21546
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We can't sharply distinguish variables, domains and values, if symbols frighten us [Russell]
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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.
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From:
Bertrand Russell (Review: Meinong 'Untersuchungen zur..' [1905], p.84)
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A reaction:
Not the best example, perhaps, of the need for precision, but a nice illustration of the new attitude Russell brought into philosophy.
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6408
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Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling]
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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.
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From:
A.C. Grayling (Russell [1996], Ch.2)
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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.
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21545
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I prefer to deny round squares, and deal with the difficulties by the theory of denoting [Russell]
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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.
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From:
Bertrand Russell (Review: Meinong 'Untersuchungen zur..' [1905], p.81)
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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?
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