Combining Texts

All the ideas for 'The Nature of Things', 'Extrinsic Properties' and 'What is Cantor's Continuum Problem?'

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


15 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
We perceive the objects of set theory, just as we perceive with our senses [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
A class is natural when everybody can spot further members of it [Quinton]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
7. Existence / E. Categories / 5. Category Anti-Realism
Extreme nominalists say all classification is arbitrary convention [Quinton]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
Being alone doesn't guarantee intrinsic properties; 'being alone' is itself extrinsic [Lewis, by Sider]
Extrinsic properties come in degrees, with 'brother' less extrinsic than 'sibling' [Lewis]
8. Modes of Existence / B. Properties / 5. Natural Properties
The naturalness of a class depends as much on the observers as on the objects [Quinton]
Properties imply natural classes which can be picked out by everybody [Quinton]
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
Uninstantiated properties must be defined using the instantiated ones [Quinton]
9. Objects / A. Existence of Objects / 5. Individuation / b. Individuation by properties
Total intrinsic properties give us what a thing is [Lewis]
An individual is a union of a group of qualities and a position [Quinton, by Campbell,K]