Combining Philosophers

All the ideas for Palle Yourgrau, Robert Grosseteste and William Poundstone

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13 ideas

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]
9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
By comparing qualities and features, reason can gradually infer the nature of substance [Grosseteste]
23. Ethics / B. Contract Ethics / 1. Contractarianism
Self-interest can fairly divide a cake; first person cuts, second person chooses [Poundstone]
23. Ethics / B. Contract Ethics / 6. Game Theory
Formal game theory is about maximising or minimising numbers in tables [Poundstone]
The minimax theorem says a perfect game of opposed people always has a rational solution [Poundstone]
23. Ethics / B. Contract Ethics / 7. Prisoner's Dilemma
Two prisoners get the best result by being loyal, not by selfish betrayal [Poundstone]
The tragedy in prisoner's dilemma is when two 'nice' players misread each other [Poundstone]
23. Ethics / B. Contract Ethics / 8. Contract Strategies
Do unto others as you would have them do unto you - or else! [Poundstone]
TIT FOR TAT says cooperate at first, then do what the other player does [Poundstone]