Combining Texts

All the ideas for 'fragments/reports', 'Ontological Ground of Alethic Modality' and 'Difficulties of Transfinite Numbers and Types'

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5 ideas

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
'Predicative' norms are those which define a class [Russell]
     Full Idea: Norms (containing one variable) which do not define classes I propose to call 'non-predicative'; those which do define classes I shall call 'predicative'.
     From: Bertrand Russell (Difficulties of Transfinite Numbers and Types [1905], p.141)
We need rules for deciding which norms are predicative (unless none of them are) [Russell]
     Full Idea: We need rules for deciding what norms are predicative and what are not, unless we adopt the view (which has much to recommend it) that no norms are predicative. ...[146] A predative propositional function is one which determines a class.
     From: Bertrand Russell (Difficulties of Transfinite Numbers and Types [1905], p.141)
     A reaction: He is referring to his 'no class' theory, which he favoured at that time.
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Lewis must specify that all possibilities are in his worlds, making the whole thing circular [Shalkowski, by Sider]
     Full Idea: If purple cows are simply absent from Lewis's multiverse, then certain correct propositions turn out to be impossible. Lewis must require a world for every possibility. But then it is circular, as the multiverse needs modal notions to characterize it.
     From: report of Scott Shalkowski (Ontological Ground of Alethic Modality [1994], 3.9) by Theodore Sider - Reductive Theories of Modality 3.9
     A reaction: [Inversely, a world containing a round square would make that possible] This sounds very nice, though Sider rejects it (p.197). I've never seen how you could define possibility using the concept of 'possible' worlds.
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
Virtue comes more from habit than character [Critias]
     Full Idea: More men are good through habit than through character.
     From: Critias (fragments/reports [c.440 BCE], B09), quoted by John Stobaeus - Anthology 3.29.41
28. God / C. Attitudes to God / 5. Atheism
Fear of the gods was invented to discourage secret sin [Critias]
     Full Idea: When the laws forbade men to commit open crimes of violence, and they began to do them in secret, a wise and clever man invented fear of the gods for mortals, to frighten the wicked, even if they sin in secret.
     From: Critias (fragments/reports [c.440 BCE], B25), quoted by Sextus Empiricus - Against the Professors (six books) 9.54