Perhaps the "annotated" Hegel's Science of Logic is better. This section sets the stage:
§1798 formal thinking lays down for its principle that contradiction is unthinkable; but as a matter of fact the thinking of contradiction is the essential moment of the Notion. However, there is more to formal logic than plain predicate logic. Foundational systems of categorical logic and of type theory (which happens to have its roots in (Russell 08)) subsume first-order logic but also allow for richer category-theoretic universal constructions such as notably adjunctions and modal operators (see at modal type theory). That adjunctions stand a good chance of usefully formalizing recurring themes of duality (of opposites) in philosophy was observed in the 1980s (Lambek 82) notably by William Lawvere. Since then, Lawvere has been proposing (review includes Rodin 14), more or less explicitly and apparently (Lawvere 95) inspired by (Grassmann 1844), that at least some key parts of Hegel’s Logic, notably his concepts of unity of opposites, of Aufhebung (sublation) and of abstract general, concrete general and concrete particular as well as the concepts of objective logic and subjective logic as such (Law94b) have an accurate, useful and interesting formalization in categorical logic. Not the least, the concept and terminology of category, modality, theory and doctrine matches well under this translation from philosophy to categorical logic. Lawvere also proposed formalizations in category theory and topos theory of various terms appearing prominently in Hegel’s Philosophy of Nature, such as the concept of intensive or extensive quantity and of cohesion. While, when taken at face value, these are hardly deep concepts in physics, and were not at Hegel’s time, in Lawvere’s formalization and then transported to homotopy type theory (as cohesive homotopy type theory), they do impact on open problems in fundamental physics and even in pure mathematics (see also at Have professional philosophers contributed to other fields in the last 20 years?), a feat that the comparatively simplistic mathematics that is considered in analytic philosophy seems to have little chance of achieving. Lawvere 92: It is my belief that in the next decade and in the next century the technical advances forged by category theorists will be of value to dialectical philosophy, lending precise form with disputable mathematical models to ancient philosophical distinctions such as general vs. particular, objective vs. subjective, being vs. becoming, space vs. quantity, equality vs. difference, quantitative vs. qualitative etc. In turn the explicit attention by mathematicians to such philosophical questions is necessary to achieve the goal of making mathematics (and hence other sciences) more widely learnable and useable. Of course this will require that philosophers learn mathematics and that mathematicians learn philosophy. nPOV. Therefore, while going through Hegel’s text, this page here attempts to spell out as much as seems possible the translation of the system to a category-theoretic or modal type-theoretic formalization (an “nPOV”). The way this formalization works in general is surveyed below in Formalization in categorical logic / in Modal type theory; a dictionary version of the formalization that we arrive at is in The formalization dictionary; and diagram showing the resulting process is in Survey diagram. @philipthrift On Tuesday, June 23, 2020 at 4:48:10 AM UTC-5 Bruno Marchal wrote: > > > On 23 Jun 2020, at 08:31, Philip Thrift <cloud...@gmail.com> wrote: > > > > > > As "digestably" presented on nLab: > > > > https://ncatlab.org/nlab/show/Science+of+Logic > > > That is very vast, and assumed a good knowledge of category theory. There > are many interesting things, but this, if used in metaphysics, might again > lead to a confusion between “[]p” and “[]p & p”, from many remarks > dispersed in the many text. > > If that is the digestible presentation, I am not sure I will try to find > the non digestible one … lol > > Bruno > > > > > > > > @philipthrift > > > > -- > > You received this message because you are subscribed to the Google > Groups "Everything List" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to everything-li...@googlegroups.com. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/6ce50147-7982-4571-96bd-ec8458361332o%40googlegroups.com. > > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/5a72bb19-d700-401f-99a4-acd6abe5505cn%40googlegroups.com.
