Ideas of B Hale / C Wright, by Theme

[British, fl. 1995, two professors based in Scotland.]

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2. Reason / F. Fallacies / 1. Fallacy
It is a fallacy to explain the obscure with the even more obscure
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Various strategies try to deal with the ontological commitments of second-order logic
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
Singular terms refer if they make certain atomic statements true
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / c. Grelling's paradox
If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / g. Incompleteness of Arithmetic
The incompletability of formal arithmetic reveals that logic also cannot be completely characterized
6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / d. Hume's Principle
Neo-logicism founds arithmetic on Hume's Principle along with second-order logic
6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / e. Caesar problem
The Julius Caesar problem asks for a criterion for the concept of a 'number'
6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / e. Structuralism critique
The structural view of numbers doesn't fit their usage outside arithmetical contexts
If structures are relative, this undermines truth-value and objectivity
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
The neo-Fregean is more optimistic than Frege about contextual definitions of numbers
Logicism might also be revived with a quantificational approach, or an abstraction-free approach
Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Are neo-Fregeans 'maximalists' - that everything which can exist does exist?
7. Existence / D. Theories of Reality / 10. Ontological Commitment / a. Ontological commitment
The identity of Pegasus with Pegasus may be true, despite the non-existence
8. Modes of Existence / B. Properties / 3. Types of Properties
Maybe we have abundant properties for semantics, and sparse properties for ontology
8. Modes of Existence / B. Properties / 10. Properties as Predicates
A successful predicate guarantees the existence of a property - the way of being it expresses
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Objects just are what singular terms refer to
18. Thought / D. Concepts / 6. Abstract Concepts / g. Abstracta by equivalence
Equivalence abstraction refers to objects otherwise beyond our grasp
Abstracted objects are not mental creations, but depend on equivalence between given entities
One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines
Abstractionism needs existential commitment and uniform truth-conditions
19. Language / D. Theories of Reference / 4. Descriptive Reference / a. Sense and reference
Reference needs truth as well as sense
19. Language / F. Analytic/Synthetic / 3. Analytic Truths
Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions