Combining Texts

Ideas for 'On the Question of Absolute Undecidability', 'Mathematical Thought from Ancient to Modern Times' and 'The Secret Connexion'

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2 ideas

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.

5. Theory of Logic / K. Features of Logics / 5. Incompleteness

17894	We have no argument to show a statement is absolutely undecidable [Koellner]
	Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable.
	From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3)