Combining Texts

All the ideas for 'The Middle Works (15 vols, ed Boydston)', 'Croce and Collingwood' and 'Thinking About Mathematics'

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25 ideas

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]
11. Knowledge Aims / A. Knowledge / 3. Value of Knowledge
The value and truth of knowledge are measured by success in activity [Dewey]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
16. Persons / B. Nature of the Self / 1. Self and Consciousness
Habits constitute the self [Dewey]
21. Aesthetics / A. Aesthetic Experience / 1. Aesthetics
By 1790 aestheticians were mainly trying to explain individual artistic genius [Kemp]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
Expression can be either necessary for art, or sufficient for art (or even both) [Kemp]
We don't already know what to express, and then seek means of expressing it [Kemp]
The horror expressed in some works of art could equallly be expressed by other means [Kemp]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
The good people are those who improve; the bad are those who deteriorate [Dewey]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
Democracy is the development of human nature when it shares in the running of communal activities [Dewey]
Democracy is not just a form of government; it is a mode of shared living [Dewey]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
Individuality is only developed within groups [Dewey]