49 ideas
| 8927 | Philosophy moves essentially in the element of universality [Hegel] |
| Full Idea: Philosophy moves essentially in the element of universality. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 01) | |
| A reaction: I would take this to be uncontroversially correct. An interesting test case is applied ethics, which seems embedded in current cultural practices. I would always take it to be searching for what is universal in each situation. |
| 21776 | Philosophy aims to reveal the necessity and rationality of the categories of nature and spirit [Hegel, by Houlgate] |
| Full Idea: For Hegel, philosophy's principal task is to disclose the enduring necessity and rationality of the categories and forms of nature and spirit that it examines. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Stephen Houlgate - An Introduction to Hegel 4 'Phenomenology' | |
| A reaction: The idea that a miserable little evolved and transient mammal on a tiny planet has direct insight into the necessities and categories of nature and spirit looks a shade optimistic to me. You have to admire the ambition, though. |
| 8935 | Without philosophy, science is barren and futile [Hegel] |
| Full Idea: Let other sciences try to argue as much as they like without philosophy - without it they can have in them neither life, Spirit, nor truth. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 67) | |
| A reaction: To be pinned up in every physics laboratory in the world. On the whole I agree with this. My slogan is 'science is the servant of philosophy'. An unphilosophical scientist is just a technologist, an artisan. |
| 22082 | Truth does not appear by asserting reasons and then counter-reasons [Hegel] |
| Full Idea: It is not difficult to see that the way of asserting a proposition, adducing reasons for it, and in the same way refuting its opposite by reasons, is not the form in which truth can appear. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], p.28), quoted by Stephen Houlgate - Hegel p.100 | |
| A reaction: This is a pretty good description of the way Plato and Aristotle do philosophy, so this idea, which must be a founding idea for the 'continental school', is extremely radical. Personally I identify rationality with believing things for good reasons. |
| 22035 | The structure of reason is a social and historical achievement [Hegel, by Pinkard] |
| Full Idea: The lesson of Hegel's Phenomenology was that the structure of reason was social, and was therefore a historical achievement. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Terry Pinkard - German Philosophy 1760-1860 10 | |
| A reaction: This must be one of the most influential ideas to have filtered into the modern world. It is a predecessor of Marxist sociology. The idea that stands against it is Frege's platonist view of logic, making it necessary, despite being historical. |
| 8932 | Truth does not come from giving reasons for and against propositions [Hegel] |
| Full Idea: The way of asserting a proposition, adducing reasons for it, and in the same way refuting its opposite by reasons, is not the form in which truth can appear. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 48) | |
| A reaction: I can't see Plato or Aristotle agreeing with this. It is obviously the prelude to Hegel's dialectical account of reasoning. However, if we don't believe things because we have good reason to, I'm not sure where we shoud start. |
| 7077 | The true is the whole [Hegel] |
| Full Idea: The true is the whole. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 20) | |
| A reaction: This is the full idealist coherence view of truth, that one only approaches the Truth (capital T) as one builds up a more and more coherent picture. It makes truth unattainable, and that strikes me as a bit silly. |
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| Full Idea: For a set to be 'well-ordered' it is required that every subset of the set has a first element. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| Full Idea: Set theory made a closer study of infinity possible. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| Full Idea: The idea of the 'power set' means that it is always possible to generate a bigger one using only the elements of that set, namely the set of all its subsets. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.14) |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| Full Idea: Axiom of Extension: Two sets are equal if and only if they have the same elements. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| Full Idea: Axiom of Pairing: For any two sets there exists a set to which they both belong. So you can make a set out of two other sets. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| Full Idea: Axiom of Unions: For every collection of sets there exists a set that contains all the elements that belong to at least one of the sets in the collection. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| Full Idea: Axiom of Infinity: There exists a set containing the empty set and the successor of each of its elements. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: This is rather different from the other axioms because it contains the notion of 'successor', though that can be generated by an ordering procedure. |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| Full Idea: Axiom of Powers: For each set there exists a collection of sets that contains amongst its elements all the subsets of the given set. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: Obviously this must include the whole of the base set (i.e. not just 'proper' subsets), otherwise the new set would just be a duplicate of the base set. |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| Full Idea: Axiom of Choice: For every set we can provide a mechanism for choosing one member of any non-empty subset of the set. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: This axiom is unusual because it makes the bold claim that such a 'mechanism' can always be found. Cohen showed that this axiom is separate. The tricky bit is choosing from an infinite subset. |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| Full Idea: Axiom of Existence: there exists at least one set. This may be the empty set, but you need to start with something. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| Full Idea: Axiom of Specification: For every set and every condition, there corresponds a set whose elements are exactly the same as those elements of the original set for which the condition is true. So the concept 'number is even' produces a set from the integers. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: What if the condition won't apply to the set? 'Number is even' presumably won't produce a set if it is applied to a set of non-numbers. |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| Full Idea: Three views of mathematics: 'pure' mathematics, where it doesn't matter if it could ever have any application; 'real' mathematics, where every concept must be physically grounded; and 'applied' mathematics, using the non-real if the results are real. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.17) | |
| A reaction: Very helpful. No one can deny the activities of 'pure' mathematics, but I think it is undeniable that the origins of the subject are 'real' (rather than platonic). We do economics by pretending there are concepts like the 'average family'. |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| Full Idea: You can think of an ordinal number as being defined by the set that comes before it, so, in the non-negative integers, ordinal 5 is defined as {0, 1, 2, 3, 4}. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| Full Idea: With ordinary finite numbers ordinals and cardinals are in effect the same, but beyond infinity it is possible for two sets to have the same cardinality but different ordinals. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| Full Idea: The 'transcendental numbers' are those irrationals that can't be fitted to a suitable finite equation, of which π is far and away the best known. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch. 6) |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| Full Idea: The realisation that brought 'i' into the toolkit of physicists and engineers was that you could extend the 'number line' into a new dimension, with an imaginary number axis at right angles to it. ...We now have a 'number plane'. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.12) |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| Full Idea: It is a chicken-and-egg problem, whether the lack of zero forced forced classical mathematicians to rely mostly on a geometric approach to mathematics, or the geometric approach made 0 a meaningless concept, but the two remain strongly tied together. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch. 6) |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| Full Idea: As far as Kronecker was concerned, Cantor had built a whole structure on the irrational numbers, and so that structure had no foundation at all. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| Full Idea: Paul Cohen showed that the Continuum Hypothesis is independent of the axioms of set theory. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| Full Idea: The 'continuum hypothesis' says that aleph-one is the cardinality of the rational and irrational numbers. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.14) |
| 15611 | I develop philosophical science from the simplest appearance of immediate consciousness [Hegel, by Hegel] |
| Full Idea: In my 'Phenomenology of Spirit' the procedure adopted was to begin from the first and simplest appearance of the spirit, from immediate consciousness, and to develop the dialectic right up to the standpoint of philosophical science. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Georg W.F.Hegel - Logic (Encyclopedia I) §25 Rem | |
| A reaction: I take metaphysics to be either Parmenidean (starting from Being) or Cartesian (starting from mind), and this (surprisingly, given his lengthy talk of Being) shows Hegel to be a quintessentially Cartesian philosopher. Aristotle is the great Parmenidean. |
| 8934 | Being is Thought [Hegel] |
| Full Idea: Being is Thought. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 54) | |
| A reaction: You won't find a more succinct slogan for idealism than that. Speaking as what Tim Williamson (referring to himself) calls a 'rottweiler realist', I can't quite get the hang of Hegel's claim. What does he think thought is, if it isn't about the world? |
| 8928 | The Absolute is not supposed to be comprehended, but felt and intuited [Hegel] |
| Full Idea: The Absolute is not supposed to be comprehended, it is to be felt and intuited. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 06) | |
| A reaction: Hegel was a rather romantic philosopher. Where does the 'supposed' come from? If the Absolute is only felt and intuited, can the resulting apprehensions be reported to others? Is this, in fact, mysticism? |
| 21774 | Genuine idealism is seeing the ideal structure of the world [Hegel, by Houlgate] |
| Full Idea: Genuine (as opposed to subjective) idealism, for Hegel, is the point of view that knows the world to have a rational, and therefore 'ideal', structure. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Stephen Houlgate - An Introduction to Hegel 04 'The Unhappy' | |
| A reaction: Compare Leibniz, whose monad theory is said to be a sort of idealism, because it places ideas at the heart of reality. Is Plato also this sort of 'genuine' idealism? Do we need different terms for 'genuine' and 'subjective' idealism? And 'transcendental'? |
| 8929 | In the Absolute everything is the same [Hegel] |
| Full Idea: In the Absolute everything is the same. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 16) | |
| A reaction: This is indistinguishable from the great spherical reality of Parmenides. It is not unreasonable to enquire about the epistemology of this claim. Is Hegel a seer, or can we all intuit this insight into reality? |
| 21773 | Experience is immediacy, unity, forces, self-awareness, reason, culture, absolute being [Hegel, by Houlgate] |
| Full Idea: Experience moves from 1) immediacy, to 2) united objects with properties, 3) its forces and laws, 4) self-consciousness in the process, 5) seeing a rational realm, 6) seeing a cultural realm, 7) seeing the absolute being of consciousness. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Stephen Houlgate - An Introduction to Hegel 03 'From certainty' | |
| A reaction: [My summary of Houlgate's summary of the key sequence of ideas in The Phenomenology of Spirit]. I stare at it with bewilderment, but cannot decide whether or not Hegel is pursuing a worthwhile project. [also Houlgate p.77 and 102] |
| 22033 | Hegel tried to avoid Kant's dualism of neutral intuitions and imposed concepts [Hegel, by Pinkard] |
| Full Idea: Hegel tried to avoid the untenable Kantian dualism between concepts and intuitions, and the Kantian mechanism of the 'imposition' of concepts on sensibility entailed by that dualism (with intuition having neutral content). | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Terry Pinkard - German Philosophy 1760-1860 09 | |
| A reaction: [Pinker is describing the opening of Phenomenology] In modern discussions this concerns the idea of The Given, which is wholly uninterpreted raw experience. Sellars and MacDowell. Kant seems to split an agent into two (Master/Slave). |
| 19699 | A Gettier case is a belief which is true, and its fallible justification involves some luck [Hetherington] |
| Full Idea: A Gettier case contains a belief which is true and well justified without being knowledge. Its justificatory support is also fallible, ...and there is considerable luck in how the belief combnes being true with being justified. | |
| From: Stephen Hetherington (The Gettier Problem [2011], 5) | |
| A reaction: This makes luck the key factor. 'Luck' is a rather vague concept, and so the sort of luck involved must first be spelled out. Or the varieties of luck that can produce this outcome. |
| 21771 | Consciousness derives its criterion of knowledge from direct knowledge of its own being [Hegel] |
| Full Idea: In what consciousness affirms from within itself as being-in-itself or the True we have the standard which consciousness itself sets up by which to measure what it knows. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], p.053), quoted by Stephen Houlgate - An Introduction to Hegel 03 'The Method' | |
| A reaction: This seems to be a very close relation of Descartes' 'clear and distinct conceptions'. This certainly places Hegel in the Rationalist camp. |
| 20741 | Consciousness is shaped dialectically, by opposing forces and concepts [Hegel, by Aho] |
| Full Idea: In 'The Phenomenology of Spirit' Hegel offers a panoptic account of Western consciousness as a dialectical process shaped by opposing principles - such as subject/object, freedom/determinism, temporal/eternal, and particular/universal. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Kevin Aho - Existentialism: an introduction 2 'Subjective' | |
| A reaction: A helpful pointer, for us poor analytic philosophers, who stare in bewilderment at Hegel's stuff, despite its apparent importance. At moment it is the politics that strikes me as most interesting in Hegel. This is cultured consciousness, pre-Marx. |
| 21770 | Consciousness is both of objects, and of itself [Hegel] |
| Full Idea: Consciousness is, on the one hand, consciousness of the object, and on the other, consciousness of itself. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], p.052), quoted by Stephen Houlgate - An Introduction to Hegel 03 'The Method' | |
| A reaction: Hume challenges whether there is any knowledge of consciousness purely in itself. Schopenhauer flatly disagreed (Idea 4166) - but then he would, wouldn't he? |
| 5647 | Hegel claims knowledge of self presupposes desire, and hence objects [Hegel, by Scruton] |
| Full Idea: Hegel seems to argue that the immediate knowledge of self (the Cartesian premise) presupposes the activity that constitutes the self, and this presupposes desire, and hence the knowledge of objects. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Roger Scruton - Short History of Modern Philosophy Ch.12 | |
| A reaction: This hardly amounts to an argument, but I find it quite sympathetic as a claim. It fits comfortably with modern externalist accounts of thought. While solipsism seems a logical possibility, it hardly amounts to a coherent account of mental life. |
| 5648 | For Hegel knowledge of self presupposes objects, and also a public and moral social world [Hegel, by Scruton] |
| Full Idea: Hegel tries to show that knowledge of self as subject presupposes not just knowledge of objects, but knowledge of a public social world, in which there is moral order and civic trust. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Roger Scruton - Short History of Modern Philosophy Ch.12 | |
| A reaction: This is not far off Wittgenstein's private language argument. It is also Popper's 'World Three', of society and language. Human reality is incomprehensible without some recognition of the culture in which we immerse, like fish in water. |
| 8930 | The in-itself must become for-itself, which requires self-consciousness [Hegel] |
| Full Idea: The in-itself has to express itself outwardly and become for itself, and this means simply that it has to posit self-consciousness as one with itself. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 26) | |
| A reaction: This famous distinction seems to be at the core of idealism, but also to be the germ of existentialism (prior to Kierkegaard), which builds on this view of what it means to exist as an individual. Self-consciousness in nature is inevitable? |
| 22034 | Modern life needs individuality, but must recognise that human agency is social [Hegel, by Pinkard] |
| Full Idea: Hegel argued that the modern world necessarily had to make space for individuals and their inviolable conscience, while not becoming so individualistic that it failed to acknowledge the deep sociality of human agency. ...Subjectivity became a right. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Terry Pinkard - German Philosophy 1760-1860 09 | |
| A reaction: [at the end of the chapter on the history of Geist in the Phenomenology] Conservatives, revolutionaries and communitarians all claim Hegel as their own. The sociality is a matter of mutual law-giving, as in the Master/Slave. |
| 8936 | Human nature only really exists in an achieved community of minds [Hegel] |
| Full Idea: Human nature only really exists in an achieved community of minds. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 69) | |
| A reaction: A lovely slogan, that makes Hegel the father of the communitarian movement. The politics of Hegel can, of course, be sinister, so one must proceed with care, and study history to see where it can all go wrong. |
| 21987 | History is the progress of the consciousness of freedom [Hegel] |
| Full Idea: The History of the World is none other than than the progress of the consciousness of freedom. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807]), quoted by Peter Singer - Marx 2 | |
| A reaction: [no ref given] Presumably there is an evolutionary view implicit in this. Presumably also later generations are hereby superior to previous generations. Since no one still has this view of history, does that invalidate Hegel? |
| 8931 | The movement of pure essences constitutes the nature of scientific method [Hegel] |
| Full Idea: The movement of pure essences constitutes the nature of scientific method in general. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 34) | |
| A reaction: This would appear to be precisely the idea of scientific essentialism - if he is saying that science seeks to understand the movement (or power) of essences as they occur in nature. |
| 8933 | Science confronts the inner necessities of objects [Hegel] |
| Full Idea: Scientific cognition demands surrender to the life of the object, or, what amounts to the same thing, confronting and expressing its inner necessity. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], Pref 53) | |
| A reaction: This strikes me as being a much better account of what science tries to do than all the modern talk about laws and theories. |
| 21775 | The God of revealed religion can only be understood through pure speculative knowledge [Hegel] |
| Full Idea: God is attainable in pure speculative knowledge alone and is only in that knowledge, and is only that knowledge itself, for He is Spirit; and this speculative knowledge is the knowledge of revealed religion. | |
| From: Georg W.F.Hegel (Phenomenology of Spirit [1807], p.461), quoted by Stephen Houlgate - An Introduction to Hegel 04 'Absolute' | |
| A reaction: If you were hoping to find out why Hegel believed in God, I fear this is the best evidence available. He is evidently opposed to natural theology. Hegel's language makes it very hard to grasp how we sees the nature of God. |
| 6917 | God is the essence of thought, abstracted from the thinker [Hegel, by Feuerbach] |
| Full Idea: In Hegel the essence of God is actually nothing other than the essence of thought, or thought abstracted from the ego, that is, from the one who thinks. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Ludwig Feuerbach - Principles of Philosophy of the Future §23 | |
| A reaction: Presumably Descartes' Cogito is the origin for this train of thought. This is Feuerbach's reading of Hegel, but the former was keen on the idea of God as idealised humanity. |
| 6915 | Hegel made the last attempt to restore Christianity, which philosophy had destroyed [Hegel, by Feuerbach] |
| Full Idea: The Hegelian philosophy is the last magnificent attempt to restore Christianity, which was lost and wrecked, through philosophy, and to restore Christianity (as usual in the modern era) by identifying it with the negation of Christianity. | |
| From: report of Georg W.F.Hegel (Phenomenology of Spirit [1807]) by Ludwig Feuerbach - Principles of Philosophy of the Future §21 | |
| A reaction: What is meant by the 'negation' of Christianity needs some untangling, but I suspect that a lot of 'continental' philosophy 1750-1950 is to do with Christianity, unlike British empiricism, which is intrinsically atheistic. |