Ideas of Øystein Linnebo, by Theme
[Norwegian, fl. 2006, Lecturer at Bristol University, then Birkbeck, London.]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
10779

A comprehension axiom is 'predicative' if the formula has no bound secondorder variables

5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10781

A 'pure logic' must be ontologically innocent, universal, and without presuppositions

10638

A pure logic is wholly general, purely formal, and directly known

5. Theory of Logic / G. Quantification / 6. Plural Quantification
10783

Plural quantification depends too heavily on combinatorial and settheoretic considerations

10778

Can secondorder logic be ontologically firstorder, with all the benefits of secondorder?

10636

Plural plurals are unnatural and need a firstlevel ontology

10639

Plural quantification may allow a monadic secondorder theory with firstorder ontology

10635

Secondorder quantification and plural quantification are different

10641

Traditionally we eliminate plurals by quantifying over sets

10633

'Some critics admire only one another' cannot be paraphrased in singular firstorder

10640

Instead of complex objects like tables, plurally quantify over mereological atoms tablewise

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
14085

'Deductivist' structuralism is just theories, with no commitment to objects, or modality

14084

Noneliminative structuralism treats mathematical objects as positions in real abstract structures

14086

'Modal' structuralism studies all possible concrete models for various mathematical theories

14087

'Settheoretic' structuralism treats mathematics as various structures realised among the sets

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
14089

Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
14090

In mathematical structuralism the small depends on the large, which is the opposite of physical structures

14083

Structuralism is right about algebra, but wrong about sets

7. Existence / C. Structure of Existence / 4. Ontological Dependence
14091

There may be a oneway direction of dependence among sets, and among natural numbers

7. Existence / D. Theories of Reality / 10. Ontological Commitment / a. Ontological commitment
10643

We speak of a theory's 'ideological commitments' as well as its 'ontological commitments'

7. Existence / D. Theories of Reality / 10. Ontological Commitment / e. Ontological commitment problems
10637

Ordinary speakers posit objects without concern for ontology

8. Modes of Existence / B. Properties / 4. Intrinsic Properties
14088

An 'intrinsic' property is either found in every duplicate, or exists independent of all externals

9. Objects / A. Existence of Objects / 1. Physical Objects
10782

The modern concept of an object is rooted in quantificational logic

19. Language / C. Assigning Meanings / 3. Predicates
10634

Predicates are 'distributive' or 'nondistributive'; do individuals do what the group does?
