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Ideas for 'The Fixation of Belief', 'Logical Consequence' and 'Philosophy of Mathematics'

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2 ideas

5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic

23447	In classical semantics singular terms refer, and quantifiers range over domains [Linnebo]
	Full Idea: In classical semantics the function of singular terms is to refer, and that of quantifiers, to range over appropriate domains of entities.
	From: Øystein Linnebo (Philosophy of Mathematics [2017], 7.1)

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth

10696	A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall]
	Full Idea: If a conclusion follows from an empty collection of premises, it is true by logic alone, and is a 'logical truth' (sometimes a 'tautology'), or, in the proof-centred approach, 'theorems'.
	From: JC Beall / G Restall (Logical Consequence [2005], 4)
	A reaction: These truths are written as following from the empty set Φ. They are just implications derived from the axioms and the rules.