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All the ideas for 'works', 'Russell' and 'Disquisitions'

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5 ideas

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism

6408	Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling]
	Full Idea: In order to deduce the theorems of mathematics from purely logical axioms, Russell had to add three new axioms to those of standards logic, which were: the axiom of infinity, the axiom of choice, and the axiom of reducibility.
	From: A.C. Grayling (Russell [1996], Ch.2)
	A reaction: The third one was adopted to avoid his 'barber' paradox, but many thinkers do not accept it. The interesting question is why anyone would 'accept' or 'reject' an axiom.

8. Modes of Existence / B. Properties / 8. Properties as Modes

16668	Modes of things exist in some way, without being full-blown substances [Gassendi]
	Full Idea: Modes are not nothing but something more than mere nothing; they are therefore 'res' of some kind, not substantial of course, but at least modal.
	From: Pierre Gassendi (Disquisitions [1644], II.3.4), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 260
	A reaction: This is the great modern atomist talking pure scholastic metaphysics. He's been reading Suárez. Gassendi seems to accept more than one type of existence.

12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence

6414	Two propositions might seem self-evident, but contradict one another [Grayling]
	Full Idea: Two propositions might contradict each other despite appearing self-evident when considered separately.
	From: A.C. Grayling (Russell [1996], Ch.2)
	A reaction: Russell's proposal (Idea 5416) is important here, that self-evidence comes in degrees. If self-evidence was all-or-nothing, Grayling's point would be a major problem, but it isn't. Bonjour explores the idea more fully (e.g. Idea 3704)

29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy

16713	Philosophers are the forefathers of heretics [Tertullian]
	Full Idea: Philosophers are the forefathers of heretics.
	From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2

29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism

6610	I believe because it is absurd [Tertullian]
	Full Idea: I believe because it is absurd ('Credo quia absurdum est').
	From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2
	A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though.