45 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. |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle. |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| Full Idea: It is surely wise to identify the positions in the natural numbers structure with their counterparts in the integer, rational, real and complex number structures. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: The point is that this might be denied, since 3, 3/1, 3.00.., and -3*i^2 are all arrived at by different methods of construction. Natural 3 has a predecessor, but real 3 doesn't. I agree, intuitively, with Shapiro. Russell (1919) disagreed. |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| Full Idea: A sequence a1,a2,... of rational numbers is 'Cauchy' if for each rational number ε>0 there is a natural number N such that for all natural numbers m, n, if m>N and n>N then -ε < am - an < ε. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.2 n4) | |
| A reaction: The sequence is 'Cauchy' if N exists. |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| Full Idea: There is a dedicated contingent who hold that the category of 'categories' is the proper foundation for mathematics. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.3 n7) | |
| A reaction: He cites Lawvere (1966) and McLarty (1993), the latter presenting the view as a form of structuralism. I would say that the concept of a category will need further explication, and probably reduce to either sets or relations or properties. |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| Full Idea: Zermelo said that for each number n, its successor is the singleton of n, so 3 is {{{null}}}, and 1 is not a member of 3. Von Neumann said each number n is the set of numbers less than n, so 3 is {null,{null},{null,{null}}}, and 1 is a member of 3. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: See Idea 645 - Zermelo could save Plato from the criticisms of Aristotle! These two accounts are cited by opponents of the set-theoretical account of numbers, because it seems impossible to arbitrate between them. |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| Full Idea: The structuralist vigorously rejects any sort of ontological independence among the natural numbers; the essence of a natural number is its relations to other natural numbers. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: This seems to place the emphasis on ordinals (what order?) rather than on cardinality (how many?). I am strongly inclined to think that this is the correct view, though you can't really have relations if there is nothing to relate. |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| Full Idea: A 'system' is a collection of objects with certain relations among them; a 'pattern' or 'structure' is the abstract form of a system, highlighting the interrelationships and ignoring any features they do not affect how they relate to other objects. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: Note that 'ignoring' features is a psychological account of abstraction, which (thanks to Frege and Geach) is supposed to be taboo - but which I suspect is actually indispensable in any proper account of thought and concepts. |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| Full Idea: The thesis that principles of arithmetic are derivable from the laws of logic runs against a now common view that logic itself has no ontology. There are no particular logical objects. From this perspective logicism is a non-starter. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 5.1) | |
| A reaction: This criticism strikes me as utterly devastating. There are two routes to go: prove that logic does have an ontology of objects (what would they be?), or - better - deny that arithmetic contains any 'objects'. Or give up logicism. |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| Full Idea: Term Formalism is the view that mathematics is just about characters or symbols - the systems of numerals and other linguistic forms. ...This will cover integers and rational numbers, but what are real numbers supposed to be, if they lack names? | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.1) | |
| A reaction: Real numbers (such as pi and root-2) have infinite decimal expansions, so we can start naming those. We could also start giving names like 'Harry' to other reals, though it might take a while. OK, I give up. |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| Full Idea: Game Formalism likens mathematics to chess, where the 'content' of mathematics is exhausted by the rules of operating with its language. ...This, however, leaves the problem of why the mathematical games are so useful to the sciences. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.2) | |
| A reaction: This thought pushes us towards structuralism. It could still be a game, but one we learned from observing nature, which plays its own games. Chess is, after all, modelled on warfare. |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| Full Idea: The Deductivist version of formalism (sometimes called 'if-thenism') says that the practice of mathematics consists of determining logical consequences of otherwise uninterpreted axioms. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.2) | |
| A reaction: [Hilbert is the source] More plausible than Term or Game Formalism (qv). It still leaves the question of why it seems applicable to nature, and why those particular axioms might be chosen. In some sense, though, it is obviously right. |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| Full Idea: Critics commonly complain that the intuitionist restrictions cripple the mathematician. On the other hand, intuitionist mathematics allows for many potentially important distinctions not available in classical mathematics, and is often more subtle. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.1) | |
| A reaction: The main way in which it cripples is its restriction on talk of infinity ('Cantor's heaven'), which was resented by Hilbert. Since high-level infinities are interesting, it would be odd if we were not allowed to discuss them. |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| Full Idea: I classify conceptualists according to what they say about properties or concepts. If someone classified properties as existing independent of language I would classify her as a realist in ontology of mathematics. Or they may be idealists or nominalists. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 2.2.1) | |
| A reaction: In other words, Shapiro wants to eliminate 'conceptualist' as a useful label in philosophy of mathematics. He's probably right. All thought involves concepts, but that doesn't produce a conceptualist theory of, say, football. |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| Full Idea: A definition of a mathematical entity is 'impredicative' if it refers to a collection that contains the defined entity. The definition of 'least upper bound' is impredicative as it refers to upper bounds and characterizes a member of this set. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: The big question is whether mathematics can live with impredicative definitions, or whether they threaten to be viciously circular, and undermine the whole enterprise. |
| 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. |
| 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? |
| 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? |
| 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'? |
| 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? |
| 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). |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| Full Idea: Rationalism is a long-standing school that can be characterized as an attempt to extend the perceived methodology of mathematics to all of knowledge. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.1) | |
| A reaction: Sometimes called 'Descartes's Dream', or the 'Enlightenment Project', the dream of proving everything. Within maths, Hilbert's Programme aimed for the same certainty. Idea 22 is the motto for the opposition to this approach. |
| 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. |
| 2799 | Bayes' theorem explains why very surprising predictions have a higher value as evidence [Horwich] |
| Full Idea: Bayesianism can explain the fact that in science surprising predictions have greater evidential value, as the equation produces a higher degree of confirmation. | |
| From: Paul Horwich (Bayesianism [1992], p.42) |
| 2798 | Probability of H, given evidence E, is prob(H) x prob(E given H) / prob(E) [Horwich] |
| Full Idea: Bayesianism says ideally rational people should have degrees of belief (not all-or-nothing beliefs), corresponding with probability theory. Probability of H, given evidence E, is prob(H) X prob(E given H) / prob(E). | |
| From: Paul Horwich (Bayesianism [1992], p.41) |
| 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? |
| 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. |
| 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. |
| 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. |