Combining Texts

All the ideas for 'fragments/reports', 'Inexpressible Properties and Propositions' and 'Sets, Aggregates and Numbers'

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12 ideas

2. Reason / C. Styles of Reason / 1. Dialectic
Like spiderswebs, dialectical arguments are clever but useless [Ariston, by Diog. Laertius]
3. Truth / H. Deflationary Truth / 3. Minimalist Truth
Instances of minimal truth miss out propositions inexpressible in current English [Hofweber]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Quantification can't all be substitutional; some reference is obviously to objects [Hofweber]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau]
Nothing is 'intrinsically' numbered [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau]
You can ask all sorts of numerical questions about any one given set [Yourgrau]
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]
19. Language / F. Communication / 6. Interpreting Language / a. Translation
Holism says language can't be translated; the expressibility hypothesis says everything can [Hofweber]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
The chief good is indifference to what lies midway between virtue and vice [Ariston, by Diog. Laertius]
23. Ethics / D. Deontological Ethics / 1. Deontology
Ariston says rules are useless for the virtuous and the non-virtuous [Ariston, by Annas]