Combining Texts

All the ideas for 'works', 'Moral Thinking: Its Levels,Method and Point' and 'The Philosophy of Mathematics'

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


14 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths and inference are characterized either syntactically or semantically [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / i. Prescriptivism
Hare says I acquire an agglomeration of preferences by role-reversal, leading to utilitarianism [Hare, by Williams,B]
If we have to want the preferences of the many, we have to abandon our own deeply-held views [Williams,B on Hare]
If morality is to be built on identification with the preferences of others, I must agree with their errors [Williams,B on Hare]
A judgement is presciptive if we expect it to be acted on [Hare]
23. Ethics / B. Contract Ethics / 8. Contract Strategies
By far the easiest way of seeming upright is to be upright [Hare]
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
Philosophers are the forefathers of heretics [Tertullian]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
I believe because it is absurd [Tertullian]