Combining Texts

All the ideas for 'Defending the Axioms', 'Summa quaestionum super Sententias' and 'Some Judgements of Perception'

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11 ideas

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]
8. Modes of Existence / A. Relations / 1. Nature of Relations
16659 Relations do not add anything to reality, though they are real aspects of the world [Olivi]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
16673 Quantity just adds union and location to the extension of parts [Olivi]
11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty
20147 Arguments that my finger does not exist are less certain than your seeing my finger [Moore,GE]
27. Natural Reality / G. Biology / 5. Species
16663 Things are limited by the species to certain modes of being [Olivi]