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
The Axiom of Choice is a non-logical principle of set-theory
The Axiom of Choice guarantees a one-one correspondence from sets to ordinals
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Maybe we reduce sets to ordinals, rather than the other way round
4. Formal Logic / G. Formal Mereology / 3. Axioms of Mereology
Extensional mereology needs two definitions and two axioms
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Plural definite descriptions pick out the largest class of things that fit the description
5. Theory of Logic / G. Quantification / 6. Plural Quantification
Plural reference will refer to complex facts without postulating complex things
Plural reference is just an abbreviation when properties are distributive, but not otherwise
A plural comprehension principle says there are some things one of which meets some condition
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
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
The theory of the transfinite needs the ordinal numbers
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
I take the real numbers to be just lengths
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
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
In arithmetic singularists need sets as the instantiator of numeric properties
Set theory is the science of infinity
7. Existence / D. Theories of Reality / 10. Ontological Commitment / a. Ontological commitment
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
The relation of composition is indispensable to the part-whole relation for individuals
Complex particulars are either masses, or composites, or sets
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
Leibniz's Law argues against atomism - water is wet, unlike water molecules
The fusion of five rectangles can decompose into more than five parts that are rectangles
18. Thought / A. Modes of Thought / 1. Thought
A thought can refer to many things, but only predicate a universal and affirm a state of affairs
27. Natural Reality / C. Space-Time / 1. Space / b. Space
We could ignore space, and just talk of the shape of matter