Combining Texts

All the ideas for 'Thinking About Mathematics', 'Quining Qualia' and 'Ontological Dependence'

expand these ideas     |    start again     |     specify just one area for these texts

28 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / c. Philosophy as generalisation
14255 We understand things through their dependency relations [Fine,K]
1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
14250 Metaphysics deals with the existence of things and with the nature of things [Fine,K]
2. Reason / D. Definition / 4. Real Definition
14259 Maybe two objects might require simultaneous real definitions, as with two simultaneous terms [Fine,K]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
8729 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
8763 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
18249 Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
8764 Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
8762 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
8760 Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
8761 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
8744 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
8749 Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
8750 Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
8752 Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
8753 Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
8731 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
8730 'Impredicative' definitions refer to the thing being described [Shapiro]
7. Existence / A. Nature of Existence / 3. Being / b. Being and existence
14253 An object's 'being' isn't existence; there's more to an object than existence, and its nature doesn't include existence [Fine,K]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
14261 There is 'weak' dependence in one definition, and 'strong' dependence in all the definitions [Fine,K]
14251 A natural modal account of dependence says x depends on y if y must exist when x does [Fine,K]
14257 An object depends on another if the second cannot be eliminated from the first's definition [Fine,K]
14254 Dependency is the real counterpart of one term defining another [Fine,K]
9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual
14252 We should understand identity in terms of the propositions it renders true [Fine,K]
9. Objects / D. Essence of Objects / 2. Types of Essence
14256 How do we distinguish basic from derived esssences? [Fine,K]
14258 Maybe some things have essential relationships as well as essential properties [Fine,K]
9. Objects / D. Essence of Objects / 4. Essence as Definition
14260 An object only essentially has a property if that property follows from every definition of the object [Fine,K]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
15. Nature of Minds / B. Features of Minds / 5. Qualia / a. Nature of qualia
6624 Dennett denies the existence of qualia [Dennett, by Lowe]