Combining Philosophers

All the ideas for Oliver,A/Smiley,T, Menedemus and Richard Cumberland

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17 ideas

2. Reason / A. Nature of Reason / 7. Status of Reason
If a decision is in accord with right reason, everyone can agree with it [Cumberland]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
The empty set is something, not nothing! [Oliver/Smiley]
We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
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
If there are different ultimate goods, there will be conflicting good actions, which is impossible [Cumberland]
23. Ethics / A. Egoism / 1. Ethical Egoism
The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
The happiness of individuals is linked to the happiness of everyone (which is individuals taken together) [Cumberland]
The happiness of all contains the happiness of each, and promotes it [Cumberland]
25. Social Practice / D. Justice / 2. The Law / c. Natural law
Natural law is immutable truth giving moral truths and duties independent of society [Cumberland]