Combining Texts

All the ideas for 'Letter to Russell', 'Languages of Art (2nd edn)' and 'Defending the Axioms'

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14 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
The main problem of philosophy is what can and cannot be thought and expressed [Wittgenstein, by Grayling]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
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
Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
Atomic facts correspond to true elementary propositions [Wittgenstein]
19. Language / D. Propositions / 4. Mental Propositions
A thought is mental constituents that relate to reality as words do [Wittgenstein]
21. Aesthetics / B. Nature of Art / 1. Defining Art
Art is a referential activity, hence indefinable, but it has a set of symptoms [Goodman]
21. Aesthetics / B. Nature of Art / 5. Art as Language
Artistic symbols are judged by the fruitfulness of their classifications [Goodman, by Giovannelli]
21. Aesthetics / B. Nature of Art / 7. Ontology of Art
A performance is only an instance of a work if there is not a single error [Goodman]
21. Aesthetics / C. Artistic Issues / 2. Copies of Art
A copy only becomes an 'instance' of an artwork if there is a system of notation [Goodman]