Combining Texts

All the ideas for 'Classical Cosmology (frags)', 'Plurals and Complexes' and 'Essays on Intellectual Powers 1: Preliminary'

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26 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10676 The Axiom of Choice is a non-logical principle of set-theory [Hossack]
10686 The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
10687 Maybe we reduce sets to ordinals, rather than the other way round [Hossack]
4. Formal Logic / G. Formal Mereology / 3. Axioms of Mereology
10677 Extensional mereology needs two definitions and two axioms [Hossack]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
10671 Plural definite descriptions pick out the largest class of things that fit the description [Hossack]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
10666 Plural reference will refer to complex facts without postulating complex things [Hossack]
10669 Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack]
10675 A plural comprehension principle says there are some things one of which meets some condition [Hossack]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
10673 Plural language can discuss without inconsistency things that are not members of themselves [Hossack]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
10680 The theory of the transfinite needs the ordinal numbers [Hossack]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10684 I take the real numbers to be just lengths [Hossack]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10674 A plural language gives a single comprehensive induction axiom for arithmetic [Hossack]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10681 In arithmetic singularists need sets as the instantiator of numeric properties [Hossack]
10685 Set theory is the science of infinity [Hossack]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
10668 We are committed to a 'group' of children, if they are sitting in a circle [Hossack]
9. Objects / C. Structure of Objects / 5. Composition of an Object
10664 Complex particulars are either masses, or composites, or sets [Hossack]
10678 The relation of composition is indispensable to the part-whole relation for individuals [Hossack]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
10682 The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack]
10665 Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack]
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
23633 Many truths seem obvious, and point to universal agreement - which is what we find [Reid]
18. Thought / A. Modes of Thought / 1. Thought
10663 A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack]
18. Thought / C. Content / 2. Ideas
23630 Only philosophers treat ideas as objects [Reid]
19. Language / A. Nature of Meaning / 9. Ambiguity
23629 The ambiguity of words impedes the advancement of knowledge [Reid]
26. Natural Theory / C. Causation / 1. Causation
23632 Similar effects come from similar causes, and causes are only what are sufficient for the effects [Reid]
27. Natural Reality / C. Space / 2. Space
10683 We could ignore space, and just talk of the shape of matter [Hossack]
27. Natural Reality / E. Cosmology / 1. Cosmology
5994 Is the cosmos open or closed, mechanical or teleological, alive or inanimate, and created or eternal? [Robinson,TM, by PG]