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
12223

It is a fallacy to explain the obscure with the even more obscure

5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
12230

Singular terms refer if they make certain atomic statements true

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / c. Grelling's paradox
10631

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 / 4. Axioms for Number / g. Incompleteness of Arithmetic
10624

The incompletability of formal arithmetic reveals that logic also cannot be completely characterized

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
8784

Neologicism founds arithmetic on Hume's Principle along with secondorder logic

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
8787

The Julius Caesar problem asks for a criterion for the concept of a 'number'

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10628

The structural view of numbers doesn't fit their usage outside arithmetical contexts

10629

If structures are relative, this undermines truthvalue and objectivity

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8788

Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology

6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neologicism
10622

The neoFregean is more optimistic than Frege about contextual definitions of numbers

8783

Logicism might also be revived with a quantificational approach, or an abstractionfree approach

12225

NeoFregeanism might be better with truthmakers, rather than quantifier commitment

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
12224

Are neoFregeans 'maximalists'  that everything which can exist does exist?

7. Existence / D. Theories of Reality / 10. Ontological Commitment / a. Ontological commitment
12226

The identity of Pegasus with Pegasus may be true, despite the nonexistence

8. Modes of Existence / B. Properties / 3. Types of Properties
12229

Maybe we have abundant properties for semantics, and sparse properties for ontology

8. Modes of Existence / B. Properties / 10. Properties as Predicates
18443

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
10626

Objects just are what singular terms refer to

18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10630

Abstracted objects are not mental creations, but depend on equivalence between given entities

8786

One firstorder abstraction principle is Frege's definition of 'direction' in terms of parallel lines

12227

Abstractionism needs existential commitment and uniform truthconditions

12228

Equivalence abstraction refers to objects otherwise beyond our grasp

19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
12231

Reference needs truth as well as sense

19. Language / E. Analyticity / 2. Analytic Truths
10627

Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions
