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All the ideas for 'On Carnap's Views on Ontology', 'Essays on Intellectual Powers 5: Abstraction' and 'Logicism in the 21st Century'

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15 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Quine rejects Carnap's view that science and philosophy are distinct [Quine, by Boulter]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright]
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 [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
Names have no ontological commitment, because we can deny that they name anything [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
We can use quantification for commitment to unnameable things like the real numbers [Quine]
8. Modes of Existence / D. Universals / 5. Universals as Concepts
Universals are not objects of sense and cannot be imagined - but can be conceived [Reid]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
Only individuals exist [Reid]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
No one thinks two sheets possess a single whiteness, but all agree they are both white [Reid]
9. Objects / F. Identity among Objects / 1. Concept of Identity
Real identity admits of no degrees [Reid]
18. Thought / A. Modes of Thought / 1. Thought
We must first conceive things before we can consider them [Reid]
18. Thought / E. Abstraction / 1. Abstract Thought
First we notice and name attributes ('abstracting'); then we notice that subjects share them ('generalising') [Reid]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines [Hale/Wright]
19. Language / E. Analyticity / 3. Analytic and Synthetic
Without the analytic/synthetic distinction, Carnap's ontology/empirical distinction collapses [Quine]