Dear Frederik, lists,
Thank you, and I agree with most of your comments, especially for
example "...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 [....]". Peirce was always that way about seeing beyond the
given formalism. He looked at reorderings of the deductive Barbara
syllogism and saw not merely invalid deductions but inductive and
abductive modes of inference and this cohered with his view that all
mental action has the _/form/_, at least, of valid inference (though
sometimes mistaking itself as to which kind of inference it is).
I hesitate at the thought (and you don't say this) that one needs to use
as theoretical basis, rather than merely take suggestion from, the idea
of the material ontological real possibility of some wife committing
suicide if HER husband goes bankrupt. The problem here seems to be to
get the logic to say that the suicide is a wife in the same marriage as
a bankrupt husband. Now imagine if mathematics of optimization,
probability, and information were unable to find ways to express such
conditions. In Peirce's system, all three of those fields will belong,
as philosophically applied mathematics, in philosophical deductive
logic, prior to ontology, if, as seems the case from Peirce's writings,
probability theory ('doctrine of chances') does. All of them involve
timelike and at least quasi-modal perspectives.
I suppose set theory gets around these problems of reference to the
_/same/_ marriage, but of course I don't know. Sticking to 1st-order logic:
We call marriage in the example a unique relation, etc., but the logical
formalism (in my previous posts' examples and in Peirce's existential
graphs) doesn't notationally express that; one has to remember it as an
added constraint. When I did my expansion into individual cases, I
forgot about it.
So let me interrupt myself here to make a correction. Of the eight
disjunct propositions, there were two sets of four such that each set
excluded the other set. I should added for clarity's sake, as I do in
dark red below (although it's already implied by the monogamy of
predicate constant '/W/', 'are wife and husband together'; and with the
subject constants /e/=Edith, /f/=Fanny, /g/=Gerald, /h/=Harold, in a
four-person universe):
*[*~/Weh/ & ~/Wfg/ &
([/Weg/ & ~/Bg/] *∨* [/Weg/ & /Se/] *∨*
[/Wfh/ & ~/Bh/] *∨* [/Wfh/ & /Sf/])*]*
*∨*
*[*~/Wef/ & ~/Wfh/ &
([/Weh/ & ~/Bh/] *∨* [/Weh/ & /Se/] *∨*
[/Wfg/ & ~/Bg/] *∨* [/Wfg/ & /Sf/])*]*
So one does not escape the 'strange rule' here - one could still end up
with /Weg/ & /Bg/ & /~Se/ & /Wfh/ & ~/Bh/ & /Sf/, but things are a
little more complicated, it's not quite the free-for-all of mixed
alternatives that it seems when one omits to mention that (~/Weh/ &
~/Wfg/) *∨* (~/Weg/ & ~/Wfg/).
Anyway, if we said that there are /x,y/ in _/a certain/_, specific
marriage relation /W/₁ which might be properly named but for which we
just use the predicate '/W/₁', then does the "strange rule" problem go
away? My guess is that it doesn't go away unless saying '/W/₁/xy/'
amounts to identifying /x,y/ with certain specific individuals such as
/e, g/ (Edith, Gerald). Not being a logician, I'd better stop here!
Best, Ben
On 3/9/2015 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
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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