Combining Texts

All the ideas for 'The Philosophy of Mathematics', 'An Outline of Philosophy' and 'works'

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17 ideas

1. Philosophy / G. Scientific Philosophy / 3. Scientism
Philosophy is not separate from or above empirical science [Neurath]
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 / 1. Nature of Ethics / d. Ethical theory
I doubt whether ethics is part of philosophy [Russell]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
'You ought to do p' primarily has emotional content, expressing approval [Russell]
22. Metaethics / B. Value / 2. Values / g. Love
Unlike hate, all desires can be satisfied by love [Russell]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
Goodness is a combination of love and knowledge [Russell]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
In wartime, happiness is hating the enemy, because it gives the war a purpose [Russell]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
Originally virtue was obedience, to gods, government, or custom [Russell]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
Act so as to produce harmonious rather than discordant desires [Russell]
25. Social Practice / D. Justice / 3. Punishment / d. Reform of offenders
Legally curbing people's desires is inferior to improving their desires [Russell]
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
We could be aware of time if senses briefly vibrated, extending their experience of movement [Russell, by Bardon]