15896
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Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]
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Full Idea:
Cantor grafted the Power Set axiom onto his theory when he needed it to incorporate the real numbers, ...but his theory was supposed to be theory of collections that can be counted, but he didn't know how to count the new collections.
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From:
report of George Cantor (The Theory of Transfinite Numbers [1897]) by Shaughan Lavine - Understanding the Infinite I
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A reaction:
I take this to refer to the countability of the sets, rather than the members of the sets. Lavine notes that counting was Cantor's key principle, but he now had to abandon it. Zermelo came to the rescue.
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8375
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'Necessary' is a predicate of a propositional function, saying it is true for all values of its argument [Russell]
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Full Idea:
'Necessary' is a predicate of a propositional function, meaning that it is true for all possible values of its argument or arguments. Thus 'If x is a man, x is mortal' is necessary, because it is true for any possible value of x.
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From:
Bertrand Russell (On the Notion of Cause [1912], p.175)
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A reaction:
This is presumably the intermediate definition of necessity, prior to modern talk of possible worlds. Since it is a predicate about functions, it is presumably a metalinguistic concept, like the semantic concept of truth.
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7903
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The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
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Full Idea:
The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
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From:
Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
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A reaction:
What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').
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4396
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The law of causality is a source of confusion, and should be dropped from philosophy [Russell]
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Full Idea:
The law of causality, I believe, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm.
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From:
Bertrand Russell (On the Notion of Cause [1912], p.173)
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A reaction:
A bold proposal which should be taken seriously. However, if we drop it from scientific explanation, we may well find ourselves permanently stuck with it in 'folk' explanation. What is the alternative?
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8379
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In causal laws, 'events' must recur, so they have to be universals, not particulars [Russell]
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Full Idea:
An 'event' (in a statement of the 'law of causation') is intended to be something that is likely to recur, since otherwise the law becomes trivial. It follows that an 'event' is not some particular, but a universal of which there may be many instances.
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From:
Bertrand Russell (On the Notion of Cause [1912], p.179)
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A reaction:
I am very struck by this. It may be a key insight into understanding what a law of nature actually is. It doesn't follow that we must be realists about universals, but the process of abstraction from particulars is at the heart of generalisation.
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