Combining Philosophers

All the ideas for Anaxarchus, Peter Koellner and Epicharmus

expand these ideas     |    start again     |     specify just one area for these philosophers


14 ideas

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]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
Additional or removal of any part changes a thing, so people are never the same person [Epicharmus]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
13. Knowledge Criteria / E. Relativism / 1. Relativism
A dog seems handsome to another a dog, and even a pig to another pig [Epicharmus]
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
Pleasures are like pirates - if you are caught they drown you in a sea of pleasures [Epicharmus]
23. Ethics / B. Contract Ethics / 1. Contractarianism
Hands wash hands; give that you may get [Epicharmus]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
Against a villain, villainy is not a useless weapon [Epicharmus]
28. God / A. Divine Nature / 3. Divine Perfections
God knows everything, and nothing is impossible for him [Epicharmus]
29. Religion / D. Religious Issues / 3. Problem of Evil / c. Human Error
Human logos is an aspect of divine logos, and is sufficient for successful living [Epicharmus]