On 5/22/2018 1:22 PM, Jerry LR Chandler wrote:
Of particular interest is Venn’s views on the role of “=“ sign.
Copula? Or predicate?
Or, in view of symbolization of the modern logic of set theory,
should the “=“ sign be banned altogether?
Wittgenstein's answer in the Tractatus is simple: The notation
"x=y" is not a relation between two things. It just says that
'x' and 'y' are two names for the same thing.
With his existential graphs, Peirce represented full first-order
logic with equality without having any sign for equality: he just
connected two or more lines of identity.
With EGs, Peirce resolved the claims by Frege and Russell about
the supposed ambiguity of the word 'is'. See slide 26 below.
Re banning '=': There is no reason to ban anything. To use
Wittgenstein's (later) terminology, languages, natural or
artificial, can be used to play an open-ended variety of games.
For any pair of language games, there may be some subsets that
can be translated accurately, and other subsets that have no
accurate translation to the other.
John
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Slide 26 of http://jfsowa.com/talks/egintro.pdf
Translating the Word 'is' to Logic
Three different translations in the algebraic notation:
● Existence: There is x. iff ∃x
● Predication: x is a cat. iff Cat(x)
● Identity: x is y. iff x=y
Do these three translations imply that English is ambiguous?
Or is the algebraic notation too complex?
In EGs, all three uses of the word 'is' map to a line of identity:
● Existence: There is x. ↔ ▬
● Predication: x is a cat. ↔ ▬Cat
● Identity: x is y. ↔ ▬▬ (a ligature of two lines)
As Peirce said, EGs are more iconic than the algebraic notation:
they relate language to logic more clearly and directly.
Frege and Russell were misled by their notations.
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