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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.

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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, 2021 at 14:28
  • See Hegel’s Dialectics and Hegel's Science of Logic: "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, 2021 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, 2021 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, 2021 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
    – Kori Peter
    Mar 29, 2021 at 14:42

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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.

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  • I agree, looking at the formalization will help understand the dialectic beyond just correspondence
    – Kori Peter
    Apr 5, 2021 at 11:10

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