|
15896
|
Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]
|
|
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.
|
|
From:
report of George Cantor (The Theory of Transfinite Numbers [1897]) by Shaughan Lavine - Understanding the Infinite I
|
|
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.
|
|
12741
|
If experience is just a dream, it is still real enough if critical reason is never deceived [Leibniz]
|
|
Full Idea:
Even if this whole life were said to be only a dream, and the visible world only a phantasm, I should call this dream or phantasm real enough if we were never deceived by it when we make good use of reason.
|
|
From:
Gottfried Leibniz (De modo distinguendi phaenomena [1685], A6.4.1502), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 7
|
|
A reaction:
I find this response more satisfactory than his response in Idea 12740. As a supporter of the coherence account of justification, I take the closest we get to knowledge to be when our full critical faculties and experience are brought to bear, and shared.
|
|
12740
|
The strongest criterion that phenomena show reality is success in prediction [Leibniz]
|
|
Full Idea:
The most powerful criterion of the reality of phenomena, sufficient even by itself, is success in predicting future phenomena from past and present ones.
|
|
From:
Gottfried Leibniz (De modo distinguendi phaenomena [1685], A6.4.1502), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 7
|
|
A reaction:
I would say that this is clutching at straws, as there is no reason at all to deny that dreams could be thoroughly coherent and predictable in their events. We must just live with these doubts, not try to defeat them.
|
|
12721
|
Light, heat and colour are apparent qualities, and so are motion, figure and extension [Leibniz]
|
|
Full Idea:
Concerning bodies I can demonstrate that not merely light, heat, color, and similar qualities are apparent but also motion, figure, and extension.
|
|
From:
Gottfried Leibniz (De modo distinguendi phaenomena [1685], A6.4.1504), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 4
|
|
A reaction:
Leibniz is not consistent on this. Here he is flirting with idealism, but he often backs away from that. In Discourse §12 he makes secondary qualities certainly subjective, and primary qualities possibly so. He admits the primaries contain eternal truths.
|