I

Before presenting the various positions, I shall clarify the range of the double shine in case the reader might be confused about why a metaphor that is thematized only in the sphere of the universal (compare SL: 533/12: 35) can also apply to the spheres of both the particular and the singular.

The main reason for the continuity of the double shine through all three moments lies in the totality of the universal. Hegel clearly explains this point before introducing the double shine in the subsequent paragraph:

Hegel uses the double shine to further illustrate this totality of the universal. The concept cannot describe the universal without the particular and the singular. In fact, in the sphere of the particular, Hegel directly equates the particular with the outward shine. ‘The particular is the universal itself, but it is its difference or reference to an other, its outwardly reflecting shine’ (SL: 534/12: 37f). In the sphere of the singular, Hegel relates the singular to the inward shine:

Keeping this clarification in mind, I now turn to the presentation of the relevant positions of the discussants. In general, Iber's view can be seen as a succinct recapitulation of Schick's interpretation. Both identify the core issue that the double shine addresses as the compatibility between the universal's ‘universality’ or ‘self-reference’ and its ‘determinacy’ (Schick Reference Schick1994: 197, 202; Iber Reference Iber, Koch and Schick2002: 192). The outward shine represents such determinacy in terms of ‘the relation to the other’ through the abstraction from the ‘particular perspective’, the ‘externally selective reception’ and the ‘comparison with the third’ (Schick Reference Schick1994: 199; Iber Reference Iber, Koch and Schick2002: 192). Because of this otherness, determinacy under the outward shine contradicts the universal's self-reference. ‘Being determinate prevents the thing from being itself’. ‘The true universal seems consequently only to be achieved through the abstract negation of determinacy’ (Schick Reference Schick1994: 199).

Conversely, the inward shine embodies the rehabilitation of the universal's self-reference by redirecting the universal's determinacy to its self-determination. Following Schick, Iber clearly shows that there are two ways of understanding the inward shine and the corresponding effort to restore the universal's self-reference confronted with external determinacy. In addition, the two methods oppose each other. One employs a type of ‘genus-character’, a ‘self-determination’ (Schick Reference Schick1994: 199) or ‘self-specification’ (Iber Reference Iber, Koch and Schick2002: 192) of the universal, while the other employs ‘the-one-concept’ (Schick Reference Schick1994: 200; Iber Reference Iber, Koch and Schick2002: 192) or ‘the highest universal’ (Schick Reference Schick1994: 202) abstracted from the species universals. The highest universal as a ‘simple negation of all particular universals’ (Schick Reference Schick1994: 199) eventually becomes an ‘indifference against all difference’ (Schick Reference Schick1994: 202) or ‘indifference and indeterminacy against all determinate concepts’ (Iber Reference Iber, Koch and Schick2002: 193). However, it is unclear what the difference is between this latter abstract way of understanding the inward shine and the abstract negation of the determinacy in the outward shine, as both lead to an indeterminate highest universal.

Because of this ambiguity, Schick has recently modified several parts of her earlier interpretation. Instead of the comparison from an external perspective, she now ascribes the cause of the outward shine or the determinacy to the universal itself by specifying the outward shine as a type of ‘essence-logical’ relation. She means that ‘the universal's own concept involves its relation to its counterpart, the particular’ (Schick Reference Schick, Quante and Mooren2018: 475), and thereby relativizes itself. This self-relativizing nature of the universal renders the higher universal that seeks to eliminate this relativization through the taxonomical abstraction of difference, let alone ‘the taxonomically highest universal’ or ‘the universal of the highest abstraction’, impossible (Schick Reference Schick, Quante and Mooren2018: 476).

The differences between Schick's earlier and recent position might be summarized as follows. First, the cause of the determinacy or the outward shine that was previously attributed to the external perspective is now located in the universality itself. The universal is determinate, not because someone externally compares it with other determinations, but in virtue of its own concept. Second, restoring the universal's self-determination using abstraction is now no longer considered to be an alternative method of the inward shine but solely belongs to the mode of the outward shine. This modification is plausible. If the characteristic of the outward shine is to adhere to the difference of the universal from others, then it is logically consequent for the outward shine to exclude the otherness from the universal to keep the universal's self-identity.

Trisokkas also identifies the problem that the double shine seeks to address with the universal's unity of ‘self-identity and utmost determinacy’ (Trisokkas Reference Trisokkas2009: 144). While the outward shine (which he calls ‘the single movement model’) represents a deficient approach to that unity, when this is complemented by the inward shine and thereby forms the double shine as a whole (so-called ‘the double movement model’), it can overcome that defect and achieve unity (2009: 149). The deficiency of the outward shine consists of its maintaining the universal's self-identity by dissolving the universal's determinacy (‘a multiplicity of universals related negatively to each other’) into a higher but indeterminate universal (Trisokkas Reference Trisokkas2009: 150). An infinite regression of the positing of an indeterminate higher universal arises when its determinacy is to be regained by redeveloping its negative relation with a multiplicity of universals.

To rectify this deficiency, the inward shine complements the outward shine by conceiving the higher universals as ‘the character of the genus’ manifesting ‘into its own determinacy’ (Trisokkas Reference Trisokkas2009: 153). Combined with the outward shine, the double shine is

What is peculiar in Trisokkas's case is his argument for the necessity of positing the highest universal. According to him, the double shine model creates an opportunity for an anomaly, namely, that a plurality of higher universals is ‘totally unconnected with each other and still totally determined’ in terms of their own species universals (Trisokkas Reference Trisokkas2009: 156). Since each of the higher universals is already sufficiently determined, they do not need to further appeal to the negative relation among them. However, this contradicts the ‘self-identity and self-containment’ of the universal as an established premise (Trisokkas Reference Trisokkas2009: 156). Therefore, to eschew this anomaly, the highest universal is needed to stop ‘the process of dissolution’ so that ‘all universals are shown to dissolve into a certain higher universal’ (Trisokkas Reference Trisokkas2009: 157) and eventually into the highest universal itself.

II

Both Schick-Iber and Trisokkas agree that the subject matter of the double shine is the compatibility between the universal's self-reference and its determinacy. They disagree on the issues of determinacy, the defect of the outward shine, the relation between the outward and the inward shine, and the highest universal.

Regarding the issue of determinacy, although both sides agree that determinacy implies some relation to the other, it seems that the ‘other’ they understand is different. In Schick's earlier position and for Iber, the ‘other’ refers to two types of thing. One is the determination that is different from the universal; the second is the external perspective from which one compares the universal with other determinations. In contrast, Trisokkas understands ‘the other’ simply as ‘other universals’. Schick has recently changed the reference of the ‘other’ to ‘the particular’ as the exclusive counterpart of the universal. However, ‘the particular’ is still different from Trisokkas's ‘other’ as ‘other universals’. Not only is the conceptual content of the particular qualitatively different from that of the universal, but its number is also different. The definite article ‘the’ expresses its singularity, which is different from the plurality of universals favoured by Trisokkas.

Concerning the defect of the outward shine, Trisokkas indicates that it consists of the indeterminacy of the higher universal. While the self-identity of the universal is secured by the dissolution of a multiplicity of species universals into a higher universal, its determinacy is dissolved simultaneously. This is because Trisokkas thinks that determinacy requires the negative relation of multiple universals. By dissolving these universals as relata of that negative relation, the determinacy of the universal is also dissolved. Without relata that are necessary for the negative relation, determinacy cannot be established. Developing multiple universals again induces the positing of a new higher universal to reduce the otherness they cause and thus postpones the emergence of the indeterminacy of the higher universal instead of permanently resolving it.

In contrast, the defect of the outward shine is diagnosed by Schick and Iber as the fact that it induces the irreducible otherness of the universal, which endangers the universal's self-reference. The universal's determinacy under the outward shine depends on the otherness (different items or external perspective) rather than the universal itself. By changing the cause of the determinacy from the external perspective to the universal's self-relativizing nature, Schick's recent exegesis modally strengthens the defect of the outward shine. The determinacy's incompatibility with the universal's self-reference now lies in the essence of determinacy under the mode of the outward shine. Otherness does not come from the outside but rather from the universal itself. It is self-otherness.

This difference in the outward shine's defect also affects the authors’ disagreement about the relation between the outward and the inward shine. For Trisokkas, the inward shine is ‘complementary’ (2009: 154, my emphasis) to the outward shine because the determinacy is not to blame for the defect of the outward shine; the universal must be determinate in any case. Rather, it is the overreaction of the outward shine model to maintain the universal's self-identity by removing any negative relation (constitutive of determinacy) of the higher universal to its lower universals that causes the higher universal's indeterminacy and thus overcompensates. The task of the inward shine is thus to counterbalance that overreaction of the universal's self-identity by additionally requiring that the dissolution of the determinacy is also the ‘manifestation of the character of the genus into (or through) its own determinacy’ (Trisokkas Reference Trisokkas2009: 153).

Conversely, Schick and Iber think that the outward shine must be reformed by the inward shine because the determinacy under the outward shine (dependence on the other through abstraction) cannot reconcile its contradiction with the universal's self-reference via some complement. It can be complemented only if it can possibly accommodate the universal's self-reference. However, for Schick and Iber, the universal acquired in the outward shine is always determined by the relation to the other, which is contradictory to its self-reference. This becomes clearer when Schick, in her recent interpretation, holds that the self-relativizing nature of the universal under the outward shine makes ‘every universal just a relative universal—even a higher universal relative to a determinate one’ and ‘provides no room for a second species of the universal’ (Schick Reference Schick, Quante and Mooren2018: 475f). Such a reconciliation would require transforming the determinacy from the relation to the other to the ‘self-determination’ under the inward shine.

Finally, there is the issue of the highest universality. Both Schick and Iber think that the highest universal as the result of the utmost abstraction is also the most indeterminate. In virtue of the relative nature of the universal under the outward shine, Schick, in her updated exegesis, denies the existence of the highest universal. In contrast, Trisokkas believes that the positing of the highest universal is necessary to avoid the anomaly of a plurality of universals ‘totally unconnected with each other and still totally determined’ in terms of their own species-universals.

Trisokkas notices this divergence and calls Schick's and Iber's position ‘the Schick-Iber argument’. He summarizes the argument as the following two objections to the positing of the highest universal: 1) dissolving the particular universals into the highest universal results in their ‘irresolvable distinction’, and 2) this distinction results in ‘the absolute indeterminacy of the highest universal’. It thus follows from Schick-Iber's conclusion that, in contrast to Trisokkas, the manifestation of a genus character that has ‘its whole being in the manifoldness and differentiation of particular universals’ is adequate for explicating ‘the determinate and self-identical universal’ (Trisokkas Reference Trisokkas2009: 158). The highest universal is not needed.

In defence, Trisokkas argues against 1) by stating that it is precisely the inward shine's function that ‘a particular universal shows itself to be the expression of the character of its own genus; it is this expression that constitutes the highest universal’. Therefore, the particular universal and the highest universal ‘simply converge’ (Trisokkas Reference Trisokkas2009: 158f), their distinction is resolved. Against 2), he argues that the two distinct premises of Schick and Iber from which they infer the absolute indeterminacy of the highest universal are false. The first premise considers the process of dissolution to be ‘a process of abstraction’, but the inward shine shows that dissolution is also the manifestation of the genus character. The second premise assumes that if the genus character is to be identified with the highest universal and the latter causally generates ‘the whole of determinacy’, then ‘it must in itself be “the totally empty substrate”’. However, since the dissolution of the particular universals is also the manifestation of the genus character, the highest universal does not have ‘an independent existence’, and causality does not apply to the relation between the highest universal and the particular universals (Trisokkas Reference Trisokkas2009: 159).

In directing readers to this discussion about the double shine in her recent interpretation, Schick responds to Trisokkas’ criticism by indicating that Hegel, in the paragraph following his introduction of the double shine (compare SL: 533/12: 36, the first two sentences of the second paragraph), denies that the self-relativizing nature (or the determinacy) of the universal can be overcome in ‘a universal of the highest degree of abstraction’ (Schick Reference Schick, Quante and Mooren2018: 476 fn. 32). Instead, it can only be reconciled with its self-reference in concrete individuals. Schick seems not to be convinced by Trisokkas’ justification of the highest universal's concreteness in its manifestation as the genus character.

III

I will now attempt to advance the existing discussion by commenting on the two conflicting positions I have described. It is uncontroversial that the compatibility between the universal's self-reference and determinacy is the subject matter of the double shine.Footnote ³ For this reason, I skip to the divergences between the aforementioned positions.

First and foremost is the issue of determinacy in terms of the relation to the other. It is not clear what Schick and Iber believe when they talk about ‘the relation to the other’, ‘the particular perspective’ and the ‘comparison with the third’. I assume that they mean our ordinary, empirical cognition, since Iber uses the word ‘ordinarily’ to describe determinacy under the outward shine (2002: 192).Footnote ⁴ For instance, one might recognize the saltiness of seawater by comparing it with tasteless freshwater in terms of gustation (a certain perspective of comparison). In this case, the other is a type of exclusive or incompatible difference, to use Brandom's term (compare Brandom Reference Brandom2019: 138).

However, the exclusive difference can only explain the spatial metaphor ‘outward’ as a being-logical negation between two items alongside each other and not the essence-logical negation, i.e., the shine. The ‘shine is the negative which has a being, but in another, in its negation; it is a non-self-subsisting-being which is sublated within and null’ (SL: 344/11: 248). In the shine, there is only one item; what seems to be is the shadow or reflection of its exclusive counterpart, that is, the essence. The shine exists by self-exclusion. The outward shine as a shine is an essence-logical negation, that is, a self-exclusion. It follows that the double shine as a concept-logical negation is a double self-exclusion, since it contains not only the outward shine but also its reverse movement, the inward shine. While the shine negates itself and indicates the being of its essence, the essence in turn negates itself and thereby reflects its shine. Because the self-exclusion of the shine in the double self-exclusion returns to itself, the double self-exclusion can be termed circular self-exclusion.

Consequently, the term ‘the other’ is inappropriate for the outward shine as an essence-logical negation, let alone the double shine as the concept-logical negation, because the outward shine is a self-exclusion (or self-otherness) rather than a mutual exclusion. Neglecting this, it is difficult to distinguish between being-logical (mutual exclusion), essence-logical (self-exclusion) and concept-logical (circular self-exclusion) forms of negation.

Although Trisokkas plausibly insists that the relation to the other can only be conducted through the universal alone, he understands ‘the other’ as merely a numerical difference. He stipulates the universal's relation to the other as ‘the negative relations a certain universal develops with other universals’, i.e., a ‘multiplicity’ of negatively related universals. If they are all universals, then they can only negate or differ from one another via their numbers, such as the first, the second, the third universal and so on. However, the numerical difference belongs to the logic of being rather than to the logic of concept. It reduces the concept-logical negation or the circular self-exclusion to a numerical indifference. Hegel indicates this in his remark on the logic of quantity:

Surely, the numerical feature can reappear in the logic of concept. In a remark to the chapter on the concept, Hegel says that ‘universality, particularity and singularity’ are ‘three determinate concepts, that is, if one wants to count them’. However, after this, he reminds readers of the aforementioned inappropriateness of the numerical form for the concept:

The relation among the three conceptual moments is far from indifferent. As the term ‘double shine’ implies, they are interlocked by circular self-exclusion. Ignoring this, the logical progress in the logic of concept would fall back into the logic of being.

In contrast, Schick's new exegesis explicitly specifies ‘the other’ as a self-exclusion in terms of essence-logical relation: ‘the universal's own concept involves its relation to its counterpart, the particular’. This seems plausible. In addition to its correspondence with the essence-logical implication of the shine, the involvement of the particular in the universal's own concept conforms to Hegel's remark that ‘the universal has determinateness in it above all as particularity’ (SL: 532/12: 35). That is, the particular is not placed alongside the universal as its exclusive counterpart but rather is a result of the universal's self-exclusion.

Schick does not clearly explain the process of self-exclusion. I propose that the universal directly bears the determination of being the universal, which excludes the determination of being the particular. However, by being determined, the universal is itself ‘a particular’ (SL: 532/12: 35). Therefore, the universal contradicts its own universality. This contradiction compels the universality (as the shine) to be excluded from that particular (as the essence or the exclusive counterpart of the universal). This way of the universal becoming the particular is its self-exclusion or self-division. As a result, opposed to the particular, we have a universal that is excluded from that particular as the universal, which will accord with its universality.

However, self-exclusion does not terminate; rather, it is repeatable when we reflect on the concept of ‘the universal itself’ opposed to the particular. Is it not determinate and hence a particular too simply by being the universal itself? Thus, so long as it is determinate, it again contradicts its own universality. A new concept, namely, ‘the universal itself itself’, is to be excluded from that particular concept of ‘the universal itself’. As such, the requirement of a truly universal itself seems to be impossible.

IV

Whether the defect of the outward shine lies in the indeterminacy of the higher universal or the irreducible otherness, rendering the self-reference of the universal impossible centres on our understanding of the higher universal and its relation to lower universals. Trisokkas believes that the self-identity of the universal can be established by dissolving the multiplicity of the universals into a higher universal. However, if this dissolution is to be understood radically as removing any negative relation between the higher universal and dissolved lower universals, then the higher universal is left with indeterminacy. Trying to determine the higher universal by redeveloping its negation with a multiplicity of universals returns us to the beginning.

It is not clear what kind of metaphor concerning negation dissolution conveys. One possibility is the abstraction that posits the universal itself as the property shared by those negatively related lower universals, similar to how all red things agree with their shared property of redness, be it in the sense of set-theoretic nominalism or metaphysical realism. However, abstraction is also a negation, which satisfies Trisokkas’ definition of determinacy (‘a structure expressive of negativity’ (2009: 150)). However, if abstraction determines the higher universal, then this contradicts Trisokkas’ view that dissolution leaves the higher universal with indeterminacy.

Another possibility is the elimination of all of the lower universals. The latter alternative seems more consistent with Trisokkas’ suggestion that dissolution would remove any negative relation between them. The relation appears to no longer exist when one of the related items is eliminated. However, there seems to be no need for the related items to continue to exist to have that relation. For example, regarding causality, birds can cause the electricity supply to short-circuit. However, the birds do not cease to be the cause of such short-circuit when they leave. In any case, dissolution as a negation does not remove any negative relation between the lower universals and the higher universal and thus determines the latter anyway.

Moreover, if this approach is correct, then the self-identity of the higher universal presumed to be established via that dissolution is untenable. The dissolved multiplicity of lower universals as the related item of the negation (dissolution) precisely constitutes the other of the higher universal. In other words, the emergence of the higher universal via the dissolution of lower universals demonstrates its dependence on the other (those lower universals) characteristic of the outward shine. The self-identity of the higher universal is also contaminated by the relation to the other. The otherness proves to be inextricable by simple negation.

I believe this inextricability of the relation to the other is also the reason why Schick and Iber think that the outward shine must be reformed rather than complemented by the inward shine. Trisokkas's idea of a complement assumes that the relation to the other (negative relation among multiple universals) is necessary for the universal to be determinate. However, he also thinks that this determinacy must be dissolved to maintain the self-reference of the universal posited now as the higher universal. Therefore, for him, the desideratum to obtain the unity of self-reference and determinacy is to relate the determinacy to that higher universal to re-establish the dissolved determinacy. The inward shine provides this desideratum as a manifestation of the genus character. However, as argued, dissolution as a negation also constitutes determinacy. As such, it breaks the self-reference of the higher universal. It cannot be removed. If the higher universal is determined by dissolving those universals, the desideratum that helps it to acquire determinacy seems to be superfluous. For the sake of the universal's self-reference, the determinacy of the higher universal must be reformed to the ‘self-determination’ or ‘genus-character’ under the inward shine.

Interestingly, despite their divergence regarding the defect of the outward shine, both Schick-Iber and Trisokkas understand the inward shine as a type of manifestation of the genus character. However, they do not specify this understanding. For instance, Trisokkas claims only that the manifestation and dissolution are ‘one and the same process’ (2009: 154). However, since the manifestation means to relate the lower universals to the genus character or the higher universal, and the dissolution means to remove any negative relation constitutive of determinacy between them, it seems to be contradictory that both removal and manifestation can exist at the same time. In any case, I do not know what that genus character exactly is or how it differs from the higher universal under the outward shine. What does that manifestation mean? Is it similar to the instantiation relation between a genus and its species, as it is the case that both Persian cats and bobcats instantiate the biological-genus cat? However, if this is so, then there seems to be no difference between the inward and outward shines.

Since I do not know the authors’ answers to the above questions, I think the following to be the case regarding the inward shine. As argued above, the self-exclusion of the universal leads to the universal's self-division into the universal itself and the particular. Further reflection on the universal itself repeats this process of self-exclusion and produces more particulars. The true universal itself appears to be unobtainable in this infinite regression. However, from a different perspective, this process of repeatable self-exclusion satisfies the core of the universal, namely, repeatability. The infinite reproduction of the particular (as shine) demonstrates the existence of the universal (as the essence or the exclusive counterpart of the particular):

The infinite reproduction of the particular reveals the nature of the universal not as a determinacy opposed to the particular but rather as a process that shows itself in virtue of its repeatable self-exclusion and reproduction of its opposite concept. As such, the particular in turn negates itself and returns to the universal. This returning from the particular to the universal or the inward shine, as explained in section IV, is the second self-exclusion and thus completes the circular self-exclusion that is the paradigmatic form of the concept-logical negation.

One might wonder if the repeatable self-exclusion here is also a numerical indifference and hence a being-logical rather than a concept-logical negation. However, as previously argued, the concept-logical negation does not necessarily exclude the numerical feature in general. Recall Hegel's reminder that the conceptual moments total three if one wants to count them. Therefore, if the repeatability is a numerical relation, it does not necessarily mean that it is absent from the domain of concept-logical negation. Moreover, the criterion that decides whether the repeatable self-exclusion is a being-logical or concept-logical negation lies in its form of negation, not whether any numerical feature can be found in it. It is the self-exclusion—in contrast to Trisokkas's numerical indifference—of the universal and the self-exclusion of the particular that cause them to be a circular self-exclusion which is characteristic of the concept-logical negation, not the numerical feature of their repeatability. This numerical feature is only a by-product or epiphenomenon of that circular self-exclusion.

V

Trisokkas's main reason to object to the Schick-Iber argument against the highest universal in terms of abstraction is his identifying the dissolution of multiple lower universals with the manifestation of the genus character or the highest universal. Since dissolution is also a manifestation, there is no irresolvable distinction between lower universals and the highest universal (i.e., the highest universal is not indeterminate because the manifestation relates it to that determinacy).

However, Trisokkas seems to present a strawman argument. In addition to the question of whether his term ‘dissolution’ means the same as Schick and Iber's use of the term ‘abstraction’, Schick and Iber do not identify the abstraction with the manifestation of the genus character. Although they confusedly assign the abstraction to the inward shine (or in the outward shine, if we follow Shick's recent exegesis),Footnote ⁵ it differs from the manifestation of the genus character. When abstraction is identified with or ‘ben[t] back’ (SL: 533/12: 36) to the manifestation of the genus-character, it is no longer abstract because it becomes a process of concretization. However, one can adhere to the abstraction and refuse to convert the abstraction into the speculative concreteness advocated by Hegel. Identifying the abstraction with the manifestation is not as unproblematic as Trisokkas believes. One can conceive the highest universal as being distinct from its lower instances as a Platonic form pure and perfect to the extent that none of its examples can compare with it.

Conversely, if the identification of the dissolution with the manifestation resolves the distinction between the highest universal and the lower universals, then the superlative degree of the highest universal would be resolved as well. In this case, calling it the genus character or the highest universal appears to be merely a matter of rhetoric. Surely Hegel speaks of ‘the truly absolute concept’ or ‘the idea of infinite spirit’ (SL: 533/12: 36), but I see no reason why they cannot be compatible with the description of the universal as the genus-character. In contrast, in addition to Hegel's identification of the true universal with the ‘concretes’ (SL: 533/12: 36) referred to by Schick in her recent interpretation, Hegel denies the highest universal in the section where he discusses the singular:

Hegel explicitly describes abstraction as the false way since the reference of the pronoun ‘Its’ is the abstraction.Footnote ⁶ The higher and the highest universal clearly result from the abstraction. Therefore, they are also part of the false way.Footnote ⁷ In my view, Hegel thinks that higher universals and the highest universal would be absent from the universal's process of determination if this process is properly understood.

The anomaly (many determinately higher universals unconnected to each other) that Trisokkas adduces to support the necessity of the highest universal seems inconsistent with Hegel's description of the universal's self-division (self-exclusion) and of the universal as the totality of its opposed and subordinated concepts (the universal itself and the particular):

Hegel does not talk of multiple universals as totalities that stand indifferent to one another but rather of the universal that diversifies into two opposed concepts. It is difficult to imagine how that anomaly could occur. If we grant the multiple universals, as Trisokkas believes to be required by the universal's determinacy, the universals remain negatively related to one another rather than unconnected.

In summary, the purpose of this paper has been to comment on and improve the existing discussion about Hegel's metaphor of the double shine in his logical theory of the concept. To accomplish that purpose, I have first outlined the positions of relevant discussants and then revealed their differences. Next, I have commented on these differences and offered improvements by explicating the details that are either unclear or implicit in the previous discussion.

By appreciating the essence-logical background of the shine, I have proposed to understand both the outward and inward shine as a self-exclusion. While the outward shine involves the universal's self-exclusion of the particular, the inward shine involves the particular's self-exclusion of the universal. Specifically, by being the universal, the universal's determinacy makes it its own exclusive counterpart, i.e., the particular. By excluding the particular from itself, it divides into the two opposed, subordinated concepts, namely, the universal itself and the particular. This is the self-exclusion of the universal (i.e., the outward shine). Self-exclusion repeats on the universal itself and thus reproduces more particulars. Conversely, from a different perspective, the repeatability and reproduction of the particulars demonstrate the existence of the universal, which is not a determinacy that is opposed to the particular but rather a process that is revealed through the particular. This is the self-exclusion of the particular (i.e., the inward shine). The outward and the inward shine combined as the double shine constitute the circular self-exclusion as the form of the concept-logical negation.Footnote ⁸