Combining Philosophers

All the ideas for Rayo,A/Uzquiasno,G, Anon (Cent) and Giuseppe Peano

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21 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
13451 The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation
13452 Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
13449 We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano]
13450 Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
13453 Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
3338 Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
13949 All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]
18113 PA concerns any entities which satisfy the axioms [Peano, by Bostock]
17634 Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell]
5897 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
15653 We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
17635 Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]
7. Existence / A. Nature of Existence / 3. Being / h. Dasein (being human)
8228 Being is revealed at the point between waking and sleep [Anon (Cent)]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / a. Other minds
8232 Neglect your self, and feel the consciousness of each other being [Anon (Cent)]
19. Language / F. Communication / 5. Pragmatics / a. Contextual meaning
13448 The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
8230 Just as you have the impulse to do something, stop [Anon (Cent)]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
8234 Bondage and liberation are relative terms, which only frighten those already terrified of the universe [Anon (Cent)]
29. Religion / C. Spiritual Disciplines / 4. Zen Buddhism
8227 Feel your whole body saturated with cosmic essence [Anon (Cent)]
8229 The serenity in blue sky beyond clouds [Anon (Cent)]
8231 Abandon attachment to body, and feel the joy of being everywhere [Anon (Cent)]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
8233 Imagine fire burning up your whole body, but not you [Anon (Cent)]