Combining Texts

All the ideas for 'fragments/reports', 'On Carnap's Views on Ontology' and 'Sets, Aggregates and Numbers'

expand these ideas     |    start again     |     specify just one area for these texts


10 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 / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau]
Nothing is 'intrinsically' numbered [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau]
You can ask all sorts of numerical questions about any one given set [Yourgrau]
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]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
If someone squashed a horse to make a dog, something new would now exist [Mnesarchus]
19. Language / E. Analyticity / 3. Analytic and Synthetic
Without the analytic/synthetic distinction, Carnap's ontology/empirical distinction collapses [Quine]