Combining Philosophers

All the ideas for Douglas Lackey, Palle Yourgrau and Keith DeRose

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13 ideas

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / b. Cantor's paradox
Sets always exceed terms, so all the sets must exceed all the sets [Lackey]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey]
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]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
A contextualist coherentist will say that how strongly a justification must cohere depends on context [DeRose]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
Classical invariantism combines fixed truth-conditions with variable assertability standards [DeRose]
We can make contextualism more precise, by specifying the discrimination needed each time [DeRose]
In some contexts there is little more to knowledge than true belief. [DeRose]
Contextualists worry about scepticism, but they should focus on the use of 'know' in ordinary speech [DeRose]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / b. Invariantism
If contextualism is about knowledge attribution, rather than knowledge, then it is philosophy of language [DeRose]