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All the ideas for 'Letters to Antoine Arnauld', 'Russell' and 'Review: Meinong 'Untersuchungen zur..''

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6 ideas

1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis

21546	We can't sharply distinguish variables, domains and values, if symbols frighten us [Russell]
	Full Idea: Whoever is afraid of symbols can hardly hope to acquire exact ideas where it is necessary to distinguish 1) the variable in itself as opposed to its value, 2) any value of the variable, 3) all values, 4) some value.
	From: Bertrand Russell (Review: Meinong 'Untersuchungen zur..' [1905], p.84)
	A reaction: Not the best example, perhaps, of the need for precision, but a nice illustration of the new attitude Russell brought into philosophy.

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

21963	It is possible that an omnipotent God might make one and two fail to equal three [Descartes]
	Full Idea: Since every basic truth depends on God's omnipotence, I would not dare to say that God cannot make it....that one and two should not be three.
	From: René Descartes (Letters to Antoine Arnauld [1645]), quoted by A.W. Moore - The Evolution of Modern Metaphysics 01.3
	A reaction: An unusual view. Most people would say that if Descartes can doubt something that simple, he should also doubt his reasons for believing in God's existence.

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.

9. Objects / A. Existence of Objects / 4. Impossible objects

21531	Common sense agrees with Meinong (rather than Russell) that 'Pegasus is a flying horse' is true [Lackey on Russell]
	Full Idea: Meinong's theory says that 'Pegasus is a flying horse' is true, while Russell's says that this assertion is false. The average man, if he knows his mythology, would probably agree with Meinong.
	From: comment on Bertrand Russell (Review: Meinong 'Untersuchungen zur..' [1905]) by Douglas Lackey - Intros to Russell's 'Essays in Analysis' p.19
	A reaction: It seems obvious that some disambiguation is needed here. Assenting to that assertion would be blatantly contextual. No one backs Pegasus at a race track.

21545	I prefer to deny round squares, and deal with the difficulties by the theory of denoting [Russell]
	Full Idea: I should prefer to say that there is no such object as 'the round square'. The difficulties of excluding such objects can, I think, be avoided by the theory of denoting.
	From: Bertrand Russell (Review: Meinong 'Untersuchungen zur..' [1905], p.81)
	A reaction: The 'theory of denoting' is his brand new theory of definite descriptions, which makes implicit claims of existence explicit, so that they can be judged. Why can't we just say that a round square can be an intentional object, but not a real object?

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)