Combining Texts

All the ideas for 'Defending the Axioms', 'Vague Identity: Evans misunderstood' and 'Understanding and Essence'

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16 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
19259 If 2-D conceivability can a priori show possibilities, this is a defence of conceptual analysis [Vaidya]
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 / 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]
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
16458 Semantic vagueness involves alternative and equal precisifications of the language [Lewis]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / c. Essentials are necessary
19262 Essential properties are necessary, but necessary properties may not be essential [Vaidya]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
19267 Define conceivable; how reliable is it; does inconceivability help; and what type of possibility results? [Vaidya]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / c. Possible but inconceivable
19268 Inconceivability (implying impossibility) may be failure to conceive, or incoherence [Vaidya]
11. Knowledge Aims / A. Knowledge / 2. Understanding
19265 Can you possess objective understanding without realising it? [Vaidya]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / b. Gettier problem
19260 Gettier deductive justifications split the justification from the truthmaker [Vaidya]
19266 In a disjunctive case, the justification comes from one side, and the truth from the other [Vaidya]
18. Thought / C. Content / 1. Content
19264 Aboutness is always intended, and cannot be accidental [Vaidya]