Gary F., list,
Thanks for catching my typo!
Yours and my readings of the "corrected" graph are equivalent. 'Not both
non-A & non-B' is equivalent to 'A or B'.
The strange rule really isn't so strange. In CP 4.569 Peirce (without
calling it the 'strange rule') says: "The logical Principle is that 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." In other words, 'there is something round or
blue' is equivalent to 'there is something round or there is something
blue'. It seems kind of strange because in the first case one seems to
mention one individual thing, while in the second case one seems to
mention possibly two things. But they have to be equivalent since their
respective negations are obviously equivalent: 'there is nothing round
or blue' is equivalent to 'there is nothing round and there is nothing
blue.'
Since the material (a.k.a. _/de inesse/_) conditional is just another
kind of alternative a.k.a. disjunction, the same thing happens, where
one seems to talk of just one thing and equivalently about possibly two
things, and that's what bothers Peirce. The 'if...then...' phrasing
makes it more confusing (and starts me thinking of 'a certain' rather
than 'one or another'). This seems really so typical of deductive logic
when focused on structures of alternatives (and I've noticed it in some
probability problems too, very simple ones, the kind that I'm capable of
dealing with). It can be very difficult to keep from reading more into
the intended austere formulation than is strictly there, but on the
other hand if one doesn't try to see more, then one doesn't see
possibilities as Peirce did, such as rearranging Barbara to see other
modes of inference.
Best, Ben
On 2/14/2015 4:12 PM, Gary Fuhrman wrote:
Ben,
I’ve been trying to disentangle some of the same knots you’re working
on here, but you’ve been one step ahead of me (if not two or three)
all along; some local busyness here has kept me from digging further
into the “Prolegomena” and the Roberts book as I’d like to. I keep
coming back to the Prolegomena, and it seems a bit less opaque each
time, but i still have a hard time reading EGs. Just a couple of
remarks on your investigation:
The passage in Roberts that you cite starts on p. 103, not 109.
As for Peirce’s “corrected” graph (Roberts Fig. 14, but it looks a bit
different there):
my tentative reading of it is: “There is someone who is not both (a)
the wife of a husband who does not fail and (b) a suicide.” That’s
reading a graph of teridentity which has its three-way junction on the
/verso/ (I’m assuming that the shading here indicates the verso). This
seems different from your reading, and maybe that of Roberts too, but
I’m not at all sure it’s right. The whole issue (including its
relation to the “strange rule”) is still unclear to me, and I think
I’ll have to come back to it later as I have so many times to the
Prolegomena already. EGs seem to do that to me. :-\
(That last comment is iconic, but not optimally … )
gary f.
*From:* Benjamin Udell
*Sent:* 13-Feb-15 4:19 PM
*To:* [email protected]
*Subject:* Re: [PEIRCE-L] Peirce in 1913 on existential graphs
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