Ideas of Øystein Linnebo, by Theme
[Norwegian, fl. 2006, Lecturer at Bristol University, then Birkbeck, London.]
green numbers give full details |
back to list of philosophers |
expand these ideas
2. Reason / D. Definition / 12. Paraphrase
|
10633
|
'Some critics admire only one another' cannot be paraphrased in singular first-order
|
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 second-order variables
|
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
|
23445
|
Naïve set theory says any formula defines a set, and coextensive sets are identical
|
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
|
10778
|
Can second-order logic be ontologically first-order, with all the benefits of second-order?
|
|
10783
|
Plural quantification depends too heavily on combinatorial and set-theoretic considerations
|
|
10635
|
Second-order quantification and plural quantification are different
|
|
10636
|
Plural plurals are unnatural and need a first-level ontology
|
|
10641
|
Traditionally we eliminate plurals by quantifying over sets
|
|
10640
|
Instead of complex objects like tables, plurally quantify over mereological atoms tablewise
|
|
10639
|
Plural quantification may allow a monadic second-order theory with first-order ontology
|
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
|
23447
|
In classical semantics singular terms refer, and quantifiers range over domains
|
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
|
23443
|
The axioms of group theory are not assertions, but a definition of a structure
|
|
23444
|
To investigate axiomatic theories, mathematics needs its own foundational axioms
|
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
|
23446
|
You can't prove consistency using a weaker theory, but you can use a consistent theory
|
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
|
23448
|
Mathematics is the study of all possible patterns, and is thus bound to describe the world
|
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
|
Non-eliminative structuralism treats mathematical objects as positions in real abstract structures
|
|
14086
|
'Modal' structuralism studies all possible concrete models for various mathematical theories
|
|
14087
|
'Set-theoretic' 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
|
14083
|
Structuralism is right about algebra, but wrong about sets
|
|
14090
|
In mathematical structuralism the small depends on the large, which is the opposite of physical structures
|
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
|
23441
|
Logical truth is true in all models, so mathematical objects can't be purely logical
|
6. Mathematics / C. Sources of Mathematics / 7. Formalism
|
23442
|
Game Formalism has no semantics, and Term Formalism reduces the semantics
|
7. Existence / C. Structure of Existence / 4. Ontological Dependence
|
14091
|
There may be a one-way 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 'non-distributive'; do individuals do what the group does?
|