Combining Texts

All the ideas for 'Defending the Axioms', 'Words without Objects' and 'Dion and Theon: an essentialist solution'

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25 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 / E. Structures of Logic / 4. Variables in Logic
12797 If plural variables have 'some values', then non-count variables have 'some value' [Laycock]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
12794 Plurals are semantical but not ontological [Laycock]
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 / 4. Using Numbers / c. Counting procedure
17694 Some non-count nouns can be used for counting, as in 'several wines' or 'fewer cheeses' [Laycock]
17695 Some apparent non-count words can take plural forms, such as 'snows' or 'waters' [Laycock]
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 / C. Structure of Existence / 8. Stuff / a. Pure stuff
12792 The category of stuff does not suit reference [Laycock]
12799 Descriptions of stuff are neither singular aggregates nor plural collections [Laycock]
7. Existence / C. Structure of Existence / 8. Stuff / b. Mixtures
12818 We shouldn't think some water retains its identity when it is mixed with air [Laycock]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
16235 Persistence conditions cannot contradict, so there must be a 'dominant sortal' [Burke,M, by Hawley]
14753 The 'dominant' of two coinciding sortals is the one that entails the widest range of properties [Burke,M, by Sider]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
16072 'The rock' either refers to an object, or to a collection of parts, or to some stuff [Burke,M, by Wasserman]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
14751 Tib goes out of existence when the tail is lost, because Tib was never the 'cat' [Burke,M, by Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
16071 Sculpting a lump of clay destroys one object, and replaces it with another one [Burke,M, by Wasserman]
16234 Burke says when two object coincide, one of them is destroyed in the process [Burke,M, by Hawley]
13278 Maybe the clay becomes a different lump when it becomes a statue [Burke,M, by Koslicki]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
14750 Two entities can coincide as one, but only one of them (the dominant sortal) fixes persistence conditions [Burke,M, by Sider]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
12795 Parts must be of the same very general type as the wholes [Laycock]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
17696 'Humility is a virtue' has an abstract noun, but 'water is a liquid' has a generic concrete noun [Laycock]
19. Language / B. Reference / 1. Reference theories
12791 It is said that proper reference is our intellectual link with the world [Laycock]