Combining Texts

Ideas for 'Function and Concept', 'What is Logic?' and 'The Problem of Empty Names'

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4 ideas

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

13837	With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking]
	Full Idea: My doctrine is that the peculiarity of the logical constants resides precisely in that given a certain pure notion of truth and consequence, all the desirable semantic properties of the constants are determined by their syntactic properties.
	From: Ian Hacking (What is Logic? [1979], §09)
	A reaction: He opposes this to Peacocke 1976, who claims that the logical connectives are essentially semantic in character, concerned with the preservation of truth.

5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic

13839	Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking]
	Full Idea: For some purposes the variables of first-order logic can be regarded as prepositions and place-holders that could in principle be dispensed with, say by a system of arrows indicating what places fall in the scope of which quantifier.
	From: Ian Hacking (What is Logic? [1979], §11)
	A reaction: I tend to think of variables as either pronouns, or as definite descriptions, or as temporary names, but not as prepositions. Must address this new idea...

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.