Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, Palle Yourgrau and Catherine Z. Elgin

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9 ideas

2. Reason / A. Nature of Reason / 6. Coherence
How can multiple statements, none of which is tenable, conjoin to yield a tenable conclusion? [Elgin]
Statements that are consistent, cotenable and supportive are roughly true [Elgin]
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
Coherence is a justification if truth is its best explanation (not skill in creating fiction) [Elgin]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]