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16150
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One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato]
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Full Idea:
If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it.
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From:
Plato (Parmenides [c.364 BCE], 144a)
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A reaction:
This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed.
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6424
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Formalists say maths is merely conventional marks on paper, like the arbitrary rules of chess [Russell]
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Full Idea:
The Formalists, led by Hilbert, maintain that arithmetic symbols are merely marks on paper, devoid of meaning, and that arithmetic consists of certain arbitrary rules, like the rules of chess, by which these marks can be manipulated.
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From:
Bertrand Russell (My Philosophical Development [1959], Ch.10)
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A reaction:
I just don't believe that maths is arbitrary, and this view pushes me into the arms of the empiricists, who say maths is far more likely to arise from experience than from arbitrary convention. The key to maths is patterns.
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6425
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Formalism can't apply numbers to reality, so it is an evasion [Russell]
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Full Idea:
Formalism is perfectly adequate for doing sums, but not for the application of number, such as the simple statement 'there are three men in this room', so it must be regarded as an unsatisfactory evasion.
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From:
Bertrand Russell (My Philosophical Development [1959], Ch.10)
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A reaction:
This seems to me a powerful and simple objection. The foundation of arithmetic is that there are three men in the room, not that one plus two is three. Three men and three ties make a pattern, which we call 'three'.
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