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All the ideas for 'Issues of Pragmaticism', 'Plurals and Complexes' and 'On Second-Order Logic'

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29 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 / A. Overview of Logic / 7. Second-Order Logic
14249 Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
10830 Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10829 A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
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 / 2. Domain of Quantification
10832 '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
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 / K. Features of Logics / 4. Completeness
10834 Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
5. Theory of Logic / K. Features of Logics / 6. Compactness
13841 Why should compactness be definitive of logic? [Boolos, by Hacking]
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
10833 Many concepts can only be expressed by second-order logic [Boolos]
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]
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]
19. Language / A. Nature of Meaning / 1. Meaning
19087 The meaning or purport of a symbol is all the rational conduct it would lead to [Peirce]
27. Natural Reality / C. Space / 2. Space
10683 We could ignore space, and just talk of the shape of matter [Hossack]