Combining Texts

All the ideas for 'The Case for Closure', 'How to Define Theoretical Terms' and 'Remarks on axiomatised set theory'

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14 ideas

2. Reason / D. Definition / 2. Aims of Definition
Defining terms either enables elimination, or shows that they don't require elimination [Lewis]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Axiomatising set theory makes it all relative [Skolem]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Mathematician want performable operations, not propositions about objects [Skolem]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
A logically determinate name names the same thing in every possible world [Lewis]
11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty
Commitment to 'I have a hand' only makes sense in a context where it has been doubted [Hawthorne]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure
How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'? [Hawthorne]
We wouldn't know the logical implications of our knowledge if small risks added up to big risks [Hawthorne]
Denying closure is denying we know P when we know P and Q, which is absurd in simple cases [Hawthorne]
14. Science / B. Scientific Theories / 8. Ramsey Sentences
A Ramsey sentence just asserts that a theory can be realised, without saying by what [Lewis]
There is a method for defining new scientific terms just using the terms we already understand [Lewis]
It is better to have one realisation of a theory than many - but it may not always be possible [Lewis]
The Ramsey sentence of a theory says that it has at least one realisation [Lewis]