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Ideas for 'Function and Concept', 'The Anti-Christ' and 'Notebooks 1914-1916'

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4 ideas

5. Theory of Logic / E. Structures of Logic / 1. Logical Form

18276	A statement's logical form derives entirely from its constituents [Wittgenstein]
	Full Idea: The logical form of the statement must already be given in the forms of its constituents.
	From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 23e)
	A reaction: This would evidently require each constituent to have a 'logical form'. It is hard to see what that could beyond its part of speech. Do two common nouns have the same logical form?

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

6563	'And' and 'not' are non-referring terms, which do not represent anything [Wittgenstein, by Fogelin]
	Full Idea: Wittgenstein's 'fundamental idea' is that the 'and' and 'not' which guarantee the truth of "not p and not-p" are meaningful, but do not get their meaning by representing or standing for or referring to some kind of entity; they are non-referring terms.
	From: report of Ludwig Wittgenstein (Notebooks 1914-1916 [1915], §37) by Robert Fogelin - Walking the Tightrope of Reason Ch.1
	A reaction: Wittgenstein then defines the terms using truth tables, to show what they do, rather than what they stand for. This seems to me to be a candidate for the single most important idea in the history of the philosophy of logic.

5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic

8490	First-level functions have objects as arguments; second-level functions take functions as arguments [Frege]
	Full Idea: Just as functions are fundamentally different from objects, so also functions whose arguments are and must be functions are fundamentally different from functions whose arguments are objects. The latter are first-level, the former second-level, functions.
	From: Gottlob Frege (Function and Concept [1891], p.38)
	A reaction: In 1884 he called it 'second-order'. This is the standard distinction between first- and second-order logic. The first quantifies over objects, the second over intensional entities such as properties and propositions.

5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic

8492	Relations are functions with two arguments [Frege]
	Full Idea: Functions of one argument are concepts; functions of two arguments are relations.
	From: Gottlob Frege (Function and Concept [1891], p.39)
	A reaction: Nowadays we would say 'two or more'. Another interesting move in the aim of analytic philosophy to reduce the puzzling features of the world to mathematical logic. There is, of course, rather more to some relations than being two-argument functions.