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All the ideas for 'Structures and Structuralism in Phil of Maths', 'A Priori Knowledge' and 'After Virtue: a Study in Moral Theory'

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51 ideas

1. Philosophy / B. History of Ideas / 5. Later European Thought
In the 17th-18th centuries morality offered a cure for egoism, through altruism [MacIntyre]
1. Philosophy / B. History of Ideas / 6. Twentieth Century Thought
Twentieth century social life is re-enacting eighteenth century philosophy [MacIntyre]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Philosophy has been marginalised by its failure in the Enlightenment to replace religion [MacIntyre]
2. Reason / A. Nature of Reason / 9. Limits of Reason
Proof is a barren idea in philosophy, and the best philosophy never involves proof [MacIntyre]
3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
'Analysis' is the theory of the real numbers [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
10. Modality / A. Necessity / 11. Denial of Necessity
Maybe modal sentences cannot be true or false [Casullo]
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
If the necessary is a priori, so is the contingent, because the same evidence is involved [Casullo]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
Epistemic a priori conditions concern either the source, defeasibility or strength [Casullo]
The main claim of defenders of the a priori is that some justifications are non-experiential [Casullo]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
Analysis of the a priori by necessity or analyticity addresses the proposition, not the justification [Casullo]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
To find empiricism and science in the same culture is surprising, as they are really incompatible [MacIntyre]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / c. Defeasibility
'Overriding' defeaters rule it out, and 'undermining' defeaters weaken in [Casullo]
14. Science / A. Basis of Science / 4. Prediction
Unpredictability doesn't entail inexplicability, and predictability doesn't entail explicability [MacIntyre]
14. Science / B. Scientific Theories / 1. Scientific Theory
Social sciences discover no law-like generalisations, and tend to ignore counterexamples [MacIntyre]
16. Persons / E. Rejecting the Self / 3. Narrative Self
I can only make decisions if I see myself as part of a story [MacIntyre]
18. Thought / B. Mechanics of Thought / 6. Artificial Thought / a. Artificial Intelligence
AI can't predict innovation, or consequences, or external relations, or external events [MacIntyre]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / c. Purpose of ethics
The good life for man is the life spent seeking the good life for man [MacIntyre]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
We still have the appearance and language of morality, but we no longer understand it [MacIntyre]
Unlike expressions of personal preference, evaluative expressions do not depend on context [MacIntyre]
Moral judgements now are anachronisms from a theistic age [MacIntyre]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
The failure of Enlightenment attempts to justify morality will explain our own culture [MacIntyre]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
Mention of 'intuition' in morality means something has gone wrong with the argument [MacIntyre]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
When 'man' is thought of individually, apart from all roles, it ceases to be a functional concept [MacIntyre]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
In trying to explain the type of approval involved, emotivists are either silent, or viciously circular [MacIntyre]
The expression of feeling in a sentence is in its use, not in its meaning [MacIntyre]
Emotivism cannot explain the logical terms in moral discourse ('therefore', 'if..then') [MacIntyre]
Nowadays most people are emotivists, and it is embodied in our culture [MacIntyre]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
Maybe we can only understand rules if we first understand the virtues [MacIntyre]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
Virtue is secondary to a role-figure, defined within a culture [MacIntyre, by Statman]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
Characters are the masks worn by moral philosophies [MacIntyre]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / h. Right feelings
If morality just is emotion, there are no external criteria for judging emotions [MacIntyre]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
Since Moore thinks the right action produces the most good, he is a utilitarian [MacIntyre]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
There are no natural or human rights, and belief in them is nonsense [MacIntyre]
28. God / A. Divine Nature / 4. Divine Contradictions
If God is omniscient, he confronts no as yet unmade decisions, so decisions are impossible [MacIntyre]