This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1912 Excerpt: ...other collections, such as cricket elevens. Hence the number 12 is neither a collection of twelve terms, nor is it something which all collections have in common; and number in general is a property of 12 or 11 or any other number, but not of the various collections that have twelve terms or eleven terms. Hence when, ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1912 Excerpt: ...other collections, such as cricket elevens. Hence the number 12 is neither a collection of twelve terms, nor is it something which all collections have in common; and number in general is a property of 12 or 11 or any other number, but not of the various collections that have twelve terms or eleven terms. Hence when, following Bergson's advice, we "have recourse to an extended image" and picture, say, twelve dots such as are obtained by throwing double sixes at dice, we have still not obtained a picture of the number 12. The number 12, in fact, is something more abstract than any picture. Before we can be said to have any understanding of the number 12, we must know what different collections of twelve units have in common, and this is something which cannot be pictured because it is abstract. Bergson only succeeds in making his theory of number plausible by confusing a particular collection with the number of its terms, and this again with number in general. The confusion is the same as if we confused a particular young man with youth, and youth with the general concept "period of human life," and were then to argue that because a young man has two legs, youth must have two legs, and the general concept "period of human life" must have two legs. The confusion is important because, as soon as it is perceived, the theory that number or particular numbers can be pictured in space is seen to be untenable. This not only disproves Bergson's theory as to number, but also his more general theory that all abstract ideas and all logic are derived from space; for the abstract 12, the common property of all dozens as opposed to any particular dozen, though it is never present to his mind, is obviously conceivable and obviously capable of ...
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