Combining Texts

All the ideas for 'Defending the Axioms', 'Philosophy of Language' and 'Frege on Knowing the Foundations'

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17 ideas

4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
15163 The interest of quantified modal logic is its metaphysical necessity and essentialism [Soames]
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 / 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 / F. Referring in Logic / 2. Descriptions / a. Descriptions
15158 Indefinite descriptions are quantificational in subject position, but not in predicate position [Soames]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
15157 Recognising the definite description 'the man' as a quantifier phrase, not a singular term, is a real insight [Soames]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
15156 The universal and existential quantifiers were chosen to suit mathematics [Soames]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17622 We come to believe mathematical propositions via their grounding in the structure [Burge]
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]
10. Modality / A. Necessity / 5. Metaphysical Necessity
15161 There are more metaphysically than logically necessary truths [Soames]
15162 We understand metaphysical necessity intuitively, from ordinary life [Soames]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
15152 To study meaning, study truth conditions, on the basis of syntax, and representation by the parts [Soames]
15153 Tarski's account of truth-conditions is too weak to determine meanings [Soames]
19. Language / D. Propositions / 4. Mental Propositions
15154 We should use cognitive states to explain representational propositions, not vice versa [Soames]