Combining Texts

All the ideas for 'poems', 'Mathematical logic and theory of types' and 'Inessential Aristotle: Powers without Essences'

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


16 ideas

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Classes can be reduced to propositional functions [Russell, by Hanna]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell]
Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave]
Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock]
Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock]
Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
Powers give explanations, without being necessary for some class membership [Chakravartty]
9. Objects / D. Essence of Objects / 5. Essence as Kind
A kind essence is the necessary and sufficient properties for membership of a class [Chakravartty]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Cluster kinds are explained simply by sharing some properties, not by an 'essence' [Chakravartty]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
Explanation of causal phenomena concerns essential kinds - but also lack of them [Chakravartty]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Nomos is king [Pindar]
26. Natural Theory / B. Natural Kinds / 4. Source of Kinds
Some kinds, such as electrons, have essences, but 'cluster kinds' do not [Chakravartty]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Many causal laws do not refer to kinds, but only to properties [Chakravartty]