Combining Philosophers

All the ideas for Richard Cumberland, Michael Hallett and Sphaerus

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11 ideas

2. Reason / A. Nature of Reason / 7. Status of Reason

6222	If a decision is in accord with right reason, everyone can agree with it [Cumberland]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

17833

The first-order ZF axiomatisation is highly non-categorical [Hallett,M]

17834

Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M]

4. Formal Logic / F. Set Theory ST / 7. Natural Sets

17837

Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis

17836

The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]

13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure

20769

Sphaerus he was not assenting to the presence of pomegranates, but that it was 'reasonable' [Sphaerus, by Diog. Laertius]

22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics

6217	Natural law is supplied to the human mind by reality and human nature [Cumberland]

22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value

6221	If there are different ultimate goods, there will be conflicting good actions, which is impossible [Cumberland]

23. Ethics / E. Utilitarianism / 1. Utilitarianism

6218	The happiness of individuals is linked to the happiness of everyone (which is individuals taken together) [Cumberland]

6220	The happiness of all contains the happiness of each, and promotes it [Cumberland]

25. Social Practice / D. Justice / 2. The Law / c. Natural law

6216	Natural law is immutable truth giving moral truths and duties independent of society [Cumberland]