Combining Texts

All the ideas for 'fragments/reports', 'Utilitarianism' and 'Mathematical logic and theory of types'

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28 ideas

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Classes can be reduced to propositional functions [Russell, by Hanna]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell]
Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave]
Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock]
Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock]
Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
The will, in the beginning, is entirely produced by desire [Mill]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
With early training, any absurdity or evil may be given the power of conscience [Mill]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
Motive shows the worth of the agent, but not of the action [Mill]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
Virtues only have value because they achieve some further end [Mill]
23. Ethics / D. Deontological Ethics / 2. Duty
Orthodox morality is the only one which feels obligatory [Mill]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
Utilitarianism only works if everybody has a totally equal right to happiness [Mill]
The English believe in the task of annihilating evil for the victory of good [Nietzsche on Mill]
Mill's qualities of pleasure is an admission that there are other good states of mind than pleasure [Ross on Mill]
Actions are right if they promote pleasure, wrong if they promote pain [Mill]
23. Ethics / E. Utilitarianism / 2. Ideal of Pleasure
Ultimate goods such as pleasure can never be proved to be good [Mill]
Only pleasure and freedom from pain are desirable as ends [Mill]
Better to be Socrates dissatisfied than a fool satisfied [Mill]
23. Ethics / E. Utilitarianism / 3. Motivation for Altruism
General happiness is only desirable because individuals desire their own happiness [Mill]
23. Ethics / E. Utilitarianism / 5. Rule Utilitarianism
Moral rules protecting human welfare are more vital than local maxims [Mill]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
Rights are a matter of justice, not of benevolence [Mill]
No individual has the right to receive our benevolence [Mill]
25. Social Practice / C. Rights / 1. Basis of Rights
A right is a valid claim to society's protection [Mill]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]