42 ideas
19635 | 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 |
8215 | 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. |
16011 | 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] |
5433 | 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. |
3301 | 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 |
19661 | 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!] |
20952 | 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. |
17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
Full Idea: In intuitionist logic double negation elimination fails. After all, proving that there is no proof that there can't be a proof of S is not the same thing as having a proof of S. | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3) | |
A reaction: I do like people like Colyvan who explain things clearly. All of this difficult stuff is understandable, if only someone makes the effort to explain it properly. |
17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
Full Idea: The intuitionist rejection of double negation elimination undermines the important reductio ad absurdum proof in classical mathematics. | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3) |
17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
Full Idea: The law of excluded middle (for every proposition P, either P or not-P) must be carefully distinguished from its semantic counterpart bivalence, that every proposition is either true or false. | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3) | |
A reaction: So excluded middle makes no reference to the actual truth or falsity of P. It merely says P excludes not-P, and vice versa. |
21777 | 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. |
17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
Full Idea: Löwenheim proved that if a first-order sentence has a model at all, it has a countable model. ...Skolem generalised this result to systems of first-order sentences. | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 2.1.2) |
17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
Full Idea: A set of axioms is said to be 'categorical' if all models of the axioms in question are isomorphic. | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 2.1.2) | |
A reaction: The best example is the Peano Axioms, which are 'true up to isomorphism'. Set theory axioms are only 'quasi-isomorphic'. |
17928 | Ordinal numbers represent order relations [Colyvan] |
Full Idea: Ordinal numbers represent order relations. | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.2.3 n17) |
17923 | Intuitionists only accept a few safe infinities [Colyvan] |
Full Idea: For intuitionists, all but the smallest, most well-behaved infinities are rejected. | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3) | |
A reaction: The intuitionist idea is to only accept what can be clearly constructed or proved. |
17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
Full Idea: The problem with infinitesimals is that in some places they behaved like real numbers close to zero but in other places they behaved like zero. | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 7.1.2) | |
A reaction: Colyvan gives an example, of differentiating a polynomial. |
17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
Full Idea: Given Dedekind's reduction of real numbers to sequences of rational numbers, and other known reductions in mathematics, it was tempting to see basic arithmetic as the foundation of mathematics. | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.1) | |
A reaction: The reduction is the famous Dedekind 'cut'. Nowadays theorists seem to be more abstract (Category Theory, for example) instead of reductionist. |
17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
Full Idea: Transfinite inductions are inductive proofs that include an extra step to show that if the statement holds for all cases less than some limit ordinal, the statement also holds for the limit ordinal. | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1 n11) |
17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
Full Idea: Most mathematical proofs, outside of set theory, do not explicitly state the set theory being employed. | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 7.1.1) |
17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
Full Idea: Structuralism is able to explain why mathematicians are typically only interested in describing the objects they study up to isomorphism - for that is all there is to describe. | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 3.1.2) |
17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
Full Idea: In re structuralism does not posit anything other than the kinds of structures that are in fact found in the world. ...The problem is that the world may not provide rich enough structures for the mathematics. | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 3.1.2) | |
A reaction: You can perceive a repeating pattern in the world, without any interest in how far the repetitions extend. |
5645 | 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'. |
5646 | 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? |
21755 | 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. |
21754 | 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. |
22079 | 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. |
9225 | 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. |
17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
Full Idea: Those who see probabilities as ratios of frequencies can't use Bayes's Theorem if there is no objective prior probability. Those who accept prior probabilities tend to opt for a subjectivist account, where probabilities are degrees of belief. | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 9.1.8) | |
A reaction: [compressed] |
17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
Full Idea: Mathematics can demonstrate structural similarities between systems (e.g. missing population periods and the gaps in the rings of Saturn). | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 6.3.2) | |
A reaction: [Colyvan expounds the details of his two examples] It is these sorts of results that get people enthusiastic about the mathematics embedded in nature. A misunderstanding, I think. |
17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
Full Idea: Mathematics can show that under a broad range of conditions, something initially surprising must occur (e.g. the hexagonal structure of honeycomb). | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 6.3.2) |
17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
Full Idea: One kind of proof that is thought to be unexplanatory is the 'reductio' proof. | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1) | |
A reaction: Presumably you generate a contradiction, but are given no indication of why the contradiction has arisen? Tracking back might reveal the source of the problem? Colyvan thinks reductio can be explanatory. |
17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
Full Idea: It might be argued that any proof by induction is revealing the explanation of the theorem, namely, that it holds by virtue of the structure of the natural numbers. | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1) | |
A reaction: This is because induction characterises the natural numbers, in the Peano Axioms. |
17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
Full Idea: The proof of the four-colour theorem raises questions about whether a 'proof' that no one understands is a proof. | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 9.1.6) | |
A reaction: The point is that the theorem (that you can colour countries on a map with just four colours) was proved with the help of a computer. |
17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
Full Idea: Another style of proof often cited as unexplanatory are brute-force methods such as proof by cases (or proof by exhaustion). | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1) |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
Full Idea: One type of generalisation in mathematics extends a system to go beyond what is was originally set up for; another kind involves abstracting away from some details in order to capture similarities between different systems. | |
From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.2) |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
21758 | 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. |
20414 | 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. |
3909 | 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?). |
4347 | 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. |
4188 | 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. |
6686 | 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? |