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Ideas for 'Metaphysics', 'Letters to Leibniz' and 'Penguin Dictionary of Philosophy'

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3 ideas

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL

562	Axioms are the underlying principles of everything, and who but the philosopher can assess their truth? [Aristotle]
	Full Idea: Axioms are more general, and the principles of all things. If this does not belong to the philosopher, who else will have the job of considering truth and falsity in their case?
	From: Aristotle (Metaphysics [c.324 BCE], 0997a09)

573	The axioms of mathematics are part of philosophy [Aristotle]
	Full Idea: A single science, that of the philosopher, also covers the axioms of mathematics.
	From: Aristotle (Metaphysics [c.324 BCE], 1005a15)

4. Formal Logic / E. Nonclassical Logics / 4. Fuzzy Logic

6888	Fuzzy logic is based on the notion that there can be membership of a set to some degree [Mautner]
	Full Idea: Fuzzy logic is based upon fuzzy set-theory, in which the simple notion of membership of a set is replaced by a notion of membership to some degree.
	From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.214)
	A reaction: The idea that something could be to some degree a 'heap of sand' sounds plausible, but Williamson and Sorensen claim that the vagueness is all in us (i.e. it is epistemological), and not in the world. This will scupper fuzzy logic.