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Hegel claims to have logically derived his philosophy;

replaced a quote that was out of context with this one

<< Hegel's Science of Logic, introduction §62

"In the Phenomenology of Mind I have expounded an example of this method in application to a more concrete object, namely to consciousness. Here we are dealing with forms of consciousness each of which in realising itself at the same time resolves itself, has for its result its own negation — and so passes into a higher form . All that is necessary to achieve scientific progress — and it is essential to strive to gain this quite simple insight — is the recognition of the logical principle that the negative is just as much positive, or that what is self-contradictory does not resolve itself into a nullity, into abstract nothingness, but essentially only into the negation of its particular content, in other words, that such a negation is not all and every negation but the negation of a specific subject matter which resolves itself, and consequently is a specific negation, and therefore the result essentially contains that from which it results; which strictly speaking is a tautology, for otherwise it would be an immediacy, not a result. Because the result, the negation, is a specific negation, it has content. It is a fresh Notion but higher and richer than its predecessor; for it is richer by the negation or opposite of the latter, therefore contains it, but also something more, and is the unity of itself and its opposite. It is in this way that the system of Notions as such has to be formed — and has to complete itself in a purely continuous course in which nothing extraneous is introduced."

He continues to say in §63

"I could not pretend that the method which I follow in this system of logic — or rather which this system in its own self follows — is not capable of greater completeness, of much elaboration in detail; but at the same time I know that it is the only true method. This is self-evident simply from the fact that it is not something distinct from its object and content; for it is the inwardness of the content, the dialectic which it possesses within itself, which is the mainspring of its advance. It is clear that no expositions can be accepted as scientifically valid which do not pursue the course of this method and do not conform to its simple rhythm, for this is the course of the subject matter itself.">>

Hegelian philosophy has been partially formalized in mathematics, particularly in adjoint-modal-type-theory where one finds deep correspondence between the two. In my perspective, it receives further justification from formalizations of math in-itself in texts like type theory in type theory (just serious math there), which can be interpreted as the self-construing method Hegel talks about, in that math doesn't need mathematicians to operate( "circular" foundations). Since Hegel worked before the existence of advanced math and considered math as a subordinate science, am interested in knowing whether anyone truly understands his dialectic enough to independently apply it (if so, how?). Preferably, a first-person point-of-view will suffice.

EDIT: To be more specific, am asking for the way Hegel understood dialectics and utilised it consistently because I believe it provides an alternative "pre-mathematical" way of doing math, without need for random ideas or symbols. Not how it corresponds to math.

Kori Peter
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  • It depends on what you mean by "logic"... Obviously, Hegel's logic is not what is named so in modern mathematics. – Mauro ALLEGRANZA Mar 29 '21 at 14:28
  • See [Hegel’s Dialectics](https://plato.stanford.edu/entries/hegel-dialectics) and [Hegel's *Science of Logic*](https://plato.stanford.edu/entries/hegel/#SciLog): "For most of the 20th century it was not received with the enthusiasm that often marked the reception of *Phenomenology of Spirit*. First, as a work of logic most have regarded it as radically outdated and relying on an Aristotelian approach that was definitively surpassed in the later nineteenth century. [...] 1/2 – Mauro ALLEGRANZA Mar 29 '21 at 14:34
  • Some advocate that the *Science of Logic* be read as a first-order ontological doctrine or as a category theory that simultaneously represents structures of being and thought , and so as having very little to do with what has traditionally been known as logic." 2/2 – Mauro ALLEGRANZA Mar 29 '21 at 14:36
  • @MauroALLEGRANZA: I think the question is about something else though: whether Hegel applied *his* logic to *his* philosophy properly / consistently. I don't know about the "type theory in type theory" stuff to say anything else about this. But since the OP linked a thesis like that, what are its conclusions? – Fizz Mar 29 '21 at 14:40
  • I tend to disagree, the fact that Hegelian philosophy corresponds to synthetic homotopy type theory indicates that Hegelian logic is logic. It is known that first-order logic is not the only logic, there are many and more general logics as you can checkout [relation between type theory and category theory](https://ncatlab.org/nlab/show/relation+between+type+theory+and+category+theory#:~:text=Type%20theory%20and%20certain%20kinds,providing%20semantics%20for%20type%20theory.) – Kori Peter Mar 29 '21 at 14:42
  • FTWT https://math.stackexchange.com/questions/2357569/can-you-explain-lawveres-work-on-hegel-to-someone-who-knows-basic-category-theo – Fizz Mar 29 '21 at 14:44
  • Not sure I understand your question. Do you mean "is it possible to do math without symbols" (such as common-sense calculations or logic?), using Hegel as an example for someone who supposedly managed to do so? – Yechiam Weiss Mar 29 '21 at 15:35
  • @YechiamWeiss, Yes, I mean that. Anybody who understands Hegel has managed to do so (for some reason I think so). Guess it might be called speculative-mode of cognition as in a text referenced above – Kori Peter Mar 29 '21 at 16:14
  • So you might want to generalize your question, as it is not about Hegel specifically (from what I understand). And then I don't understand your question - what's wrong with [common sense](https://en.wikipedia.org/wiki/Common_sense)? – Yechiam Weiss Mar 29 '21 at 17:11
  • I don't know why you don't get me. I didn't argue against common-sense, more for it. The only way a person can prove that Hegel was logical is by proving it himself (by doing the same)not quoting other people who quote other people. – Kori Peter Mar 29 '21 at 17:49
  • Hegelian dialectics does not correspond to synthetic homotopy type theory or anything else formal, those are loosely inspired limited interpretations. Hegel was interested in spontaneous generation of ever more complex concepts, the historical "movement of thought", *that* is the point of his Logic, formalization can only formalize what is already generated and conceptualized. Hegel believed that there is a cogent "method" to it, but his own practice does not instill confidence, as Peirce noted he reaches "*each category from the last preceding by virtually calling 'next!'*" – Conifold Apr 02 '21 at 12:09
  • @YechiamWeiss, I see why there was a misunderstanding, the quote I took was out of context, sorry for that. It is in the preface which I had not read and the text I used had made an omission. I will try to fix that – Kori Peter Apr 04 '21 at 07:22
  • Was listening to an In Our Time about the analytic-continental split, that identified being influenced or not by Hegel as key, relating it to the dialectic as cultural development & discourse, whether that can lead to new truth, or not. Kuhn & paradigms are on that. I am very interested in strange-loops & tangled hierarchies, and I really liked this interpretation of their use in work of various philosophers https://absoluteirony.wordpress.com/2014/09/17/nagarjuna-nietzsche-rorty-and-their-strange-looping-trick/amp/ I'd relate this to hypothesis development as non-recursively enumarable. – CriglCragl Apr 04 '21 at 23:07

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...[I] am interested in knowing whether anyone truly understands his dialectic enough to independently apply it.

If anyone understands his dialectic enough to formalize it, then you would only know by looking at that formal system.

There have been plenty of attempts to formalize Hegel, and Hegel's Science of Logic in particular. The best shot seems to be nLab, but the level of math there is currently beyond by ability to assess if it's a coherent and faithful representation of his philosophy.

psitae
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