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Ideas for 'What is Logic?st1=Ian Hacking', 'The Development of Logic' and 'Grundlagen (Foundations of Theory of Manifolds)'

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2 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...