Dear Frederik, lists,
In your example, (A) 'Something is blue AND round' and (B) 'Something is
blue AND something is round' are indeed non-equivalent in standard
logic. (A) implies but is not implied by (B), so that does not seem to
be what raises the question for Peirce. What troubles him is the
equivalence between (C) 'Something is blue OR round' and (D) 'Something
is blue OR something is round' in standard logic, and that's where the
question becomes more evident. It's a situation where there seem two
things regarding which it doesn't matter whether they are connected by a
line of identity or not.
That irrelevance of connection certainly threw me for a loop when I
first saw it (and I'm generally rusty anyway). One can explain it away:
language is inexact; alternatives among cases, although spatially
diagrammed, are not really spatial; and shouldn't deduction in logic,
typically from whole to parts, be prized for results that give the
premisses a new and even counter-intuitive aspect? and so on. It seems
Peirce's way not to let matters rest there, but to set out in search of
something that one was maybe not so wrong-headed to expect after all;
looking at rearrangements of Barbara, he saw not only induction but
abduction.
I just looked up Hintikka's IF (independence-friendly) logic that you
mentioned, and branching quantifiers do seem like something that would
have interested Peirce in the above context.
Best, Ben
On 1/17/2015 11:43 PM, Frederik Stjernfelt wrote:
Dear Ben -
The Gamma graph paper where P discusses these things is pretty late
(1908) - I do not think he ever finalizes this revision. But of
course, giving up the "strange rule" is equivalent with Beta becoming
different from FOL with rules of passage (as the strange rule is such
a rule).
Ahti Pietarinen has argued that Peirce here anticipates Hintikka's
IF-logic with independent quantifiers.
The question becomes more evident with existential quantification, is
it not? - the non-equivalence of "X is blue and Y is round" and "X is
blue and round".
Best
F
Den 18/01/2015 kl. 04.38 skrev Benjamin Udell <bud...@nyc.rr.com
<mailto:bud...@nyc.rr.com> >
:
Dear Frederik, lists,
Thank you. My questions are: does Peirce revise the Beta graph system
to remove the "strange rule", and wouldn't that render the Beta graph
system non-equivalent to first-order logic? Or is it only the Gamma
graph system that's affected? If he did revise the Beta system
accordingly, then how is one to think of 'all is blue and round' as
differing in meaning from 'all is blue and all is round' ?
Best, Ben
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