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All the ideas for 'works', 'Thinking About Mathematics' and 'The Myth of the Aesthetic Attitude'

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36 ideas

1. Philosophy / B. History of Ideas / 5. Later European Thought
Hegel produced modern optimism; he failed to grasp that consciousness never progresses [Hegel, by Cioran]
1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / d. Nineteenth century philosophy
Hegel was the last philosopher of the Book [Hegel, by Derrida]
1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Hegel doesn't storm the heavens like the giants, but works his way up by syllogisms [Kierkegaard on Hegel]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
For Hegel, things are incomplete, and contain external references in their own nature [Hegel, by Russell]
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
On the continent it is generally believed that metaphysics died with Hegel [Benardete,JA on Hegel]
2. Reason / B. Laws of Thought / 2. Sufficient Reason
Making sufficient reason an absolute devalues the principle of non-contradiction [Hegel, by Meillassoux]
2. Reason / C. Styles of Reason / 1. Dialectic
Rather than in three stages, Hegel presented his dialectic as 'negation of the negation' [Hegel, by Bowie]
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]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
Negation of negation doubles back into a self-relationship [Hegel, by Houlgate]
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]
7. Existence / A. Nature of Existence / 3. Being / c. Becoming
The dialectical opposition of being and nothing is resolved in passing to the concept of becoming [Hegel, by Scruton]
7. Existence / A. Nature of Existence / 5. Reason for Existence
Hegel gives an ontological proof of the existence of everything [Hegel, by Scruton]
7. Existence / E. Categories / 4. Category Realism
For Hegel, categories shift their form in the course of history [Hegel, by Houlgate]
Our concepts and categories disclose the world, because we are part of the world [Hegel, by Houlgate]
7. Existence / E. Categories / 5. Category Anti-Realism
Hegel said Kant's fixed categories actually vary with culture and era [Hegel, by Houlgate]
12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic
Hegel reputedly claimed to know a priori that there are five planets [Hegel, by Field,H]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
The aesthetic attitude is nothing more than paying close attention [Dickie, by Giovannelli]
23. Ethics / F. Existentialism / 1. Existentialism
Humans have no fixed identity, but produce and reveal their shifting identity in history [Hegel, by Houlgate]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
Hegel's Absolute Spirit is the union of human rational activity at a moment, and whatever that sustains [Hegel, by Eldridge]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
Society isn’t founded on a contract, since contracts presuppose a society [Hegel, by Scruton]
26. Natural Theory / A. Speculations on Nature / 1. Nature
When man wills the natural, it is no longer natural [Hegel]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
Hegel's entire philosophy is nothing but a monstrous amplification of the ontological proof [Schopenhauer on Hegel]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Hegel said he was offering an encyclopaedic rationalisation of Christianity [Hegel, by Graham]