Hegel’s Keplerian Revolution in Philosophy

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper seeks to clarify the relation between Hegel and Kant's approaches by drawing an analogy to the astronomical revolutions of Copernicus, Bruno, and Kepler. The author argues that Kant's philosophy is better described as following a "Brunian" revolution, while Hegel's path was more "Keplerian." The paper explores the implications of this distinction, particularly in relation to the role of mathematics and logic in science and the conception of infinity. The paper argues that Hegel's philosophy, much like Kepler’s astronomy, incorporates elements that challenge modern scientific paradigms, particularly through Kepler’s use of projective geometry and the concept of the "music of the spheres."  It suggests that Hegel's support for Kepler's approach, including the "musical" analysis and projective geometry, was justified and sheds light on Hegel's form of idealism.

 

According to this reviewer, this is an excellent paper. It presents a novel and intriguing perspective on the comparison between Hegel and Kant by extending the astronomical analogy to include Bruno and Kepler. The strength of the article lies in its innovative analogy, thorough historical analysis, and the fresh perspective it brings to understanding Hegel’s idealism and his conception of infinity. The paper is well-structured and presents a clear argument. 

The paper's exploration of projective geometry is a particularly commendable aspect. The author's decision to delve into this non-Euclidean geometry, which was pivotal in the work of mathematicians like Desargues and Kepler, provides a fascinating insight into Hegel's philosophical strategy, particularly in how Hegel adopted a “Keplerian” approach to understanding the observable universe from a specific point of view within it. 

 

The topic is highly relevant, offering a new lens through which to view Hegel's philosophy, which can significantly contribute to contemporary Hegel scholarship. It is also well-covered, with a comprehensive examination of the historical context. The manuscript is sound in both its historical and theoretical analysis. The historical and philosophical methodologies employed are appropriate for the paper’s aims. The references are comprehensive, including primary texts from Hegel and Kant, and secondary sources from contemporary scholarship. The conclusions are consistent with the arguments presented.

 

While, in this reviewer’s opinion, the acceptance of the paper is not conditioned upon any request for change, I here provide three suggestions that might improve the final version of the article:

1. The latter part of Section 5 and, to a lesser extent, some portions of Section 6 are very detailed. While I understand the need to provide the specifics of the topic under investigation, a non-specialist reader could easily get lost within these details. Perhaps these sections can be shortened. The shortening of Section 5 and 6 might provide room for two possible extensions, one specific and the other general.

2. The specific extension concerns a clearer explanation of how the “musical” analysis relates to Hegel’s philosophy. Why the argument is present, its significance is not immediately clear to the reader.

3. In terms of a general extension, I finished the paper with a desire to know more about the impact that this novel interpretation can have on current philosophical debates within Hegel scholarship. I realise this is a vast topic, but perhaps a few conclusive remarks along these lines could helpfully wrap up the paper.

In conclusion, the paper presents a compelling and novel perspective on the relation between Hegel and Kant's philosophical approaches, drawing an insightful parallel with the astronomical revolutions of Copernicus, Bruno, and Kepler. The article is recommended for publication, as it provides a valuable addition to the scholarly debate.

Author Response

Reviewer 1. I’m very grateful to the reviewer for their thoughtful characterization of the paper’s aims and approach and their very encouraging remarks. In relation to the suggestions made in the second part of the review, I have altered the paper along the lines suggested (this was also in response to criticisms offered by the other reviewers). The original sections 5 and 6 have been shortened by both cutting some of the detail of the original version and dropping the section on Hegel, Carnot and the problem of infinitesimals entirely. This has been done to allow elaboration of Hegel’s treatment of judgments in The Science of Logic, now done in section 3 showing the contrast with Kant’s treatment of judgments in the Critique of Pure Reason, second edition, and Hegel’s theory of the syllogism, done in section 5 in conjunction with a discussion of Plato’s “musical” treatment of the cosmic animal in the Timaeus and comments on this by Proclus. In relation to the discussion of the Timaeus, passages on Plato from Hegel’s Lectures on the History of Philosophy are brought to bear. I think these changes bring the paper more into line with the suggestions made by this reviewer.

Reviewer 2 Report

Comments and Suggestions for Authors

The paper aims to make a point about Hegel's improvement on Kant by analogy to astronomical models. As far as the analysis of these models, and relevant geometrical and mathematical concepts are concerned, it does an excellent job (to the extent that I can tell. I am not an expert on the subject). The problem is that the paper has relatively little to say on either Kant or Hegel, and what it does say is poorly demonstrated in terms of citations from primary sources or treatment of secondary literature. If the paper would have presented itself as about the philosophical significance of different astonomical models this would be less troubling. I think that some revisions to the abstract and introduction would help narrow the gap between the expressed intentions of the paper and what it actually does.

In Section 3 much of the argument concerning judgments of perception vs. experience and judgments of existence vs. reflection is dense and lacking evidence from the primary sources. The author references his/her previous work so I cannot fully judge the quality of the argument, but it seems contentious. It is unclear that Hegel's judgments of existence essentially contain demonstratives (see the examples in the relevant section in the Encyclopedia), and it is clear that judgments of reflection do sometimes contain demonstratives. It is also unclear why in the latter case the author claims that the proposition is negated entirely as opposed to the predicate alone. In a judgment like "this plant has healing powers", which Hegel gives as an example for reflective judgments, what would be negated is the predicate. In fact, the distinction between negating a proposition as a whole vs. negating the predicate is not clear in general and its validity needs to be proved. 

In the Conclusion the author writes: "Hegel, following Kepler and Carnot, emphasized this finitude and turned it against the views of Kant himself, questioning the purity of the mathematical and logical structures appropriate for applicable human knowledge." This does not directly follow from anything in the text. While the text shows that Hegel had a certain view of infinity, nothing ties this view to human finitude. The sections from the Science of Logic dealing with infinitude,to which the text refer, do not explicitly deal with the difference beween human finitude or perspective and a divine point-of-view. The author should have made the connection more explicit and convincing. 

Also in the Conclusion, the author clarifies the point of the paper by arguing that whole Kant viewed perspective-dependent judgments as limitations in relation to an ideal, non-perspectival, whole, Hegel reversed this view and claimed that the non-perspectival is metaphysically prior. This appears strange with respect to Hegel, who has criticized the understanding as limited, abstract and false in relation to the ideal whole - the Concept. In that regard the Concept or the Idea, do not appear as extensions of finite understanding but as somehow prior to it. Of course the relation between perspectival judgments and other kinds need not be analoguous to the relation between understanding and reason but this is a move suggested by the author. The perspectival vs. absolute forms of judgment are compared to Kant's transcendental ideal vs. particular judgments. I do not know why that is, and how this is supposed to fit with the earlier comparison between judgment of perspective with judgments of experience. More needs to be said about this.

Author Response

I am extremely grateful to reviewer 2 for their particularly relevant criticism of the unbalanced nature of the originally submitted manuscript. The criticism that there is “relatively little to say on either Kant or Hegel” and that what is said is “poorly demonstrated in terms of citations from primary sources” (similar comments were made by reviewer 3) is entirely justified. In response to these concerns, section 3 has been entirely rewritten such that there are now about four new paragraphs on Kant’s treatment of judgments across three different texts and six new paragraphs on Hegel’s treatment of judgment in Book III of The Science of Logic (there is also further material on his treatment of syllogisms in section 6). In the rewriting I have paid particular attention to this reviewer’s specific criticisms of the earlier account. These may or may not now satisfy them (Hegel interpretation is a particularly contested subject) but I believe the case for my own interpretation is now much clearer and more explicit in the rewritten version as well as offering much more in the way of textual justification. I’m again grateful to this reviewer’s carefully thought-through criticisms for allowing me to see where further work was required.

To give myself the needed space for these additions I have jettisoned that part of the paper relating to Hegel’s attitude to infinitesimals and the role played by Carnot in Hegel’s thinking and streamlined some of the other material treated in sections 5 and 6. This makes some of the specific criticisms made in the second half of the reviewer’s comments now beside the point, but they nevertheless have been taken into consideration, especially in my further elaboration of Hegel’s discussion of the syllogism, now added to section 6. I think together with the added material in section 3 the new material goes quite a way to answering the general worries that the reviewer has made about the relation of perspectival and non-perspectival judgments in my account of Hegel’s logic. But again, these are difficult areas in which opposing views can surely persist.

Reviewer 3 Report

Comments and Suggestions for Authors

The paper is stimulating, interesting and highly original.  The research also seems thorough and detailed.  To be honest, I felt myself less in command of the material of the paper as I read through it than I expected to be, based on the abstract.  I take myself to be familiar with interpretive issues and scholarship concerning Hegel’s method of philosophy, particularly as it relates to Kant’s revolution in philosophical method, but the author’s paper is more about the history of astronomical cosmology (in Copernicus, Bruno, Kepler, and others) and the relation of this history to the history of the development of non-Euclidian geometries in the same period than it is about Hegel and Kant.  The author does relate the history of science and mathematics that he discusses in the paper in a very interesting way to Hegel, but the center of gravity of the paper, so to speak, seems to lie more in the story the author tells about Kepler and Carnot and others than it does in any analysis of Hegel’s work in the paper.  It is almost as if this paper is the first of a two-part work, the second of which would consist in an analysis of the difference that this history makes in how we ought to interpret Hegel.   The thin-ness of analysis and interpretation of Hegel in the paper might be considered a weakness, though, if one understands the paper as a prolegomenon to a reading of Hegel’s Keplerian revolution in philosophy rather than itself such a reading, then the paper no longer has this weakness.

                  Despite the fact that I find the paper very interesting and engaging, I cannot recommend publication as is, because taken as a paper meant to enlighten the reader about Hegel’s thought, there just isn’t enough detail in the interpretation of Hegel to pass muster.  And, I can only take the paper in that way, because I am not an expert on the matters in the history of science and mathematics that the author is largely concerned with.  However, I would encourage the author to keep working on this material, because it strikes me as very interesting and promising material.

 

n  I find the end of the second paragraph of the Introduction unclear.  In writing that “he” is not a Copernican, to whom does “he” refer?  I also found the last sentence of that paragraph unclear.

n  In presenting ways of interpreting what Kant means by the Copernican Revolution that Kant presents himself as effecting in epistemology, the author does not present – at least not explicitly – what I take to be the standard reading.  Copernicus explains apparent motions of the heavenly bodies (especially the sun) as to be explained by actual motion of the observing subject;  similarly, on Kant’s revolution in epistemology, we account for apparent features of the objects of experience (intuitive and conceptual) on the basis of the activities and structures of the knowing subject.  Perhaps the author is indicating this interpretation with the quotation from Schelling in the third paragraph of section 2 in the paper (bottom of p. 2), but it could be clearer and more explicit. 

n  Also pertaining to section 2 of the paper:  With respect to the question of whether a system affirms or denies an anthropocentric model, I think one must make further distinctions, beyond those the author makes, in order to be clear.  Yes, one could claim that Kant’s critical system of idealism centers the human standpoint, but, the defender of Kant should reply that this centering of the human standpoint is made by Kant only relative to knowledge, not in relation to position in space, and, in any event, with respect to practical reason, the human is again subordinated to the divine standpoint, on Kant’s view.  At the end of section 2, Bruno’s “acentric” view is aligned with Descartes’ and Newton’s, over against Copernicus’s, which is heliocentric.  But, as the author notes, Bruno’s position is (at least as Hegel reads it) Spinozistic, pantheistic, whereas Descartes’ and Newton’s positions are emphatically not.  Perhaps Descartes’ and Newton’s physical systems should be understood, in contrast to Copernicus’s heliocentric system, as without center.  But then one must distinguish between the physical system and the metaphysical system, because for both Descartes and Newton (perhaps unlike Bruno), God is the center metaphysically/ epistemologically. 

n  The author’s account of “logical space” in Kant’s and Hegel’s accounts of judgment in section 3 of the paper is interesting and thought-provoking.  I have a few questions or comments about it.  First, the first sentence of the second paragraph (p. 4) has a typo.  But, more importantly, the author refers there to “reflective judgment” in the context of Kant’s Critique of Pure Reason, even though Kant does not make his distinction between determinative and reflective judgment in that work.  This is confusing and unclear, I find.  (Is the author using “reflective judgment” as Kant himself defines it in his Critique of Judgment?)  What the author writes in this paragraph about the distinction from the Prolegomena between judgments of perception and of experience is interesting and thought-provoking, but I felt in need of more elaboration and justification of the author’s interpretive claims here.  Third, I am confused by the author’s claim in the next paragraph that “experience becomes radically decentered in a way that…mirrors Bruno’s radically decentered universe” when Kant, for the second-edition of his First Critique, conceives judgment itself as objectively valid (-- dispensing with the merely subjectively valid judgments of perception).  Experience as such, for Kant, is constituted by our (human) forms of space/ time and the categories.  Isn’t that some sort of centering?  It’s true that the realm of possible experience for Kant, insofar as that is equivalent to nature itself, is not perspectivally apprehended in science; our natural science is not from a particular point of view within nature.  But the whole realm of nature, for Kant, is constituted from the human point of view.  Fourth, the author’s claim that Hegel re-instates something like ‘judgments of perception’ of Kant’s Prolegomenon [sic; should read “Prolegomena”] calling them judgments of ‘existence’ and ‘inherence’ [see bottom of p. 4] is interesting and thought-provoking, but here too I felt in need of more elaboration and defense of this claim than was provided in the remainder of the section.  (Admittedly, the author cites other published work by him/herself on this matter.). I do find the author’s claim that “the projective geometric tradition”, emerging out of or influenced by the exploration of laws of perspectival painting in the Renaissance, play a role in the development of Hegel’s logic to be very provocative, suggestive and interesting, even if I feel myself wanting more elaboration and explanation of this claim. 

n  Sections 4 and 5 of the paper contain a lot of interesting material about Kepler and projective geometries.  This material is very interesting, though I do find myself relatively incompetent to assess it.  The author makes the claim that Koyre, who is an important source for the paper, “misses the point of Kepler’s resistance to the Brunian infinite universe” (p. 6).  The author argues that Kepler’s resistance to Bruno “reflected a greater fidelity to Cusan Neoplatonism”.  This is an interesting claim about Kepler, it seems, and the case for it is intriguing, but I am unable to assess it.  The author goes into some depth in describing the development of projective geometries in the fifth section of the paper.  The material is interesting; but, as I stand back from it, I do ask myself:  what does this have to do with Hegel?  The author comes back to this and makes the connection at the end of the section (p. 13).  In a single, relatively short, paragraph.  I worry that the author must say more about this to justify the paper as a paper centered on Hegel interpretation. 

n  In accord with the theme of these remarks, I find the author’s claims and analysis in section 6 of the paper also to be very interesting and thought-provoking.  The author tells us at the beginning of the section that we cannot understand what Hegel has to say about calculus and the problem of infinitesimals in the Science of Logic apart from the influence on him of the ideas of Lazare Carnot. The author goes on in the section to explain clearly Carnot’s influence on Hegel’s attitude to infinitesimals.  This is interesting and compelling.  But then, at the end, the author draws a larger implication from this discussion.  The author writes that “Hegel would employ a version of the idea of the translation of divine ‘ideas’ into practically human ones.  This would be the translation of Kant’s logically perfect “judgments of experience” into the imperfect but nevertheless applicable “judgments of perception”” (16).  This does not seem to me a claim that has been made out in the paper. 

n  The conclusion should be labeled “7”, not “6”. 

Author Response

Reviewer 3.

I’m very grateful to this reviewer for their very encouraging comments on the project in general (as might be guessed, this is a much broader project of which this paper is one aspect). I’m equally grateful for the very clearly pin-pointed criticisms of the inadequacies of the originally submitted version. Here the criticisms are very much in the same spirit as those made by one of the other readers. The original paper was very lop-sided—while presented as a paper explicitly about Hegel “there just isn’t enough detail in the interpretation of Hegel to pass muster”. This criticism is entirely justified and the paper has been extensively rewritten in an attempt to establish the right balance between what is addressed in relation to Hegel and Kant on the one hand and the material on Kepler, Bruno, geometry and astronomy on the other.

To this end section 4 has been extensively rewritten, with about four new paragraphs devoted to Kant’s account of judgments in the Critique of Pure Reason, the Prolegomena to any Future Metaphysics, and the Attempt to Introduce the Concept of Negative Magnitudes into Philosophy, and about six new paragraphs on Hegel’s account of judgment in The Science of Logic as well as further discussion, in section 6, on Hegel’s account of the syllogism.

The reviewer also has a list of specific criticisms in the second half of their review. Those, like point no. 1, that refer to simple unclarities have been emended. In point 2, the reviewer complains that I do not make sufficiently clear the “standard reading” of Kant’s “Copernican revolution”. I’ve addressed this to a degree, but also wanted to avoid the need to address the huge amount of secondary literature on this topic as this is not central to the aims of the paper. To this end, I have now presented the “Brunian” interpretation of Kant’s Copernican turn as something of a foil to Hegel’s “Keplerian” interpretation of it and so presented as representative of Kant only in the sense as seen from Hegel’s point of view. This is to relieve myself of the need to justify this reading of Kant. Even were it unfair to Kant, it may still be helpful in making clear the reading I wish to give to Hegel.

In relation to point 3, I have rewritten parts of section 2 to try to make clearer the issues having to do with anthropocentrism and its counter. I think this is now a lot clearer and I’m grateful to this reader for their criticisms and queries.

In relation to the four specific points made about Kant’s and Hegel’s respective accounts of “logical space” in section 4, I have taken these all into account in the extensive rewriting of this section. I think the rewriting goes a long way to address the legitimate concerns brought up here, but with as difficult a writer as Hegel there will be always much scope for fair disagreement. In any case, in the new sections I have striven to back up all interpretative claims with passages from the text itself.

The reviewer raises concerns with the neo-Platonist material discussed, as having left them with the question “what does this have to do with Hegel”? The original justification for this association had been to refer to other work published by me. Clearly this is useless in a blind review process, but I agree that it is frustrating for any reader to be given only this. To address this particular point I have added material in section 6 in relation to Hegel’s treatment of the syllogism that concerns his specific reading of Plato’s Timaeus in the Lectures on the History of Philosophy and I have added some material on specific neo-Platonist readings, like that of Proclus, that I think sheds light on the main claims. Space constraints have meant that this is fairly condensed but I think enough is given to establish the sort of prima facie case appropriate for a context such as this one. 

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

[I do not have a separate set of comments for the author.   My comments are for the editor, but it is fine to show them to the author.  I provided extensive comments to the original submission some weeks ago. This is my response to the author's resubmission of the revised paper.  Accordingly, my comments here are brief.]

The author was responsive to my questions/ comments on the original version in the revision.  I find the revised paper to be improved relative to the issues I raised with respect to the original version.  I found the paper, in the original version, to be highly original, interesting and stimulating, but somewhat under-developed with respect to the interpretive claims about Hegel.  The interpretive claims about Hegel's positions seemed more suggestive than developed in the original version of the paper.  There was very interesting material in the paper about Kepler and Bruno and the history of projective geometry, but how this material affected how one should understand Hegel's conception of judgment or his idealism seemed relatively un-developed in that original version of the paper.

The revision is improved in this respect.  My judgment now is that the current version has sufficient development to be published as is, and that the originality and interest of the paper justifies publication as is.  I am left, in the revised paper, still wanting more, in terms of the interpretation of Hegel in light of the interesting background that the author provides.  But there is a limit to how much one can do in an article-length work, and leaving the reader wanting more is not a bad thing in a philosophical paper.  

I have only the following suggestions for revision:

On p. 15 of 21, lines 752-756, there is an unclear sentence, in need of revision.  Also, the endnote at the end of this sentence, #39, is not included in the endnotes.  Also, the endnote #40 at line 763 is also not included in the endnotes.