Ideas of Øystein Linnebo, by Theme
[Norwegian, fl. 2006, Lecturer at Bristol University, then Birkbeck, London.]
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2. Reason / D. Definition / 12. Paraphrase
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10633
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'Some critics admire only one another' cannot be paraphrased in singular first-order
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
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10779
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A comprehension axiom is 'predicative' if the formula has no bound second-order variables
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
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23445
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Naïve set theory says any formula defines a set, and coextensive sets are identical
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5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
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10781
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A 'pure logic' must be ontologically innocent, universal, and without presuppositions
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10638
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A pure logic is wholly general, purely formal, and directly known
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5. Theory of Logic / G. Quantification / 6. Plural Quantification
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10778
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Can second-order logic be ontologically first-order, with all the benefits of second-order?
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10783
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Plural quantification depends too heavily on combinatorial and set-theoretic considerations
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10635
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Second-order quantification and plural quantification are different
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10640
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Instead of complex objects like tables, plurally quantify over mereological atoms tablewise
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10641
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Traditionally we eliminate plurals by quantifying over sets
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10636
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Plural plurals are unnatural and need a first-level ontology
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10639
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Plural quantification may allow a monadic second-order theory with first-order ontology
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5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
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23447
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In classical semantics singular terms refer, and quantifiers range over domains
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
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23443
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The axioms of group theory are not assertions, but a definition of a structure
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23444
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To investigate axiomatic theories, mathematics needs its own foundational axioms
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
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23446
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You can't prove consistency using a weaker theory, but you can use a consistent theory
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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23448
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Mathematics is the study of all possible patterns, and is thus bound to describe the world
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
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14085
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'Deductivist' structuralism is just theories, with no commitment to objects, or modality
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14084
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Non-eliminative structuralism treats mathematical objects as positions in real abstract structures
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14086
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'Modal' structuralism studies all possible concrete models for various mathematical theories
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14087
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'Set-theoretic' structuralism treats mathematics as various structures realised among the sets
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
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14089
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Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
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14083
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Structuralism is right about algebra, but wrong about sets
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14090
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In mathematical structuralism the small depends on the large, which is the opposite of physical structures
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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23441
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Logical truth is true in all models, so mathematical objects can't be purely logical
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
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23442
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Game Formalism has no semantics, and Term Formalism reduces the semantics
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7. Existence / C. Structure of Existence / 4. Ontological Dependence
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14091
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There may be a one-way direction of dependence among sets, and among natural numbers
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7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
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10643
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We speak of a theory's 'ideological commitments' as well as its 'ontological commitments'
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7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
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10637
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Ordinary speakers posit objects without concern for ontology
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8. Modes of Existence / B. Properties / 4. Intrinsic Properties
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14088
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An 'intrinsic' property is either found in every duplicate, or exists independent of all externals
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9. Objects / A. Existence of Objects / 1. Physical Objects
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10782
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The modern concept of an object is rooted in quantificational logic
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19. Language / C. Assigning Meanings / 3. Predicates
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10634
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Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does?
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