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1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeDec 3rd 2014
   • (edited Dec 3rd 2014)
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexContinuing from [here](http://nforum.mathforge.org/discussion/6352/necessity-and-possibility/?Focus=50990#Comment_50990), where Urs writes >...under our running $(Hegel \leftrightarrow ModalTypeTheory)$-dictionary Hegel's "determinate" ("bestimmt") translates to "at a higher [[level of a topos|level]]" in the essential subtopos lattice. >For instance Hegel's "pure being" is the right adjoint in $(\emptyset \dashv \ast)$ and the determination of that to "determinate being" is the right adjoint of the higher $(\flat \dashv \sharp)$ in the sense defined at _[Aufhebung](http://ncatlab.org/nlab/show/Aufhebung#Aufhebung)_. >That's anyway how "we" currently read it, following that page 21 or the like of "Some thoughts on the future of category theory". I thought we had interpreted this passage as merely the adjoint cyclinder: >§187 The more precise meaning and expression which being and nothing receive, now that they are moments, is to be ascertained from the consideration of determinate being as the unity in which they are preserved. Being is being, and nothing is nothing, only in their contradistinction from each other; but in their truth, in their unity, they have vanished as these determinations and are now something else. Being and nothing are the same; but just because they are the same they are no longer being and nothing, but now have a different significance. In becoming they were coming-to-be and ceasing-to-be; in determinate being, a differently determined unity, they are again differently determined moments. This unity now remains their base from which they do not again emerge in the abstract significance of being and nothing. $$ \emptyset \to X \to \ast. $$ Are these points of view compatible?

   Continuing from here, where Urs writes

   …under our running $(Hegel \leftrightarrow ModalTypeTheory)$-dictionary Hegel’s “determinate” (“bestimmt”) translates to “at a higher level” in the essential subtopos lattice.

   For instance Hegel’s “pure being” is the right adjoint in $(\emptyset \dashv \ast)$ and the determination of that to “determinate being” is the right adjoint of the higher $(\flat \dashv \sharp)$ in the sense defined at Aufhebung.

   That’s anyway how “we” currently read it, following that page 21 or the like of “Some thoughts on the future of category theory”.

   I thought we had interpreted this passage as merely the adjoint cyclinder:

   §187 The more precise meaning and expression which being and nothing receive, now that they are moments, is to be ascertained from the consideration of determinate being as the unity in which they are preserved. Being is being, and nothing is nothing, only in their contradistinction from each other; but in their truth, in their unity, they have vanished as these determinations and are now something else. Being and nothing are the same; but just because they are the same they are no longer being and nothing, but now have a different significance. In becoming they were coming-to-be and ceasing-to-be; in determinate being, a differently determined unity, they are again differently determined moments. This unity now remains their base from which they do not again emerge in the abstract significance of being and nothing.

   $$\emptyset \to X \to \ast.$$

   Are these points of view compatible?

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeDec 3rd 2014
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexSo to determinate negation. First a whole book on the subject, [Hegel's Conception of the Determinate Negation](http://www.brill.com/products/book/hegels-conception-determinate-negation), blurb >“The determinate negation” has by Robert Brandom been called Hegel’s most fundamental conceptual tool. In this book, Terje Sparby agrees about the importance of the term, but rejects Brandom’s interpretation of it. Hegel’s actual use of the term may at first seem to be inconsistent, something that is reflected in the scholarship. However, on closer inspection, three forms of determinate negations can be discerned in Hegel’s texts: A nothing that is something, a moment of transformation through loss (like the Phoenix rising from the ashes), and a unity of opposites. Through an in-depth interpretation of Hegel’s work, a comprehensive account of the determinate negation is developed in which these philosophically challenging ideas are seen as parts of one overarching process. Second, from a [glossary'](http://www.london.ac.uk/fileadmin/documents/students/philosophy/ba_course_materials/ba_19thc_hegel_glossary_01.pdf) >DETERMINE, DETERMINATION, DETERMINATE, DETERMINACY/DETERMINATENESS (bestimmen, Bestimmung, bestimmt, Bestimmtheit). To determine something is to conceptualise, articulate, identify, particularise, specify it. Solomon suggests that the term plays a similar role in Hegel to 'constitute' in Kant. Determination and determinacy presuppose negation – i.e. (Inwood:) a thing is determinate only in so far as it contrasts with other things or concepts which are determined in a way in which it is not. The determinacy of a thing consists in its features, in the broadest possible sense. >NEGATIVE, NEGATION, NEGATIVITY, NEGATE (negativ, Negation, Negativität, negieren). Hegel use of negation, like his use of truth, is usually remote from its familiar sense in application to judgements or propositions: things and concepts are for Hegel negations of one another (negativities). The negative is that which is different from, opposed to, other than. Negation is for Hegel determinate, as determinate as what is negated, and the phrase 'determinate negation' figures often. Hegel's thought characteristically observes the dialectical sequence: (1) affirmation, (2) negation, (3) negation of negation = affirmation of something new. In application to consciousness, per Pinkard, negativity refers to the capacity of consciousness to critically undermine its own form of rationality; (determinate) negation is the skeptical undermining of a form of rationality. Third, from [SEP: Hegel](http://plato.stanford.edu/entries/hegel/) >Such a method invoking “determinate negation” is often described as deriving from Spinoza's claim that “all determination is negation,” but it can be just as readily seen as a consequence of Hegel's use of Aristotle's term logic. In term logics, negation is understood as a relation existing primarily between terms of the same type: a colour concept such as “red,” for example, will be understood as meaningful in as much as it stands in opposition to an array of contrary colour terms such as “blue, ” “green, ” and so on. In contrast, in logics which take the proposition as the fundamental semantic unit (such as the classical predicate calculus deriving from Frege and accepted by most analytic philosophers), negation is typically regarded as applying primarily to whole propositions rather than to sub-sentential units. Hegel exploits the role of negation at a variety of levels. For example, the relation between the bare demonstratives “this” and “that” instantiates the relation of determinate negation, as does that between qualitative predicates, as for example, “red” and “green“ as instances of the more universal concept, colour. Typically, problems of determination at one level are resolved by invoking the next more complex level: even if we could indicate contrastively what we meant by “this” by invoking a contrasting “that,” we will be reliant on the presupposed ability to refer to the kind of thing we have in mind, as when we refer to “this colour” or “this shape” and so on.

   So to determinate negation.

   First a whole book on the subject, Hegel’s Conception of the Determinate Negation, blurb

   “The determinate negation” has by Robert Brandom been called Hegel’s most fundamental conceptual tool. In this book, Terje Sparby agrees about the importance of the term, but rejects Brandom’s interpretation of it. Hegel’s actual use of the term may at first seem to be inconsistent, something that is reflected in the scholarship. However, on closer inspection, three forms of determinate negations can be discerned in Hegel’s texts: A nothing that is something, a moment of transformation through loss (like the Phoenix rising from the ashes), and a unity of opposites. Through an in-depth interpretation of Hegel’s work, a comprehensive account of the determinate negation is developed in which these philosophically challenging ideas are seen as parts of one overarching process.

   Second, from a glossary’

   DETERMINE, DETERMINATION, DETERMINATE, DETERMINACY/DETERMINATENESS (bestimmen, Bestimmung, bestimmt, Bestimmtheit). To determine something is to conceptualise, articulate, identify, particularise, specify it. Solomon suggests that the term plays a similar role in Hegel to ’constitute’ in Kant. Determination and determinacy presuppose negation – i.e. (Inwood:) a thing is determinate only in so far as it contrasts with other things or concepts which are determined in a way in which it is not. The determinacy of a thing consists in its features, in the broadest possible sense.

   NEGATIVE, NEGATION, NEGATIVITY, NEGATE (negativ, Negation, Negativität, negieren). Hegel use of negation, like his use of truth, is usually remote from its familiar sense in application to judgements or propositions: things and concepts are for Hegel negations of one another (negativities). The negative is that which is different from, opposed to, other than. Negation is for Hegel determinate, as determinate as what is negated, and the phrase ’determinate negation’ figures often. Hegel’s thought characteristically observes the dialectical sequence: (1) affirmation, (2) negation, (3) negation of negation = affirmation of something new. In application to consciousness, per Pinkard, negativity refers to the capacity of consciousness to critically undermine its own form of rationality; (determinate) negation is the skeptical undermining of a form of rationality.

   Third, from SEP: Hegel

   Such a method invoking “determinate negation” is often described as deriving from Spinoza’s claim that “all determination is negation,” but it can be just as readily seen as a consequence of Hegel’s use of Aristotle’s term logic. In term logics, negation is understood as a relation existing primarily between terms of the same type: a colour concept such as “red,” for example, will be understood as meaningful in as much as it stands in opposition to an array of contrary colour terms such as “blue, ” “green, ” and so on. In contrast, in logics which take the proposition as the fundamental semantic unit (such as the classical predicate calculus deriving from Frege and accepted by most analytic philosophers), negation is typically regarded as applying primarily to whole propositions rather than to sub-sentential units. Hegel exploits the role of negation at a variety of levels. For example, the relation between the bare demonstratives “this” and “that” instantiates the relation of determinate negation, as does that between qualitative predicates, as for example, “red” and “green“ as instances of the more universal concept, colour. Typically, problems of determination at one level are resolved by invoking the next more complex level: even if we could indicate contrastively what we meant by “this” by invoking a contrasting “that,” we will be reliant on the presupposed ability to refer to the kind of thing we have in mind, as when we refer to “this colour” or “this shape” and so on.

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeDec 3rd 2014
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexThe third of these is by Paul Redding whose book on the revival of Hegel we've been reading. It seems to be soaked in type theoretic thinking. E.g., there is no plain 'this', but always 'This such' $$ this A: A. $$ We can only ask whether 'this' and 'that' are the same in terms of a type $$ Id_A(this A, that A). $$

   The third of these is by Paul Redding whose book on the revival of Hegel we’ve been reading. It seems to be soaked in type theoretic thinking. E.g., there is no plain ’this’, but always ’This such’

   $$this A: A.$$

   We can only ask whether ’this’ and ’that’ are the same in terms of a type

   $$Id_A(this A, that A).$$
4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeDec 3rd 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexI suppose WdL is not quite consistent in the use of the terms, we'll need to make a choice. Earlier [§88](http://ncatlab.org/nlab/show/Science%20of%20Logic#88) says that > The truth of being as well as of nothing is therefore the unity of both; this unity is becoming. Under the Lawverian translation of "unity" of opposites as their adjunction, I take that to mean that the adjunction $(\emptyset \dashv \ast)$ is to be called "becoming". Next by [§191](http://ncatlab.org/nlab/show/Science%20of%20Logic#191) "determinate being" instead is the sublation of this, > becoming, lies behind it; it has sublated itself and determinate being appears and by the formalization at _[[Aufhebung]]_ this means first of all that becoming must be an adjoint modality (because that's what has sublation, by that formalization) and that determinate being must be $\sharp$ (because that indeed is the Aufhebung of $(\emptyset \dashv \ast)$, at least over cohesive sites of definition). This harmonizes well with [§194](http://ncatlab.org/nlab/show/Science%20of%20Logic#194) > Determinate being corresponds to being in the previous sphere in view of the level inclusion $\ast \lt \sharp$. There won't be a formalization that matches every verse in WdL, one needs something like a best fit.

   I suppose WdL is not quite consistent in the use of the terms, we’ll need to make a choice. Earlier §88 says that

   The truth of being as well as of nothing is therefore the unity of both; this unity is becoming.

   Under the Lawverian translation of “unity” of opposites as their adjunction, I take that to mean that the adjunction $(\emptyset \dashv \ast)$ is to be called “becoming”.

   Next by §191 “determinate being” instead is the sublation of this,

   becoming, lies behind it; it has sublated itself and determinate being appears

   and by the formalization at Aufhebung this means first of all that becoming must be an adjoint modality (because that’s what has sublation, by that formalization) and that determinate being must be $\sharp$ (because that indeed is the Aufhebung of $(\emptyset \dashv \ast)$, at least over cohesive sites of definition).

   This harmonizes well with §194

   Determinate being corresponds to being in the previous sphere

   in view of the level inclusion $\ast \lt \sharp$.

   There won’t be a formalization that matches every verse in WdL, one needs something like a best fit.