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All the ideas for 'talk', 'Quodlibeta' and 'The Nature of Mathematical Knowledge'

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80 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / c. Classical philosophy
For the truth you need Prodicus's fifty-drachma course, not his one-drachma course [Socrates]
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
A philosopher is one who cares about what other people care about [Socrates, by Foucault]
1. Philosophy / D. Nature of Philosophy / 6. Hopes for Philosophy
Socrates opened philosophy to all, but Plato confined moral enquiry to a tiny elite [Vlastos on Socrates]
1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
Philosophical discussion involves dividing subject-matter into categories [Socrates, by Xenophon]
1. Philosophy / F. Analytic Philosophy / 2. Analysis by Division
Socrates began the quest for something universal with his definitions, but he didn't make them separate [Socrates, by Aristotle]
2. Reason / C. Styles of Reason / 1. Dialectic
It is legitimate to play the devil's advocate [Socrates]
2. Reason / C. Styles of Reason / 2. Elenchus
In Socratic dialogue you must say what you believe, so unasserted premises are not debated [Vlastos on Socrates]
Socrates was pleased if his mistakes were proved wrong [Socrates]
The method of Socrates shows the student is discovering the truth within himself [Socrates, by Carlisle]
Socrates always proceeded in argument by general agreement at each stage [Socrates, by Xenophon]
2. Reason / D. Definition / 6. Definition by Essence
Socrates sought essences, which are the basis of formal logic [Socrates, by Aristotle]
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
Socrates developed definitions as the basis of syllogisms, and also inductive arguments [Socrates, by Aristotle]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Kitcher, by Resnik]
Mathematical a priorism is conceptualist, constructivist or realist [Kitcher]
The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher]
The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers stand to measurement as natural numbers stand to counting [Kitcher]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / j. Complex numbers
Complex numbers were only accepted when a geometrical model for them was found [Kitcher]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
A one-operation is the segregation of a single object [Kitcher]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
The old view is that mathematics is useful in the world because it describes the world [Kitcher]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
With infinitesimals, you divide by the time, then set the time to zero [Kitcher]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher]
Mathematical intuition is not the type platonism needs [Kitcher]
If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Mathematical knowledge arises from basic perception [Kitcher]
My constructivism is mathematics as an idealization of collecting and ordering objects [Kitcher]
We derive limited mathematics from ordinary things, and erect powerful theories on their basis [Kitcher]
The defenders of complex numbers had to show that they could be expressed in physical terms [Kitcher]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
Arithmetic is an idealizing theory [Kitcher]
Arithmetic is made true by the world, but is also made true by our constructions [Kitcher]
We develop a language for correlations, and use it to perform higher level operations [Kitcher]
Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher]
If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher]
7. Existence / E. Categories / 3. Proposed Categories
Substance, Quantity and Quality are real; other categories depend on those three [Henry of Ghent]
8. Modes of Existence / A. Relations / 1. Nature of Relations
The only reality in the category of Relation is things from another category [Henry of Ghent]
8. Modes of Existence / B. Properties / 8. Properties as Modes
Accidents are diminished beings, because they are dispositions of substance (unqualified being) [Henry of Ghent]
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
Socrates did not consider universals or definitions as having separate existence, but Plato made Forms of them [Socrates, by Aristotle]
9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
Abstract objects were a bad way of explaining the structure in mathematics [Kitcher]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
Kant says things-in-themselves cause sensations, but then makes causation transcendental! [Henry of Ghent, by Pinkard]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
A priori knowledge comes from available a priori warrants that produce truth [Kitcher]
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
In long mathematical proofs we can't remember the original a priori basis [Kitcher]
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge [Kitcher]
12. Knowledge Sources / A. A Priori Knowledge / 10. A Priori as Subjective
We have some self-knowledge a priori, such as knowledge of our own existence [Kitcher]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
A 'warrant' is a process which ensures that a true belief is knowledge [Kitcher]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / c. Defeasibility
If experiential can defeat a belief, then its justification depends on the defeater's absence [Kitcher, by Casullo]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
For Socrates our soul, though hard to define, is our self [Vlastos on Socrates]
18. Thought / A. Modes of Thought / 5. Rationality / b. Human rationality
Socrates first proposed that we are run by mind or reason [Socrates, by Frede,M]
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
No one willingly commits an evil or base act [Socrates]
Socrates did not accept the tripartite soul (which permits akrasia) [Vlastos on Socrates]
People do what they think they should do, and only ever do what they think they should do [Socrates, by Xenophon]
Socrates was shocked by the idea of akrasia, but observation shows that it happens [Aristotle on Socrates]
The common belief is that people can know the best without acting on it [Socrates]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
For Socrates, wisdom and prudence were the same thing [Socrates, by Xenophon]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
For Socrates, virtues are forms of knowledge, so knowing justice produces justice [Socrates, by Aristotle]
Socrates was the first to base ethics upon reason, and use reason to explain it [Taylor,R on Socrates]
All human virtues are increased by study and practice [Socrates, by Xenophon]
The wise perform good actions, and people fail to be good without wisdom [Socrates, by Xenophon]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
Socrates despised good looks [Socrates, by Plato]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Socrates conservatively assumed that Athenian conventions were natural and true [Taylor,R on Socrates]
22. Metaethics / B. Value / 2. Values / b. Successful function
A well-made dung basket is fine, and a badly-made gold shield is base, because of function [Socrates, by Xenophon]
22. Metaethics / B. Value / 2. Values / h. Fine deeds
Things are both good and fine by the same standard [Socrates, by Xenophon]
22. Metaethics / C. The Good / 1. Goodness / e. Good as knowledge
The only good is knowledge, and the only evil is ignorance [Socrates, by Diog. Laertius]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
Socrates was the first to put 'eudaimonia' at the centre of ethics [Socrates, by Vlastos]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
By 'areté' Socrates means just what we mean by moral virtue [Vlastos on Socrates]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
Socrates is torn between intellectual virtue, which is united and teachable, and natural virtue, which isn't [PG on Socrates]
Socrates agrees that virtue is teachable, but then denies that there are teachers [Socrates, by MacIntyre]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
We should ask what sort of people we want to be [Socrates]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / j. Unity of virtue
Socrates believed that basically there is only one virtue, the power of right judgement [Socrates, by Williams,B]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
Socrates made the civic values of justice and friendship paramount [Socrates, by Grayling]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
Courage is scientific knowledge [Socrates, by Aristotle]
23. Ethics / F. Existentialism / 1. Existentialism
Socrates emphasises that the knower is an existing individual, with existence his main task [Socrates, by Kierkegaard]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
Obedience to the law gives the best life, and success in war [Socrates, by Xenophon]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
Socrates was the first to grasp that a cruelty is not justified by another cruelty [Vlastos on Socrates]
25. Social Practice / F. Life Issues / 5. Sexual Morality
A lover using force is a villain, but a seducer is much worse, because he corrupts character [Socrates, by Xenophon]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
Socrates holds that right reason entails virtue, and this must also apply to the gods [Vlastos on Socrates]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
A new concept of God as unswerving goodness emerges from Socrates' commitment to virtue [Vlastos on Socrates]