9145
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We form the image of a cardinal number by a double abstraction, from the elements and from their order [Cantor]
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Full Idea:
We call 'cardinal number' the general concept which, by means of our active faculty of thought, arises when we make abstraction from an aggregate of its various elements, and of their order. From this double abstraction the number is an image in our mind.
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From:
George Cantor (Beitrage [1915], §1), quoted by Kit Fine - Cantorian Abstraction: Recon. and Defence Intro
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A reaction:
[compressed] This is the great Cantor, creator of set theory, endorsing the traditional abstractionism which Frege and his followers so despise. Fine offers a defence of it. The Frege view is platonist, because it refuses to connect numbers to the world.
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21379
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Man's three basic ethical incentives are egoism, malice and compassion [Schopenhauer]
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Full Idea:
Man's three fundamental ethical incentives, egoism, malice and compassion, are present in everyone in different and incredibly unequal proportions. In accordance with them, motives will operate on man and actions will ensue.
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From:
Arthur Schopenhauer (On the Basis of Morality [1841], p.192), quoted by Christopher Janaway - Schopenhauer 7 'Egoism'
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A reaction:
A well chosen trio. Kant would be shocked that he has left out duty, which is supposed to rise above such feelings.
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21376
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Philosophy treats animals as exploitable things, ignoring the significance of their lives [Schopenhauer]
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Full Idea:
In philosophical morals animals are mere 'things', mere means to any end whatsoever. ...Shame on such a morality, that fails to recognise the eternal essence that lives in every living thing, and shines forth with inscrutable significance from all eyes.
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From:
Arthur Schopenhauer (On the Basis of Morality [1841], p.96), quoted by Christopher Janaway - Schopenhauer 7 'Against'
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A reaction:
Good. I find Kant's theoretical indifference to animals very creepy (despite his kind attitude to them). And I also think the utilitarians are wrong to only value animals for their pain, as if any animal could be shredded for fun, if it felt no pain.
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