### Ideas of Keith Hossack, by Theme

#### [British, fl. 2007, Lecturer at Birkbeck College, London.]

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###### 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
 10686 The Axiom of Choice guarantees a one-one correspondence from sets to ordinals
###### 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
 23623 Predicativism says only predicated sets exist
###### 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
 23624 The iterative conception has to appropriate Replacement, to justify the ordinals
###### 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
 23625 Limitation of Size justifies Replacement, but then has to appropriate Power Set
###### 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
###### 4. Formal Logic / G. Formal Mereology / 3. Axioms of Mereology
 10677 Extensional mereology needs two definitions and two axioms
###### 5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
 23628 The connective 'and' can have an order-sensitive meaning, as 'and then'
###### 5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
 23627 'Before' and 'after' are not two relations, but one relation with two orders
###### 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
###### 5. Theory of Logic / G. Quantification / 6. Plural Quantification
 10666 Plural reference will refer to complex facts without postulating complex things
 10675 A plural comprehension principle says there are some things one of which meets some condition
 10669 Plural reference is just an abbreviation when properties are distributive, but not otherwise
###### 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
###### 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
 10680 The theory of the transfinite needs the ordinal numbers
###### 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
 10684 I take the real numbers to be just lengths
###### 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
 23626 Transfinite ordinals are needed in proof theory, and for recursive functions and computability
###### 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
###### 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
 10685 Set theory is the science of infinity
###### 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
 23621 Numbers are properties, not sets (because numbers are magnitudes)
###### 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
 23622 We can only mentally construct potential infinities, but maths needs actual infinities
###### 7. Existence / D. Theories of Reality / 10. Ontological Commitment / a. Ontological commitment
 10668 We are committed to a 'group' of children, if they are sitting in a circle
###### 9. Objects / C. Structure of Objects / 5. Composition of an Object
 10664 Complex particulars are either masses, or composites, or sets
 10678 The relation of composition is indispensable to the part-whole relation for individuals
###### 9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
 10665 Leibniz's Law argues against atomism - water is wet, unlike water molecules
 10682 The fusion of five rectangles can decompose into more than five parts that are rectangles
###### 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
###### 27. Natural Reality / C. Space / 2. Space
 10683 We could ignore space, and just talk of the shape of matter