ONT Re: Implication
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Stanley N. Salthe wrote:
>
> to Jon Awbrey from Stan Salthe, re: implicatiion
>
> You said:
> >
> > Implication | (X (Y)) | (X (Z)) | (Y (Z)) |
> > | X=>Y | X=>Z | Y=>Z |
>
> I guess I am misinterpreting your symbols, but I suppose X => Y would
> seem to mean X implies Y. But in the definition we have (X (Y)), which
> seems to put Y as a subset of X. In that case Y would imply X, not the
> other way round.
>
> STAN
Stan,
I am using here a character string version of CSP's Existential Graphs (ExG).
In the "alpha part" of ExG (tantamount to what we call propositional calculus,
sentential logic, or "zeroth order logic" (ZOL)), Peirce wrote propositions,
or the symbols thereof, on an initially blank page of paper called the
"sheet of assertion" (SA), that all by itself has a value of "true".
To scribe a number of propositional expressions on the same SA is
a way to form their logical conjunction. To circumscribe a "cut"
around a propositional expression is a way to form its negation.
These two primitive operations are enough to generate all of
the rest of the logical connectives among any k propositions.
In text form, one transcribes these two operations by means
of concatenation and parenthesization: for example, we have
the readings "A B C" = "A and B and C", while "(A)" = "not A".
So then, "((A)(B)(C))" = "A or B or C", and "(A (B))", which is
readable as "not A without B", has the same meaning as "A => B".
From Peirce's initial system of logical graphs, I have developed
what I call the "reflective extension of logical graphs" (RefLog),
which I use in all of my fundamental logical work, and for which
I wrote a package of computational parsers, processors, and tools.
More anon,
Jon
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