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All the ideas for '', 'Reflections on Value' and 'Defending the Axioms'

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17 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
23881 All thought about values is philosophical, and thought about anything else is not philosophy [Weil]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
23885 Philosophy aims to change the soul, not to accumulate knowledge [Weil]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
23886 Systems are not unique to each philosopher. The platonist tradition is old and continuous [Weil]
3. Truth / A. Truth Problems / 1. Truth
23884 Truth is a value of thought [Weil]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
17610 The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11211 If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
17620 Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11212 The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
11210 Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615 Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
19. Language / F. Communication / 3. Denial
11214 We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
22. Metaethics / B. Value / 1. Nature of Value / e. Means and ends
23882 Ends, unlike means, cannot be defined, which is why people tend to pursue means [Weil]
22. Metaethics / B. Value / 2. Values / a. Normativity
23883 Minds essentially and always strive towards value [Weil]