Combining Texts

All the ideas for 'talk', 'Absolute Necessities' and 'The Theory of Logical Types'

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14 ideas

5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
'Propositional functions' are ambiguous until the variable is given a value [Russell]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell]
Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
A one-variable function is only 'predicative' if it is one order above its arguments [Russell]
10. Modality / A. Necessity / 2. Nature of Necessity
Absolute necessity might be achievable either logically or metaphysically [Hale]
10. Modality / A. Necessity / 3. Types of Necessity
Maybe not-p is logically possible, but p is metaphysically necessary, so the latter is not absolute [Hale]
A strong necessity entails a weaker one, but not conversely; possibilities go the other way [Hale]
'Relative' necessity is just a logical consequence of some statements ('strong' if they are all true) [Hale]
10. Modality / A. Necessity / 5. Metaphysical Necessity
Metaphysical necessity says there is no possibility of falsehood [Hale]
10. Modality / A. Necessity / 6. Logical Necessity
'Broadly' logical necessities are derived (in a structure) entirely from the concepts [Hale]
Logical necessities are true in virtue of the nature of all logical concepts [Hale]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
Conceptual necessities are made true by all concepts [Hale]
14. Science / C. Induction / 3. Limits of Induction
Maybe induction is only reliable IF reality is stable [Mitchell,A]