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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Virtues of the Mind' and 'The Facts of Causation'

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55 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Unlike knowledge, wisdom cannot be misused [Zagzebski]
1. Philosophy / A. Wisdom / 2. Wise People
Wisdom is the property of a person, not of their cognitive state [Zagzebski, by Whitcomb]
2. Reason / D. Definition / 2. Aims of Definition
Precision is only one of the virtues of a good definition [Zagzebski]
2. Reason / E. Argument / 1. Argument
Objection by counterexample is weak, because it only reveals inaccuracies in one theory [Zagzebski]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
We might use 'facta' to refer to the truth-makers for facts [Mellor, by Schaffer,J]
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]
11. Knowledge Aims / A. Knowledge / 2. Understanding
Modern epistemology is too atomistic, and neglects understanding [Zagzebski]
Epistemology is excessively atomic, by focusing on justification instead of understanding [Zagzebski]
11. Knowledge Aims / A. Knowledge / 3. Value of Knowledge
Truth is valuable, but someone knowing the truth is more valuable [Zagzebski]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
Some beliefs are fairly voluntary, and others are not at all so [Zagzebski]
11. Knowledge Aims / A. Knowledge / 5. Aiming at Truth
Knowledge either aims at a quantity of truths, or a quality of understanding of truths [Zagzebski]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / b. Gettier problem
For internalists Gettier situations are where internally it is fine, but there is an external mishap [Zagzebski]
Gettier problems are always possible if justification and truth are not closely linked [Zagzebski]
We avoid the Gettier problem if the support for the belief entails its truth [Zagzebski]
Gettier cases arise when good luck cancels out bad luck [Zagzebski]
13. Knowledge Criteria / B. Internal Justification / 1. Epistemic virtues
Intellectual virtues are forms of moral virtue [Zagzebski]
Intellectual and moral prejudice are the same vice (and there are other examples) [Zagzebski]
We can name at least thirteen intellectual vices [Zagzebski]
A reliable process is no use without the virtues to make use of them [Zagzebski]
A justified belief emulates the understanding and beliefs of an intellectually virtuous person [Zagzebski]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
Epistemic perfection for reliabilism is a truth-producing machine [Zagzebski]
16. Persons / C. Self-Awareness / 2. Knowing the Self
The self is known as much by its knowledge as by its action [Zagzebski]
18. Thought / A. Modes of Thought / 3. Emotions / d. Emotional feeling
The feeling accompanying curiosity is neither pleasant nor painful [Zagzebski]
20. Action / C. Motives for Action / 1. Acting on Desires
Motives involve desires, but also how the desires connect to our aims [Zagzebski]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
Modern moral theory concerns settling conflicts, rather than human fulfilment [Zagzebski]
22. Metaethics / C. The Good / 1. Goodness / i. Moral luck
Moral luck means our praise and blame may exceed our control or awareness [Zagzebski]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
Nowadays we doubt the Greek view that the flourishing of individuals and communities are linked [Zagzebski]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
Every moral virtue requires a degree of intelligence [Zagzebski]
Virtue theory is hopeless if there is no core of agreed universal virtues [Zagzebski]
A virtue must always have a corresponding vice [Zagzebski]
Eight marks distingush skills from virtues [Zagzebski, by PG]
Virtues are deep acquired excellences of persons, which successfully attain desire ends [Zagzebski]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
Virtue theory can have lots of rules, as long as they are grounded in virtues and in facts [Zagzebski]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / j. Unity of virtue
We need phronesis to coordinate our virtues [Zagzebski]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
For the virtue of honesty you must be careful with the truth, and not just speak truly [Zagzebski]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
The courage of an evil person is still a quality worth having [Zagzebski]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
Causal statements relate facts (which are whatever true propositions express) [Mellor, by Psillos]
26. Natural Theory / C. Causation / 8. Particular Causation / e. Probabilistic causation
Probabilistic causation says C is a cause of E if it increases the chances of E occurring [Mellor, by Tooley]