In Night Thoughts Henry Harris made plain that Hegel imbibed naturalism deeply in Jena. Harris states:

The Stoics were uncompromising materialists and naturalists. Harris (1998, 492) admitted, however, that Night Thoughts is less successful than Towards the Sunlight because he didn't have detailed knowledge of contemporaneous natural science and so could not explicate Hegel's philosophy of nature effectively. Similarly, Hegel's 1804–05 philosophy of nature is omitted from the collective translation of Hegel's Jena system edited by Burbidge and di Giovanni because

This lack of interest leaves two members of Hegel's philosophical system – his logic and metaphysics – precariously imbalanced because they lack their third supporting member, the philosophy of nature. This can only result in serious distortion of our understanding of Hegel's system.

At first sight Robert Brandom's two essays on Hegel in his book Tales of the Mighty Dead appear barely to be about Hegel at all. The first essay on holism and idealism, for example, talks of ‘sense dependence’ and ‘reference dependence’, and even invokes a point in logic made by Gilbert Harman (TMD 191-2, 194). Scarcely normal fare for the average commentator on Hegel. Brandom himself is acutely conscious of the impression his work on Hegel (and on the other philosophers discussed in Tales of the Mighty Dead) might have on his readers. ‘I am aware’, he writes, ’that the relations between the stories told here and my own philosophical views [ … ] may seem to some particularly problematic’ (TMD 90). In the section of his book called ‘Pretexts’, however, Brandom provides a subtle defence of his approach and makes it clear that he is by no means simply ‘foisting’ his ideas on the helpless dead (TMD 91; see also 389). He does so by distinguishing between two different modes of interpretation: de dicto and de re.

Brandom states that interpretation of a philosophical text seeks to establish the claims made in it and to determine what follows from them. This task, however, presupposes a ‘context’ of interpretation (TMD 95).

When a text is given a de dicto interpretation, the context is supplied by the author's own commitments. The aim is thus to determine what the author himself would have said in response to questions of clarification, given those commitments (TMD 99).

Recent debates about Hegel's theoretical philosophy are marked by a surprising lack of agreement, extending all the way down to the most basic question: what is Hegel talking about? On the one hand, proponents of ‘metaphysical’ interpretations generally read Hegel as aiming to articulate the overall structure or organisation of reality itself, and the nature of a highest or most fundamental being. Particularly influential is the idea that Hegel is reviving and modifying a form of Spinoza's metaphysical monism, according to which the organised whole of everything is the highest being, providing a ground or reason for everything real. On the other hand, proponents of ‘non-metaphysical’ interpretations argue Hegel's topic is something else entirely. The idea is that Hegel agrees with Kant in finding pre-critical forms of metaphysics to be uncritical or dogmatic. And the topic of Hegel's positive project is supposed to be not the nature of reality itself, nor any most fundamental being, but rather ‘forms of thought’ akin to Kant's categories and the objectivity, legitimacy, or normative authority of those forms of thought.

This is of course only a rough sketch of the most basic recent debate, about which there is more to say than can fit in this paper. My focus here is on what Hegel has to say about nature and natural kinds, in ‘Observing Reason’ from the Phenomenology, and also in similar material from the Logic and Encyclopedia. I intend to argue that this material suggests a surprising way of stepping beyond the fundamental debate sketched above. There can of course be no question of elaborating and defending here a complete interpretation of Hegel's entire theoretical philosophy. I will have to restrict myself to arguing for the unlikely conclusion that there is an approach that can combine and integrate the strongest points made by both sides in the most basic debate shaping recent Hegel interpretation.

Hegel's Phenomenology is among the most difficult, if it is not in fact the most difficult, philosophical treatise ever published. Owing to its opacity of form and content, the Phenomenology, which Hegel quite accurately describes as the highway of despair upon which natural consciousness travels to its absolute knowing, has had its share of hitchhikers (§78). In their efforts to comprehend the scenery along this highway, many readers of this text rely on any number of analytical commentaries and expositions. Westphal (2003) offers a welcomed contribution to this kind of secondary literature.

As its title suggests, Westphal's text seeks to introduce Hegel's Phenomenology in a novel way, namely with explicit reference to the epistemological issue at its core. This is the Dilemma of the Criterion from Sextus Empiricus' Outlines of Pyrrhonism. (Benson 1996). In addition to introducing the central features and characteristics of the epistemological aim of the Phenomenology, Westphal devotes considerable effort to showing how, that is by what method, Hegel responds to at least Pyrrhonian skepticism.

Westphal's examination of Hegel's method is framed by two questions. The first question is: what is Hegel's method? The answer that Westphal offers, namely that Hegel employs a phenomenological method, agrees with a host of classic and contemporary commentators, including Ivan Iljin (1946:126), Alexandre Kojève (1980: Ch. 7), Kenley R. Dove (1969-70), William Maker (1982), Wendy Lynn Clark and J.M. Fritzman (2002). Nevertheless, Westphal does offer a detailed, sophisticated, and novel account of the characteristics of Hegel's phenomenological method that is unrivaled in the extant literature.

In the popular press and the halls of politics, controversies over evolution are increasingly strident these days. Hegel is relevant in this connection, even though he rejected the theories of evolution he knew about, because he wants rational understanding and a larger process to comprehend natural processes and their history, but without any claims for intelligent design. The way current debates get publicised, there appear to be two extreme positions. The first is a reductionist materialism: all complex systems are describable purely in terms of the qualities of their most basic components, and the systems themselves result from Darwinian selection. No teleological concepts at all need be applied. At the other extreme is total teleology; all systems and their interactions and development are the result of preconceived conscious purposeful design by a powerful designer. The ontological status of the designer is usually filled out with theological notions.

Throughout his life, Hegel showed great interest in physics and mathematics. His most sustained, surviving treatment of Euclidean geometry is his early work ‘Geometrische Studien’, which he completed while he was a private tutor [Hoffmeister] in Frankfurt, shortly before leaving for Jena to join Schelling. GS is not easy reading, but despite that, it seems to me that Hegel presents in it a remarkably erudite as well as interesting and insightful critique of geometry. He investigates some of the themes from the foundations of geometry, in particular from the first book of the Elements of Euclid. Like the mathematical philosophies of Kant and Frege, Hegel's understanding of geometry is conceptually based, but unlike them, it is also grounded in the classical Greek philosophy of mathematics, which achieved its definitive expression in Proclus's great commentary on Euclid 1. Much of this classical philosophy of geometry is forgotten nowadays, under the influence of the great modern mathematical philosophers (in particular, Cantor, Frege and Gödel). In my view, it well deserves reconsideration, especially since, as illustrated by Gödel's incompleteness theorems, modern mathematical philosophy has failed in its attempt to ground mathematics within the framework of formal systems.

Much of GS has not survived, and what remains is condensed and fragmentary. It seems that originally, Hegel covered all of the propositions of Euclid 1 rather than just the 14 propositions (1-12, 26, 29) that are covered in what remains of the original GS. I have given detailed treatment of GS together with related material in Hegel's Jena dissertation elsewhere (Paterson 2004/2005). The objective of the present paper is to introduce the translation of GS.

The fragmentary nature of GS makes it difficult to read as it stands, and for this reason, I have rearranged the material slightly so that it falls into four primary, reasonably coherent, parts. Their titles are: ‘The nature of mathematical objects’, ‘Thirteen propositions of Euclid 1’, ‘The philosophy of parallel lines’ and ‘On the algebra of geometrical figures’. GS actually starts with ‘Thirteen propositions of Euclid 1’. The justification for the reversal of order in the translation is to have Hegel's philosophical basis for geometry available first, to provide a context for his detailed discussion of geometrical propositions. The reader can easily reconstruct the original order of GS as follows. Interchange the first and second parts and also the third and fourth parts. Next, move the passages marked a …. a', b …. b',c …. c' to the places in the text marked a-a', b-b' and c-c'. For the reader wishing to locate the original German passages in Dok., the page and paragraph for each of these passages are given at the start of that passage.

In addition, subtitles for sections in these parts have been added which do not appear in the original. They are included in the translation to help orient the reader. I have inserted in some places words not in the original in order to clarify the meaning of the text. These insertions as well as my comments on the text are also enclosed within square brackets. Further clarifications can be found in the appended endnotes.