Combining Texts

All the ideas for 'works', 'Infinity: Quest to Think the Unthinkable' and 'Two Chief World Systems'

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41 ideas

1. Philosophy / B. History of Ideas / 5. Later European Thought
19635 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
8215 Hegel was the last philosopher of the Book [Hegel, by Derrida]
1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
16011 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
5433 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
3301 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
19661 Making sufficient reason an absolute devalues the principle of non-contradiction [Hegel, by Meillassoux]
2. Reason / C. Styles of Reason / 1. Dialectic
20952 Rather than in three stages, Hegel presented his dialectic as 'negation of the negation' [Hegel, by Bowie]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
10859 A set is 'well-ordered' if every subset has a first element [Clegg]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
10857 Set theory made a closer study of infinity possible [Clegg]
10864 Any set can always generate a larger set - its powerset, of subsets [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
10872 Extensionality: Two sets are equal if and only if they have the same elements [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
10875 Pairing: For any two sets there exists a set to which they both belong [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
10876 Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
10878 Infinity: There exists a set of the empty set and the successor of each element [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
10877 Powers: All the subsets of a given set form their own new powerset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10879 Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
10871 Axiom of Existence: there exists at least one set [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
10874 Specification: a condition applied to a set will always produce a new set [Clegg]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
21777 Negation of negation doubles back into a self-relationship [Hegel, by Houlgate]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
10880 Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
10860 An ordinal number is defined by the set that comes before it [Clegg]
10861 Beyond infinity cardinals and ordinals can come apart [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10854 Transcendental numbers can't be fitted to finite equations [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / k. Imaginary numbers
10858 By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
10853 Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10866 Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10869 The Continuum Hypothesis is independent of the axioms of set theory [Clegg]
10862 The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg]
7. Existence / A. Nature of Existence / 3. Being / c. Becoming
5645 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
5646 Hegel gives an ontological proof of the existence of everything [Hegel, by Scruton]
7. Existence / E. Categories / 4. Category Realism
21755 For Hegel, categories shift their form in the course of history [Hegel, by Houlgate]
21754 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
22079 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
9225 Hegel reputedly claimed to know a priori that there are five planets [Hegel, by Field,H]
23. Ethics / F. Existentialism / 1. Existentialism
21758 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
20414 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
3909 Society isn’t founded on a contract, since contracts presuppose a society [Hegel, by Scruton]
26. Natural Theory / A. Speculations on Nature / 1. Nature
4347 When man wills the natural, it is no longer natural [Hegel]
27. Natural Reality / A. Classical Physics / 1. Mechanics / b. Laws of motion
19673 Galileo mathematised movement, and revealed its invariable component - acceleration [Galileo, by Meillassoux]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
4188 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
6686 Hegel said he was offering an encyclopaedic rationalisation of Christianity [Hegel, by Graham]