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Ideas for 'Metaphysics', 'Mad Pain and Martian Pain' and 'Apriority and Existence'

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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 / D. Modal Logic ML / 4. Alethic Modal Logic

8859	The main modal logics disagree over three key formulae [Yablo]
	Full Idea: Lewis's different systems of modal logic differed about such formulae as □P implies □□P; ◊□P implies □P; and ◊S implies □◊S
	From: Stephen Yablo (Apriority and Existence [2000], §06)
	A reaction: Yablo's point is that the various version don't seem to make much difference to our practices in logic, mathematics and science. The problem, says Yablo, is deciding exactly what you mean by 'necessarily' and 'possibly'.