Re: Non-Implication

Re: Tom Gollier
(1) http://permalink.gmane.org/gmane.science.philosophy.peirce/8765
(2) http://permalink.gmane.org/gmane.science.philosophy.peirce/8794
Cf: http://diagrammaticthinking.blogspot.com/2012/10/non-implications.html

Tom,

Copying here what I wrote on your blog:

JA: I think he means "implies not", in other words, "excludes".

JA: Graphically speaking:

JA: (A ((B))) = (A B)

JA: This is what makes sense in terms of adding information
     to a term in order to make it more precise, which is the
     sense of "implication" that Peirce uses when he equates it
     with "information".

TG: Good to hear from you.  I'm not sure of your symbolism.
     Are you saying that for the implication, if X then Y,
     the non-implication is, X and not-Y? I do think that's
     a possibility, and I'll try to respond in more length
     on Peirce-L.

JA: That's a parenthetical rendition of Peirce's Alpha Graphs.

JA: A => B graphs as (A (B)), "Not A without B".

JA: A => ~B graphs as (A ((B))).

JA: Removing the double negation, we get (A B),
     which can be read as "Not both A and B",
     or "A and B are mutually exclusive".

JA: Venn diagrams are informative here.

I will look up a few passages from Peirce that tug at my mind
in this connection and elaborate if I can tonight or tomorrow.

Regards,

Jon

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