Combining Texts

All the ideas for 'The Epistemology of Modality', 'The Search After Truth' and 'Grundlagen (Foundations of Theory of Manifolds)'

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5 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
15946 Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine]
     Full Idea: Cantor's development of set theory began with his discovery of the progression 0, 1, ....∞, ∞+1, ∞+2, ..∞x2, ∞x3, ...∞^2, ..∞^3, ...∞^∞, ...∞^∞^∞.....
     From: report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite VIII.2
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
15911 Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine]
     Full Idea: Ordinal numbers are generated by two principles: each ordinal has an immediate successor, and each unending sequence has an ordinal number as its limit (that is, an ordinal that is next after such a sequence).
     From: report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite III.4
8. Modes of Existence / B. Properties / 8. Properties as Modes
16669 Everything that exists is either a being, or some mode of a being [Malebranche]
     Full Idea: It is absolutely necessary that everything in the world be either a being or a mode [manière] of a being.
     From: Nicolas Malebranche (The Search After Truth [1675], III.2.8.ii), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 13.4
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
19440 How do you know you have conceived a thing deeply enough to assess its possibility? [Vaidya]
     Full Idea: The main issue with learning possibility from conceivability concerns how we can be confident that we have conceived things to the relevant level of depth required for the scenario to actually be a presentation or manifestation of a genuine possibility.
     From: Anand Vaidya (The Epistemology of Modality [2015], 1.2.2)
     A reaction: [He cites Van Inwagen 1998 for this idea] The point is that ignorant imagination can conceive of all sorts of absurd things which are seen to be impossible when enough information is available. We can hardly demand a criterion for this.
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
12726 In a true cause we see a necessary connection [Malebranche]
     Full Idea: A true cause is one in which the mind perceives a necessary connection between the cause and its effect.
     From: Nicolas Malebranche (The Search After Truth [1675], 1.649 (450)), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 5
     A reaction: Presumably Hume was ignorant of 'true' causes, since he says he never saw this connection. But then is the perception done by the mind, or by the senses?