I have no background knowledge in logic so I am a little lost about where to begin.
This is the photo I am trying to learn about and it is from Frege’s Begriffsschrift.
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1Some clues here. en.wikipedia.org/wiki/Begriffsschrift#Notation_and_the_system– user4894Commented Sep 3, 2020 at 4:57
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4If you know which proposition this is from Mendelsohn has them rewritten in Begriffsschrift in Modern Notation. See also On Frege’s Begriffsschrift notation for propositional logic by Schlimm if you really want to learn it. But not even Frege himself used this notation afterwards.– ConifoldCommented Sep 3, 2020 at 5:08
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Great! Thank you.– user13772496Commented Sep 3, 2020 at 6:12
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1 Answer
The formula is used into the third part of Begriffsschrift (1879), regarding the General theory of sequences, not translated in modern symbols by Mendelsohn.
You have to look at: G.Landini, Frege’s Notations: What They Are and How They Mean (2012).
The basic component of the complex formula is the "gamma-on-beta of f(x,y)" symbol.
It is defined in §27 (formula 76): it is used to symbolize the ancestral relation for objects and reads:
"x follows y in the f-sequence".
The snippet depicts the substitution used in the derivation of Th.(132): the last but one theorem.
Formula (132) is derived from previous formula (131) using the propositional law (9) [see Mendelshon's translation in modern symbols]:
(c ⊃ b) ⊃ ((b ⊃ a) ⊃ (c ⊃ a)).
The "complex" formulas on the right of the snippet must be substituted in place of a,c,b respectively and (132) follows from (131) by detachment.
A very useful brief explanation of this part of Frege's work with the "modern reconstruction" of the proof of (132) and (133) is: George Boolos, Reading the Begriffsschrift (Mind, 1985).
answered Sep 3, 2020 at 8:06
