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All the ideas for 'Russell's Mathematical Logic', 'The Right and the Good' and 'Sentences'

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52 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Reference to a totality need not refer to a conjunction of all its elements [Gödel]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Mathematical objects are as essential as physical objects are for perception [Gödel]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
Impredicative definitions are admitted into ordinary mathematics [Gödel]
8. Modes of Existence / A. Relations / 1. Nature of Relations
The single imagined 'interval' between things only exists in the intellect [Auriol]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
The goodness of opinions depends on their grounds, and corresponding degrees of conviction [Ross]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
Knowledge is superior to opinion because it is certain [Ross]
12. Knowledge Sources / B. Perception / 7. Causal Perception
I prefer the causal theory to sense data, because sensations are events, not apprehensions [Ross]
14. Science / B. Scientific Theories / 5. Commensurability
Two goods may be comparable, although they are not commensurable [Ross]
17. Mind and Body / D. Property Dualism / 5. Supervenience of mind
Identical objects must have identical value [Ross]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
Aesthetic enjoyment combines pleasure with insight [Ross]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
Beauty is neither objective nor subjective, but a power of producing certain mental events [Ross]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / e. Ethical cognitivism
Moral duties are as fundamental to the universe as the axioms of mathematics [Ross]
The beauty of a patch of colour might be the most important fact about it [Ross]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
Ross said moral principles are self-evident from the facts, but not from pure thought [Ross, by Dancy,J]
The moral convictions of thoughtful educated people are the raw data of ethics [Ross]
22. Metaethics / B. Value / 1. Nature of Value / a. Nature of value
Value is held to be either a quality, or a relation (usually between a thing and a mind) [Ross]
The arguments for value being an objective or a relation fail, so it appears to be a quality [Ross]
22. Metaethics / B. Value / 1. Nature of Value / c. Objective value
The thing is intrinsically good if it would be good when nothing else existed [Ross]
All things being equal, we all prefer the virtuous to be happy, not the vicious [Ross]
22. Metaethics / B. Value / 1. Nature of Value / e. Means and ends
An instrumentally good thing might stay the same, but change its value because of circumstances [Ross]
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
We can ask of pleasure or beauty whether they are valuable, but not of goodness [Ross]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
The four goods are: virtue, pleasure, just allocation of pleasure, and knowledge [Ross]
The three intrinsic goods are virtue, knowledge and pleasure [Ross]
22. Metaethics / C. The Good / 1. Goodness / c. Right and good
'Right' and 'good' differ in meaning, as in a 'right action' and a 'good man' [Ross]
If there are two equally good acts, they may both be right, but neither a duty [Ross]
In the past 'right' just meant what is conventionally accepted [Ross]
Goodness is a wider concept than just correct ethical conduct [Ross]
Motives decide whether an action is good, and what is done decides whether it was right [Ross]
22. Metaethics / C. The Good / 1. Goodness / d. Good as virtue
Virtue is superior to pleasure, as pleasure is never a duty, but goodness is [Ross]
22. Metaethics / C. The Good / 1. Goodness / e. Good as knowledge
All other things being equal, a universe with more understanding is better [Ross]
Morality is not entirely social; a good moral character should love truth [Ross]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
We clearly value good character or understanding, as well as pleasure [Ross]
No one thinks it doesn't matter whether pleasure is virtuously or viciously acquired [Ross]
23. Ethics / B. Contract Ethics / 3. Promise Keeping
Promise-keeping is bound by the past, and is not concerned with consequences [Ross]
Promises create a new duty to a particular person; they aren't just a strategy to achieve well-being [Ross]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
Prima facie duties rest self-evidently on particular circumstance [Ross]
23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect
People lose their rights if they do not respect the rights of others [Ross]
23. Ethics / D. Deontological Ethics / 2. Duty
We should do our duty, but not from a sense of duty [Ross]
We like people who act from love, but admire more the people who act from duty [Ross]
Be faithful, grateful, just, beneficent, non-malevolent, and improve yourself [Ross, by PG]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
An act may be described in innumerable ways [Ross]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
We should use money to pay debts before giving to charity [Ross]
25. Social Practice / C. Rights / 1. Basis of Rights
Rights were originally legal, and broadened to include other things [Ross]
25. Social Practice / F. Life Issues / 6. Animal Rights
Rights can be justly claimed, so animals have no rights, as they cannot claim any [Ross]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / b. Prime matter
Prime matter lacks essence, but is only potentially and indeterminately a physical thing [Auriol]
28. God / A. Divine Nature / 4. Divine Contradictions
God can do anything non-contradictory, as making straightness with no line, or lightness with no parts [Auriol]