Combining Texts

All the ideas for 'fragments/reports', 'Introduction to Zermelo's 1930 paper' and 'How to Define Theoretical Terms'

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12 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
The first-order ZF axiomatisation is highly non-categorical [Hallett,M]
Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
A logically determinate name names the same thing in every possible world [Lewis]
14. Science / B. Scientific Theories / 8. Ramsey Sentences
The Ramsey sentence of a theory says that it has at least one realisation [Lewis]
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]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]