commits suicide if HER husband etc.
This is not full necessity, but "real possibility" (because other
wives with bankrupt husbands may escape suicide even if threatened
by it as a real possibility). So - I think - Peirce's idea is that
the strange rule equates the "mere possibility" of "There is some
married woman who will commit suicide in case A husband fails in
business." with the real possibility in the claim connecting the
two: "There is some married woman who will commit suicide in case
HER husband fails in business." - which he did not like because he
wanted to distinguish those two types of possibilities.
Of course, real possibility is not logic, it is material ontology
not even captured by standard modal logic.
As Ben rightly indicated, this unease comes from reading more
(ordinary language) meaning into logical expressions than their
formal definition allows for. But simultaneously, this excessive
meaning is scientifically important - the mature Peirce, after 1897,
seeing "real possibilities" as implied by scientific laws,
regularities, tendencies, patterns etc., regarding how certain
predicates, more or less strongly, determine others. This can not be
logically expressed in any simple way, and I think that was what
tormented Peirce …
Best
F
Den 18/02/2015 kl. 15.41 skrev Benjamin Udell <bud...@nyc.rr.com>:
Peirce said "there is some one individual of which one or other of
two predicates is true" ABOUT a specific proposition that he was
discussing. So you need to read that specific proposition in order
to understand what Peirce meant by "there is some one individual"
etc.: "There is some married woman who will commit suicide in case
her husband fails in business." which, Peirce finds, turns out to
be equivalent to "if every married man fails in business some
married woman will commit suicide".
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