Hegel : science de la logique dans ncatlab

Ici :

https://ncatlab.org/nlab/show/Science+of+Logic#Phen760

« Hence we formalize Wesen by ∞-topos « 

un cadre mathématique pour la doctrine hégélienne de l’Essence (Wesen) est choisi dans #HoTT et #HigherToposTheory :

»In (homotopy) type theory the appearance of a reflection of the type system in itself is a type universe Type∈H here) see also §833. This was introduced as a type theoretical reflection principle in Martin-Löf 74, p. 6 »

«

Adding a universe is a reflection process (Stanf. Enc. Phil. Extensions of Type System)

Introducing universes can be considered as a reflection principle: such a universe reflects those types whose names are its objects. Luo 11, section 2.5«

«

§827 It is the immediacy of non-being that constitutes illusory being; but this non-being is nothing else but the negativity of essence present within it. In essence, being is non-being. Its intrinsic nothingness is the negative nature of essence itself. But the immediacy or indifference which this non-being contains is essence’s own absolute being-in-itself. The negativity of essence is its equality with itself or its simple immediacy and indifference. Being has preserved itself in essence in so far as the latter in its infinite negativity has this equality with itself; it is through this that essence itself is being. The immediacy of the determinateness in illusory being over against essence is consequently nothing other than essence’s own immediacy; but the immediacy is not simply affirmative [seiend], but is the purely mediated or reflected immediacy that is illusory being-being, not as being, but only as the determinateness of being as opposed to mediation; being as a moment.«

«

§823 1. Being is illusory being. The being of illusory being consists solely in the sublatedness of being, in its nothingness; this nothingness it has in essence and apart from its nothingness, apart from essence, illusory being is not. It is the negative posited as negative.«

« Notice that here the text begins to say Nichtigkeit (∼ §803 this ultimate Aufhebung is the trivial unity of opposites id⊣id id encodes no determination and hence encodes “nothing”, but this is rather different from the sense of Nichts, Nichtsein (again ∼

We will read Nichtigkeit (∼ §823. This seems to match well with its use here, in particular with the repeated statemens §835 that movement of the essence is not like that of being from something (some determination, really) to something else (some other determination, oppose of sublated), but moves from nothing to nothing. This is hence speaking of id⊣id §827«

«827 It is the immediacy of non-being that constitutes illusory being; but this non-being is nothing else but the negativity of essence present within it. In essence, being is non-being. Its intrinsic nothingness is the negative nature of essence itself. But the immediacy or indifference which this non-being contains is essence’s own absolute being-in-itself. The negativity of essence is its equality with itself or its simple immediacy and indifference. Being has preserved itself in essence in so far as the latter in its infinite negativity has this equality with itself; it is through this that essence itself is being. The immediacy of the determinateness in illusory being over against essence is consequently nothing other than essence’s own immediacy; but the immediacy is not simply affirmative [seiend], but is the purely mediated or reflected immediacy that is illusory being-being, not as being, but only as the determinateness of being as opposed to mediation; being as a moment.

§828 These two moments, namely the nothingness which yet is and the being which is only a moment, or the implicit negativity and the reflected immediacy that constitute the moments of illusory being, are thus the moments of essence itself. What we have here is not an illusory show of being in essence, or an illusory show of essence in being; the illusory being in essence is not the illusory being of an other, but is illusory being per se, the illusory being of essence itself. What we have here is not an illusory show of being in essence, or an illusory show of essence in being; the illusory being in essence is not the illusory being of an other, but is illusory being per se, the illusory being of essence itself«

Reading Nichtigkeit here via §823 is id⊣id and reflektierte Unmittelbarkeit as the self-reflection of the  type universe via §833, then §828 says that the two moments of the Essence are

(id⊣id),Typewhich in turn is the ambient category and its type universe. Hence this gives again that Essence is the ambient ∞-topos

In (homotopy) type theory/(infinity,1)-topos theory the appearance of a reflection of the type system in itself is called type universe/object classifier (see there references listed here).

§834 Das Wesen ist Reflexion;…

§834 Essence is reflection…

See discussion at Wesen als Reflexion in Ihm Selbst

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