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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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8207
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The quest for simplicity drove scientists to posit new entities, such as molecules in gases [Quine]
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Full Idea:
It is the quest for system and simplicity that has kept driving the scientist to posit further entities as values of his variables. By positing molecules, Boyles' law of gases could be assimilated into a general theory of bodies in motion.
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From:
Willard Quine (On Multiplying Entities [1974], p.262)
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A reaction:
Interesting that a desire for simplicity might lead to multiplications of entities. In fact, I presume molecules had been proposed elsewhere in science, and were adopted in gas-theory because they were thought to exist, not because simplicity is nice.
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8208
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In arithmetic, ratios, negatives, irrationals and imaginaries were created in order to generalise [Quine]
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Full Idea:
In classical arithmetic, ratios were posited to make division generally applicable, negative numbers to make subtraction generally applicable, and irrationals and finally imaginaries to make exponentiation generally applicable.
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From:
Willard Quine (On Multiplying Entities [1974], p.263)
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A reaction:
This is part of Quine's proposal (c.f. Idea 8207) that entities have to be multiplied in order to produce simplicity. He is speculating. Maybe they are proposed because they are just obvious, and the generality is a nice side-effect.
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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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