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All the ideas for '', 'Set Theory and the Continuum Hypothesis' and 'At the Existentialist Caf'

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7 ideas

1. Philosophy / H. Continental Philosophy / 2. Phenomenology
Later phenomenologists tried hard to incorporate social relationships [Bakewell]
     Full Idea: Ever since Husserl, phenomenologists and existentialists had been trying to stretch the definition of existence to incorporate our social lives and relationships.
     From: Sarah Bakewell (At the Existentialist Café [2016], 08)
     A reaction: I see a parallel move in Wittgenstein's Private Language Argument. Husserl's later work seems to have been along those lines. Putnam's Twin Earth too.
Phenomenology begins from the immediate, rather than from axioms and theories [Bakewell]
     Full Idea: Traditional philosophy often started with abstract axioms or theories, but the German phenomenologists went straight for life as they experienced it, moment to moment.
     From: Sarah Bakewell (At the Existentialist Café [2016], 01)
     A reaction: Bakewell gives this as the gist of what Aron said to Sartre in 1933, providing the bridge from phenomenology to existentialism. The obvious thought is that everybody outside philosophy starts from immediate experience, so why is this philosophy?
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
     Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation.
     From: Ian Rumfitt ("Yes" and "No" [2000], II)
     A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts.
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
     Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table.
     From: Ian Rumfitt ("Yes" and "No" [2000])
     A reaction: This is the standard view which Rumfitt sets out to challenge.
The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
     Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious.
     From: Ian Rumfitt ("Yes" and "No" [2000], III)
     A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
We could accept the integers as primitive, then use sets to construct the rest [Cohen]
     Full Idea: A very reasonable position would be to accept the integers as primitive entities and then use sets to form higher entities.
     From: Paul J. Cohen (Set Theory and the Continuum Hypothesis [1966], 5.4), quoted by Oliver,A/Smiley,T - What are Sets and What are they For?
     A reaction: I find this very appealing, and the authority of this major mathematician adds support. I would say, though, that the integers are not 'primitive', but pick out (in abstraction) consistent features of the natural world.
19. Language / F. Communication / 3. Denial
We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
     Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A.
     From: Ian Rumfitt ("Yes" and "No" [2000], IV)
     A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role).