Combining Philosophers

All the ideas for Geoffrey Gorham, Peter Koellner and Peter Forrest

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17 ideas

3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
The truth-maker principle is that every truth has a sufficient truth-maker [Forrest]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Arithmetical undecidability is always settled at the next stage up [Koellner]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
Structural universals might serve as possible worlds [Forrest, by Lewis]
14. Science / A. Basis of Science / 6. Falsification
Why abandon a theory if you don't have a better one? [Gorham]
If a theory is more informative it is less probable [Gorham]
14. Science / B. Scientific Theories / 1. Scientific Theory
Is Newton simpler with universal simultaneity, or Einstein simpler without absolute time? [Gorham]
Structural Realism says mathematical structures persist after theory rejection [Gorham]
Structural Realists must show the mathematics is both crucial and separate [Gorham]
14. Science / B. Scientific Theories / 3. Instrumentalism
For most scientists their concepts are not just useful, but are meant to be true and accurate [Gorham]
Theories aren't just for organising present experience if they concern the past or future [Gorham]
14. Science / D. Explanation / 2. Types of Explanation / d. Consilience
Consilience makes the component sciences more likely [Gorham]
26. Natural Theory / A. Speculations on Nature / 1. Nature
Aristotelian physics has circular celestial motion and linear earthly motion [Gorham]