Combining Texts

All the ideas for 'Thinking About Mathematics', 'The Theory of Objects' and 'Virtues of the Mind'

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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]
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
So-called 'free logic' operates without existence assumptions [Meinong, by George/Van Evra]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
'Impredicative' definitions refer to the thing being described [Shapiro]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
There can be impossible and contradictory objects, if they can have properties [Meinong, by Friend]
9. Objects / A. Existence of Objects / 3. Objects in Thought
There are objects of which it is true that there are no such objects [Meinong]
Meinong says an object need not exist, but must only have properties [Meinong, by Friend]
9. Objects / A. Existence of Objects / 4. Impossible objects
Meinong said all objects of thought (even self-contradictions) have some sort of being [Meinong, by Lycan]
The objects of knowledge are far more numerous than objects which exist [Meinong]
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]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
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]
A reliable process is no use without the virtues to make use of them [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 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
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]
Every moral virtue requires a degree of intelligence [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]