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All the ideas for 'works', 'Wiener Logik' and 'Remarks on the definition and nature of mathematics'

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26 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]
     Full Idea: Hegel is chiefly responsible for modern optimism. How could he have failed to see that consciousness changes only its forms and modalities, but never progresses.
     From: report of Georg W.F.Hegel (works [1812]) by E.M. Cioran - A Short History of Decay 5
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]
     Full Idea: Hegel was the last philosopher of the Book.
     From: report of Georg W.F.Hegel (works [1812]) by Jacques Derrida - Positions p.64
     A reaction: Reference to 'the Book' connects this to the great religions which rely on one holy text. The implication is that Hegel was proposing one big solution to all problems. It is doubtful if many philosophers before Hegel dreamt of that either.
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]
     Full Idea: Hegel is a Johannes Climacus who does not storm the heavens, like the giants, by putting mountain upon mountain, but climbs aboard them by way of his syllogisms.
     From: comment on Georg W.F.Hegel (works [1812]) by Søren Kierkegaard - The Journals of Kierkegaard 2A
     A reaction: [Idea from SY] This appears to be an attempt at insulting Hegel for his timidity, but it seems to be describing the cautious approach which most modern philosophers take to be correct. [PG]
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]
     Full Idea: The basis of Hegel's system is that what is incomplete must not be self-subsistent, and needs the support of other things; whatever has relations to things outside itself must contain some reference to those outside things in its own nature.
     From: report of Georg W.F.Hegel (works [1812]) by Bertrand Russell - Problems of Philosophy Ch.14
     A reaction: This leads to the idealist doctrine of 'internal relations'. It has some plausibility if you think about the physicist's definition of mass, which has to refer to forces etc. Presumably there is one essence for all of reality, instead of separate ones.
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]
     Full Idea: In continental Europe it is widely believed that the metaphysical game was played out in Hegel.
     From: comment on Georg W.F.Hegel (works [1812]) by José A. Benardete - Metaphysics: the logical approach Intro
2. Reason / B. Laws of Thought / 2. Sufficient Reason
Making sufficient reason an absolute devalues the principle of non-contradiction [Hegel, by Meillassoux]
     Full Idea: Hegel saw that the absolutization of the principle of sufficient reason (which marked the culmination of the belief in the necessity of what is) required the devaluation of the principle of non-contradiction.
     From: report of Georg W.F.Hegel (works [1812], 3) by Quentin Meillassoux - After Finitude; the necessity of contingency 3
     A reaction: I pass this on without understanding it, though a joint study of my collection of ideas on sufficient reason and non-contradiction might make it clear. [Let me know if you can explain it!]
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]
     Full Idea: Hegel's 'dialectic' is often characterised in terms of the triad of thesis, antithesis and synthesis. This is, however, not the way he presents it. The core of the dialectic is rather what Hegel terms the 'negation of the negation'.
     From: report of Georg W.F.Hegel (works [1812]) by Andrew Bowie - Introduction to German Philosophy
     A reaction: Interestingly, this connects it to debates about intuitionist logic, which denies that double-negation necessarily makes a positive. Presumably Marx emphasised the first reading.
2. Reason / D. Definition / 2. Aims of Definition
A simplification which is complete constitutes a definition [Kant]
     Full Idea: By dissection I can make the concept distinct only by making the marks it contains clear. That is what analysis does. If this analysis is complete ...and in addition there are not so many marks, then it is precise and so constitutes a definition.
     From: Immanuel Kant (Wiener Logik [1795], p.455), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc'
     A reaction: I think Aristotle would approve of this. We need to grasp that a philosophical definition is quite different from a lexicographical definition. 'Completeness' may involve quite a lot.
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic gives us the necessary rules which show us how we ought to think [Kant]
     Full Idea: In logic the question is not one of contingent but of necessary rules, not how to think, but how we ought to think.
     From: Immanuel Kant (Wiener Logik [1795], p.16), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Trans'
     A reaction: Presumably it aspires to the objectivity of a single correct account of how we all ought to think. I'm sympathetic to that, rather than modern cultural relativism about reason. Logic is rooted in nature, not in arbitrary convention.
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]
     Full Idea: For Hegel, the 'negation of negation' is negation that, as it were, doubles back on itself and 'relates itself to itself'.
     From: report of Georg W.F.Hegel (works [1812]) by Stephen Houlgate - An Introduction to Hegel 6 'Space'
     A reaction: [ref VNP 1823 p.108] Glad we've cleared that one up.
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]
     Full Idea: In the study of formal systems we do not confine ourselves to the derivation of elementary propositions step by step. Rather we take the system, defined by its primitive frame, as datum, and then study it by any means at our command.
     From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The formalist')
     A reaction: This is what may potentially lead to an essentialist view of such things. Focusing on bricks gives formalism, focusing on buildings gives essentialism.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
It is untenable that mathematics is general physical truths, because it needs infinity [Curry]
     Full Idea: According to realism, mathematical propositions express the most general properties of our physical environment. This is the primitive view of mathematics, yet on account of the essential role played by infinity in mathematics, it is untenable today.
     From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The problem')
     A reaction: I resist this view, because Curry's view seems to imply a mad metaphysics. Hilbert resisted the role of the infinite in essential mathematics. If the physical world includes its possibilities, that might do the job. Hellman on structuralism?
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Saying mathematics is logic is merely replacing one undefined term by another [Curry]
     Full Idea: To say that mathematics is logic is merely to replace one undefined term by another.
     From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'Mathematics')
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]
     Full Idea: The concept of being contains within itself it own negation - nothing - and the dialectical opposition between these two concepts is resolved only in the passage to a new concept, becoming, which contains the truth of the passage from nothing to being.
     From: report of Georg W.F.Hegel (works [1812]) by Roger Scruton - Short History of Modern Philosophy Ch.12
     A reaction: The idea that one concept 'contains' another, or that an opposition could be 'resolved' by a new concept, sounds doubtful to me. For most analytical philosophers, and for Aristotle, oppositions are contradictions, and cannot and should not be 'resolved'.
7. Existence / A. Nature of Existence / 5. Reason for Existence
Hegel gives an ontological proof of the existence of everything [Hegel, by Scruton]
     Full Idea: It would not be unfair to say that Hegel's metaphysics consists of an ontological proof of the existence of everything.
     From: report of Georg W.F.Hegel (works [1812]) by Roger Scruton - Short History of Modern Philosophy Ch.12
     A reaction: This is so gloriously far from David Hume that we must all find some appeal in it. The next question would be whether necessary existence has been proved. If so, given death, decay and entropy, what is it that has to exist? 2nd Law of Thermodynamics?
7. Existence / E. Categories / 4. Category Realism
For Hegel, categories shift their form in the course of history [Hegel, by Houlgate]
     Full Idea: For Hegel, the categories of thought are not fixed, eternal forms that remain unchanged throughout history, but are concepts that alter their meaning in history.
     From: report of Georg W.F.Hegel (works [1812]) by Stephen Houlgate - An Introduction to Hegel 01
     A reaction: This results from a critique of Kant's rather rigid view of categories. This idea is very influential, and certainly counts among Hegel's better ideas.
Our concepts and categories disclose the world, because we are part of the world [Hegel, by Houlgate]
     Full Idea: For Hegel, the structure of our concepts and categories is identical with, and thus discloses, the structure of the world itself, because we ourselves are born into and so share the character of the world we encounter.
     From: report of Georg W.F.Hegel (works [1812]) by Stephen Houlgate - An Introduction to Hegel 01
     A reaction: This is a reasonable speculation, but it makes more sense in the context of natural selection, and an empiricist theory of concepts.
7. Existence / E. Categories / 5. Category Anti-Realism
Hegel said Kant's fixed categories actually vary with culture and era [Hegel, by Houlgate]
     Full Idea: Hegel's disagreement with Kant is that categories are not unambiguously universal forms of human understanding, but are conceived in subtly different ways in different cultures and in different historical epochs.
     From: report of Georg W.F.Hegel (works [1812]) by Stephen Houlgate - Hegel p.95
     A reaction: This may be Hegel's most influential idea. Though he hoped that categories would contain truth, by arising untrammelled from reason, and thereby matching reality. His successors seem to have given up on that hope, and settled for relativism.
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]
     Full Idea: Hegel is reputed to have claimed to have deduced on a priori grounds that the number of planets is exactly five.
     From: report of Georg W.F.Hegel (works [1812]) by Hartry Field - Recent Debates on the A Priori 1
     A reaction: Even if this is a wicked travesty of Hegel, it will do nicely to represent the extremes of claims to a priori synthetic knowledge. Field doesn't offer any evidence. I would love it to be true.
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / b. Pro-externalism
If we knew what we know, we would be astonished [Kant]
     Full Idea: If we only know what we know ...we would be astonished by the treasures contained in our knowledge.
     From: Immanuel Kant (Wiener Logik [1795], p.843), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc'
     A reaction: Nice remark. He doesn't require immediat recall of knowledge. You can't be required to know that you know something. That doesn't imply externalism, though. I believe in securely founded internal knowledge which is hard to recall.
23. Ethics / F. Existentialism / 1. Existentialism
Humans have no fixed identity, but produce and reveal their shifting identity in history [Hegel, by Houlgate]
     Full Idea: For Hegel, the absolute truth of humanity is that human beings have no fixed, given identity, but rather determine and produce their own identity and their world in history, and that they gradually come to the recognition of this fact in history.
     From: report of Georg W.F.Hegel (works [1812]) by Stephen Houlgate - An Introduction to Hegel 01
     A reaction: This quintessentially existentialist idea, most obvious in Sartre, seems to have originated with this view of Hegel's.
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]
     Full Idea: We may take Hegel's Absolute Spirit to be the union of collective, human rational activity at a historical moment with its proper object, the forms of social and individual life that the rational activity is devoted to understanding and sustaining.
     From: report of Georg W.F.Hegel (works [1812]) by Richard Eldridge - G.W.F. Hegel (aesthetics) 1
     A reaction: From this formulation it sounds as if the whole human race might have momentary union, but presumably it is more local 'peoples' that can exhibit this.
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]
     Full Idea: For Hegel, society cannot be founded on a contract, since contracts have no reality until society is in place.
     From: report of Georg W.F.Hegel (works [1812]) by Roger Scruton - Modern Philosophy:introduction and survey 28.2
     A reaction: Interesting, and reminiscent of the private language argument, but contracts surely start as deals between individuals (on a desert island?).
26. Natural Theory / A. Speculations on Nature / 1. Nature
When man wills the natural, it is no longer natural [Hegel]
     Full Idea: When man wills the natural, it is no longer natural.
     From: Georg W.F.Hegel (works [1812]), quoted by Rosalind Hursthouse - On Virtue Ethics Ch.4
     A reaction: Sounds good, though I'm not sure what it means. The application of the word 'natural' seems a bit arbitrary to me. No objective joint exists between the natural and unnatural. The default position has to be that everything is natural.
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]
     Full Idea: Hegel's entire philosophy is nothing but a monstrous amplification of the ontological proof.
     From: comment on Georg W.F.Hegel (works [1812]) by Arthur Schopenhauer - Abstract of 'The Fourfold Root' Ch.II
     A reaction: All massive a priori metaphysics is summed up in this argument, which is right at the core of philosophy.
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Hegel said he was offering an encyclopaedic rationalisation of Christianity [Hegel, by Graham]
     Full Idea: Hegel claimed that his philosophy was nothing less than an encyclopaedic rationalisation of the Christian religion.
     From: report of Georg W.F.Hegel (works [1812]) by Gordon Graham - Eight Theories of Ethics Ch.5
     A reaction: Why did he pick Christianity to rationalise? How can you reason properly if you start with a dogma?