Skip to main content Accessibility help
Hostname: page-component-684899dbb8-c97xr Total loading time: 0.391 Render date: 2022-05-26T10:38:58.530Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true }

Hegel's Hat Trick

Published online by Cambridge University Press:  23 June 2015

John W. Burbidge*
Trent University
Get access


“Hegel achieved the most miraculous things,” wrote Karl Popper. “A master logician it was child's play for his powerful dialetical method to draw real physical rabbits out of purely metaphysical hats”.

It is a serious charge, supported by Hegel's preference for Kepler over Newton, his ‘deduction of the actual position of the planets’ while ignoring the recent discovery of the planet Ceres, and his claim that ‘magnetizing iron increases its weight’.

Because Popper is so convinced that Hegel is a fraud, he does not deign to investigate the actual pattern of Hegel's argument. The obscure, abstract vocabulary is dismissed as bombast and tautology.

Hegel's Logic and Metaphysics
Copyright © The Hegel Society of Great Britain 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


1 Popper, K.R., The Open Society and its Enemies, Vol. II. The High Tide of Prophecy: Hegel, Marx and the Aftermath (Princeton: Princeton University Press, 1963), 27 Google Scholar.

2 See in particular Wandschneider, D., Raum, Zeit, Relativität (Frankfurt: Klostermann, 1982)Google Scholar, and Halper, Edward, “The Logic of Hegel's Philosophy of Nature,’ in Houlgate, S., ed. Hegel and the Philosophy of Nature (Albany: SUNY Press, 1998), 3155 Google Scholar.

3 Although a student of Kant, Richter, J.B. in Anfangsgründe der Stöchyometrie; oder Meßkunst chymischer Elemente (Breslau u. Hirschberg, 1792)Google Scholar did develop the insights of Proust and others into the quantitative calculation of chemical combinations.

4 Trans. E.E. Harris and P. Heath (Cambridge: Cambridge University Press, 1988.)

5 A good example is Euclid's proof of the Pythagorean theorem where a network of triangles and rectangles is constructed within the right-angled triangle and its appended squares.

6 Just as Euclid's proof does not create the truth of the Pythagorean theorem, a construction in the philosophy of nature does not produce the physical reality. It rather is a way of demonstrating the underlying rationality of the phenomena. The validity of the argument was established by the congruence between the results of the construction and the evident structure of experience.

7 This is the text concerning the planets that Popper derides in his outburst. With respect to Hegel's critique of Newton that is expressed in the dissertation, Nasti de Vincentis and Ferrini have shown that not only was Hegel relying on a subtle criticism of Newton's mathematics developed by L.-B. Castel, but also that the criticism was well founded. Ferrini, C., “Chi Newton's Demonstration of Kepler's Second Law in Hegel's De Orbitis Planetarum (1801),” Philosophia Naturalis 31, 1 (1994): 150–70Google Scholar; de Vincentis, M. Nasti, “Hegel's Worm in Newton's Apple”, in Hegel and the Philosophy of Nature, 257–89Google Scholar.

8 The method of construction and proof is outlined in the Logic of 1803-4 under Proportion and applied throughout the Philosophy of Nature. On the former, see Hegel, G.W.F., The Jena System, 1804-5: Logic and Metaphysics, ed. Burbidge, J. & di Giovanni, G. (Montreal and Kingston: McGill-Queen's University Press, 1986), 109–30Google Scholar. For example: “This bringing back of the division of construction to the unity of definition is proof” (119). The full text is found in Volume 7 of Hegel, G.W.F., Gesammelte Werke (Hamburg: Meiner, 1971)Google Scholar [henceforth referred to as HGW], For the 1804-5 lectures which contain only the Philosophy of Nature and Spirit but no discussion of method, see Volume 8. In neither case has the material on the Philosophy of Nature been translated.

9 This point is made explicitly in the first two paragraphs of the Philosophy of Nature, §§245-6. Teleology does provide the basis for Hegel's discussion of history. On this see Burbidge, J.W., “The Cunning of Reason,” in Final Causality in Nature and Human Affairs, ed. Hassing, Richard F. (Washington: Catholic University of America Press, 1997), 151–62Google Scholar.

10 This section of the larger Logic was published in 1816, whereas the Philosophy of Nature text we shall explore came from the 1830 Encyclopaedia. Since the Encyclopaedia Logic is a cryptic set of theses to be expanded in lectures, it presumes the logical transitions rather than develops them in detail.

I explicate the text to show the logical derivations that lead from one concept or set of concepts to another. While I attempt to do justice to every major step introduced by Hegel, the Ariadne's thread I use to find my way through the maze is my own proposal and not found in the text itself. Ultimately any interpreter of Hegel's logic has to propose some guidelines for explaining the shifts and moves Hegel makes. The one I use takes seriously Hegel's claim that his Logic is the systematic description of thought thinking its own concepts. [The Logic is to be grasped as the system of pure reason, as the kingdom of pure thinking.” HGW 21, 34.6-7Google Scholar; Hegel's Science of Logic, tr. Miller, (London: Allen & Unwin, 1969), 50, hereafter (Miller)Google Scholar.] It is an approach that has been honed in a number of previous studies that, together, analyze thirteen of the twenty-seven chapters in the larger Logic: The Necessity of Contingency,” in Art and Logic in Hegel's Philosophy, ed. Steinkraus, Schmitz and O'Malley, (New Jersey: Humanities, Sussex: Harvester, 1980), 201–18Google Scholar and Chapter 5 in Hegel on Logic and Religion (Albany: State University of New York Press, 1992)Google Scholar [Actuality]; On Hegel's Logic, Fragments of a Commentary (New Jersey: Humanities, 1981)Google Scholar [Being, Determinate Being, Show, The Essentialities, Ground, Concept, Judgement, Syllogism, Absolute Idea]; Real Process: How Logic and Chemistry Combine in Hegel's Philosophy of Nature (Toronto, University of Toronto Press, 1996)Google Scholar [Real Measure, Chemism, with outlines of Specific Quantity and Mechanism]; and “The Cunning of Reason” cited above [Teleology].

11 I shall indicate the paragraphs that underlie my reading: HGW 12, 182. 17ff; (Miller) 764: “The Notion of life …”

12 Hegel often refines what a term means in a specific context by distinguishing it from the way that term has been used earlier in the Logic.

13 Notice that ‘inhering’ and ‘subsuming’ are two ways subjects and predicates are related in a simple judgement: in “a rose is red”, red on the one hand is said to inhere in the rose, but on the other hand the rose is subsumed into the larger class of red things. These two particular relationships acquire a distinctive sense in this setting.

14 HGW 12, 182.30ff; (Miller) 765: “The determinations …”

15 HGW 12, 183.18ff; (Miller) 765: “In respect of content…”

16 HGW 12, 183.23ff and 34ff; (Miller) 765: “This is in the first place …” and 766 “Now because …”

17 See my The First Chapter of Hegel's Larger Logic,” The Owl of Minerva, XXI, 2 (1990): 177–83Google Scholar, reprinted as Chapter 2, Hegel on Logic and Religion.

18 HGW 12, 184.24ff; (Miller) 767: “This process …

19 HGW 12, 185.6ff; (Miller) 767: “Now the Idea …”

20 HGW 12, 185.21; (Miller) 768: “Thus it is …”. It is important to note that sensitivity, irritability and reproduction first occur with regard to the relationships among members of the living individual. Only later are they applied to the interaction of individual and environment.

21 HGW 12, 185.36ff; (Miller) 768: “The second determination …”

22 HGW 12, 186.9ff; (Miller) 768: “According to this …”

23 Hegel uses ‘idea’ to characterize the thinking that integrates concept with reality. In one sense ‘life’ is already an idea because it integrates subjectivity and objectivity. Since the concept/reality relationship is a relative one, it reemerges at this later stage, once the initial concept of life has been articulated into the structure of the self-producing individual.

24 HGW 12, 186.30; (Miller) 769: “With reproduction …”. Here again there is an implicit contradiction. The living individual is a singular entity, yet it also functions as one particular among many. Considered simply on their own ‘singular’ and ‘particular’ are opposites. So the logic investigates the process within which they can both function as moments.

25 HGW 12, 187.3ff and 19ff, the cited phrase is found at line 34; (Miller) 769: “The living individual …” and 770: “This process …”

26 HGW 12, 188.18ff; (Miller) 771: mid-paragraph: “In so far as the object…”

27 HGW 12, 188.28 and 189.1; (Miller) 771: “Now the subject …” and “With the seizure …”

28 HGW 12, 189.17ff; (Miller) 772: “The immediate Idea …”. Certainly this is not yet the sense of ‘genus’ used by the biologists. It is an embryonic sense that has emerged from the previous analysis but has yet to be fleshed out. The Oxford English Dictionary (1933) defines the logical sense of genus as “a class or kind of things which includes a number of subordinate kinds (called species) as sharing in certain common attributes; a general concept.” Genus thus serves logically as the common attribute that the individual continues to embody even through a number of assimilations.

29 HGW 12, 189.31ff; (Miller) 772: “The living individual …”

30 HGW 12, 190.3ff and 10ff; (Miller) 773: “But the further…” and “This universal …”

31 HGW 12, 190.16ff; (Miller) 773: “Now because …”

32 Any reality that cancels differences is one of Hegel's negative unities.

33 HGW 12, 190.28ff; (Miller) 773: “The identity with …”

34 HGW 12, 191.7ft; (Miller) 774: “The reflection …”

35 HGW 12, 191.17ft; (Miller) 774: “That is to say …”

36 Hegel calls an infinite regress a “bad” infinite. But like contradictions, such bad infinites are the engine of progress, for one looks, not at the endless series, but the recurring motor that drives them on, and identifies their essential character.

37 It is perhaps useful to cite a critical passage from the Preface to the second (1831) edition of the Science of Logic: “The forms of thought are, in the first instance, displayed and stored in human language. Nowadays we cannot be too often reminded that it is thinking which distinguishes man from the beasts. Into all that becomes something inward for men, becomes in any way a conception, into all that he makes his own, language has penetrated, and everything that he has transformed into language and expresses in it contains a category — concealed, mixed with other forms or clearly determined as such. So much is logic his natural element, indeed his own peculiar nature.” HGW 21,10.24-30; (Miller) 31 (modified).

Hegel assumes that everyday speech reflects our experience of the world. And he argues that logic simply explores systematically the conventions of meaning that are inherent in that experience. For the Science of Logic presupposes the science of the experience of consciousness outined in the Phenomenology of Spirit: “In the Phenomenology of Spirit I have exhibited consciousness in its movement onwards from the first immediate opposition of itself and object to absolute knowing. The path of this movement goes through every form of the relation of consciousness to its object and has the concept of science for its result.” HGW 21, 32.23-7; (Miller) 48.

38 In the Phenomenology, Observing Reason understands the externally observed nervous, muscular and reproductive systems in terms of the inner sensitive, irritable and visceral functions which are their universal principle (HGW 9, 151.3-7; §267). So the logical distinction between inner and outer is finding expression in this development within the Philosophy of Nature.

39 Compare again the Phenomenology: “These properties [i.e. sensibility, irritability and reproduction], at least the first two, seem indeed to refer not to organism in general, but only to the animal organism. As a matter of fact the vegetable organism expresses only the simple concept of the organism, which does not develop its moments” (HGW 9, 150.18-21; §265).

40 The term also appears in four of the Remarks that Hegel appended to paragraphs within this chapter (§358, §359, §368, §373) and in eight of the paragraphs from “Animal Nature” (§352, §353, §354, §360, §362, §366, §368 and §374). In the first seven of this latter eight, “concept” refers, not to concept in general, but to the logical discussion of life in particular, including the basic division into form, assimilation and genus, the moments of sensibility, irritability and reproduction, needs as the basis for assimilation, the realization or objectivity of the concept, and the kinds or genders that differentiate the genus. In §374 the actual animal is seen to be inadequate to this concept. In the remarks Hegel often compares the empirical phenomena with the conceptual framework. In all of these references, then, he is comparing what is found empirically in the animal realm (the most complete instantiation of the concept) with the logical template we earlier analyzed.

For those who are using English translations, please note that I am basing my analysis exclusively on the original text of the 1830 Encyclopaedia. The lecture material which has been added (the Zusätze) must be treated with a grain of salt when we are concerned with the systematic development. Not only are we dependent on the perspicacity of the students taking the notes, but Michelet has collated into one text material from a number of different lecture series ranging from 1805 to 1830.

41 Burbidge, J.W., Real Process: How Logic and Chemistry Combine in Hegel's Philosophy of Nature, 185–6Google Scholar.

42 “Das gleichgültig-bestehende Körperliche ist dadurch nur als Moment der Individualität gesetzt, und der Begriff in der ihm entsprechenden Realität, die in Einem, aus der Besonderung der unterschiedenen Körperlichkeiten sich hervorbringende concrete Einheit mit sich, welche die Thätigkeit ist, diese ihre einseitige Form der Beziehung auf sich zu negiren, sich in die Momente des Begriffs zu dirimiren und zu besondem und ebenso in jene Einheit zurückzuführen, — so der unendliche sich selbst anfachende und unterhaltende Proceß, — der Organismus.” HGW 20, 343.11-17; §336.

43 §337 is a kind of “introduction”, and as such not part of the systematic development. Hegel steps outside of the strict logical “argument” and sets the context for the whole section on Organic Physics. In this more informal setting, he can exploit the universal/particular/singular trichotomy.

44 As Perry points out: Prior to Pasteur (1822-1895), the concept was used to account for internal parasites, infusoria and bacteria” (Hegel's Philosophy of Nature, [London & New York: 1970] III, 244)Google Scholar. Perry also cites Needham, J.T., “Observations upon the generation, composition and decomposition of Animal and Vegetable Substances” (London, 1749)Google Scholar and Knight, T.A., “Transactions of the Horticultural Society of LondonII, 83 (London, 1818)Google Scholar.

45 “Diese Trennung des allgemeinen, sich äußerlichen Organismus und dieser nur punktuellen, vorübergehenden Subjectivität hebt sich vermöge der an sich seyenden Identität ihres Begriffs zur Existenz dieser Identität, zum belebten Organismus, der an ihr selbst sich gliedernden Subjectivität auf, welche den nur an sich seyenden Organismus, die physische allgemeine und individuelle Natur von sich ausschließt und ihr gegenübertritt, aber zugleich an diesen Mächten die Bedingung ihrer Existenz, die Erregung wie das Material ihres Processes, hat.” HGW20,347.16-23; §342.

46 “Was aber im Begriffe gesetzt worden, ist, daß der Proceß die mit sich selbst zusammengegangene Individualität darstellt, und die Theile, die zunächst als Individuen sind, auch als der Vermittlung angehörige und in ihr vorübergehende Momente, somit die unmittelbare Einzelnheit und das Außereinander des vegetabilischen Lebens als aufgehoben zeigt. Diß Moment der negativen Bestimmung begründet den Uebergang in den wahrhaften Organismus, worin die äußere Gestaltung mit dem Begriffe übereinstimmt, daß die Theile wesentlich Glieder and die Subjectivität als die durchdringende Eine des Ganzen existiert.” HGW 20, 352.2-9; §349.

47 As noted above in note 37, this section frequently relies on the logical analysis of life to define conceptually the framework for investigating empirical application. Begriff plays this role in §§352-4, §360, §362, §366 and §368.

48 In addition to the term Begriff, Hegel in each of these paragraphs stresses unity (Eine, Einheit) and exploits his Lieblingskind: “aufheben”. This reinforces the impression that conceptual thought brings the previous moments together into an integrated unity.

49 “Aber diese erreichte Identität mit dem Allgemeinen ist das Aufheben des formellen Gegensatzes, der unmittelbaren Einzelnheit und der Allgemeinheit der Individualität, und diß nur die eine und zwar die abstracte Seite, der Tod des Natürlichen. Die Subjectivität ist aber in der Idee des Lebens der Begriff, sie ist so an sich das absolute Insichseyn der Wirklichkeit und die concrete Allgemeinheit; durch das aufgezeigte Aufheben der Unmittelbarkeit ihrer Realität ist sie mit sich selbst zusammengegangen; das letzte Außersichseyn der Natur ist aufgehoben, und der in ihr nur an sich seyende Begriff ist damit für sich geworden. — Die Natur ist damit in ihrer Wahrheit übergegangen, in die Subjectivität des Begriffs, deren Objectivität selbst die aufgehobene Unmittelbarkeit der Einzelnheit, die concrete Allgemeinheit ist, so dass der Begriff gesetzt ist, welcher die ihm entsprechende Realität zu seinem Daseyn hat, — der Geist.” HGW 20, 375.9-21; §376.

One has to move past the introductory discussions of the Philosophy of Spirit to §388 to get to the next step in the systematic development. The first stage of spirit draws itself into itself out of the externality of nature and is simply the soul that was identified early on in the logic of life.

Save article to Kindle

To save this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the or variations. ‘’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Hegel's Hat Trick
Available formats

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Hegel's Hat Trick
Available formats

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Hegel's Hat Trick
Available formats

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *