Combining Texts

All the ideas for 'The Evolution of Modern Metaphysics', 'The Theory of Transfinite Numbers' and 'Basic Problems of Phenomenology'

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6 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
21959 Metaphysics is the most general attempt to make sense of things [Moore,AW]
     Full Idea: Metaphysics is the most general attempt to make sense of things.
     From: A.W. Moore (The Evolution of Modern Metaphysics [2012], Intro)
     A reaction: This is the first sentence of Moore's book, and a touchstone idea all the way through. It stands up well, because it says enough without committing to too much. I have to agree with it. It implies explanation as the key. I like generality too.
4. Formal Logic / F. Set Theory ST / 1. Set Theory
9616 A set is a collection into a whole of distinct objects of our intuition or thought [Cantor]
     Full Idea: A set is any collection into a whole M of definite, distinct objects m ... of our intuition or thought.
     From: George Cantor (The Theory of Transfinite Numbers [1897], p.85), quoted by James Robert Brown - Philosophy of Mathematics Ch.2
     A reaction: This is the original conception of a set, which hit trouble with Russell's Paradox. Cantor's original definition immediately invites thoughts about the status of vague objects.
5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
15571 The idea of an atemporal realm of validity is as implausible as medieval theology [Heidegger]
     Full Idea: The whole idea of an atemporal realm of validity is an invention that is no less doubtful than medieval speculation about angels.
     From: Martin Heidegger (Basic Problems of Phenomenology [1927], p.215), quoted by Richard Polt - Heidegger: an introduction 2 'Theory'
     A reaction: This seems to be flatly opposed to the view of Frege, and shows why continental philosophy has largely eschewed a study of logic. It is hard for a philosopher to pursue logic extensively without commitment to the Fregean Third Realm.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
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.
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
21958 Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW]
     Full Idea: Appearances in general are nothing outside our representations, which is just what we mean by transcendental ideality.
     From: A.W. Moore (The Evolution of Modern Metaphysics [2012], B535/A507)
23. Ethics / F. Existentialism / 6. Authentic Self
15581 Dasein is always only that which it has chosen to be [Heidegger]
     Full Idea: Dasein is always only that which it has chosen to be.
     From: Martin Heidegger (Basic Problems of Phenomenology [1927], p.278), quoted by Richard Polt - Heidegger: an introduction 3.§39-42
     A reaction: I take it as significant that this is what it 'has' chosen, and not what it now 'chooses'. I might accept that my mode of existence results from past choices, but certainly not that I can choose it now. Ossified brain.