Combining Texts

All the ideas for 'Leibniz', 'Inexpressible Properties and Propositions' and 'Mathematical logic and theory of types'

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14 ideas

3. Truth / H. Deflationary Truth / 3. Minimalist Truth
Instances of minimal truth miss out propositions inexpressible in current English [Hofweber]
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 / G. Quantification / 4. Substitutional Quantification
Quantification can't all be substitutional; some reference is obviously to objects [Hofweber]
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 / B. Properties / 1. Nature of Properties
Since properties have properties, there can be a typed or a type-free theory of them [Hofweber]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
The Identity of Indiscernibles is really the same as the verification principle [Jolley]
19. Language / F. Communication / 6. Interpreting Language / a. Translation
Holism says language can't be translated; the expressibility hypothesis says everything can [Hofweber]