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Ideas for 'fragments/reports', 'Mathematical Thought from Ancient to Modern Times' and 'First-Order Modal Logic'

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5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction

9725	'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn]
	Full Idea: 'Predicate abstraction' is a key idea. It is a syntactic mechanism for abstracting a predicate from a formula, providing a scoping mechanism for constants and function symbols similar to that provided for variables by quantifiers.
	From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], Pref)

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation

17606	Axioms reveal the underlying assumptions, and reveal relationships between different areas [Kline]
	Full Idea: The axiomatic method ....revealed precisely what assumptions underlie each branch [of mathematics] and made possible the comparison and clarification of the relationships of various branches.
	From: Morris Kline (Mathematical Thought from Ancient to Modern Times [1972], p.1027), quoted by Penelope Maddy - Defending the Axioms 1.3
	A reaction: I take this to be the 'fruitfulness' which marks out the discovery of the essence of something.