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ABSTRACT
Hegel’s Doctrine of the Concept advances a theory of conceptual determinacy. As I will demonstrate, Hegel’s theory of conceptual determinacy leads him to endorse self-predication and existential implication as features endemic to conceptual content. I first demonstrate some features of this logic, and some of its entailments. Following the reconstruction of Hegel’s logic of self-predication, I apply this logic to illuminate Hegel’s critique of formal logic. Finally, the self-predicative feature of Hegel’s logics offers a measure by which to determine the potential and the limitations of any formal account of Hegel’s logic.
Notes
1 Hegel Citation2015, 529–549/12.32–12.52.
2 Also see Hegel Citation2015, 516/12.19, where the formal is defined as that which abstracts from content. Although a formal concept ‘abstracts from content’, for Hegel this does not necessarily entail that the abstraction is performed by an external agency, such as a mind.
3 See Hegel’s Introduction to SL, Hegel Citation2015, 24–25/21.28–21.30, in which he characterizes the formality of logic as operating under the assumption of a separation of form and content. Concerning formal logic, Hegel writes: ‘Whenever logic is taken as the science of thinking in general, it is thereby understood that this “thinking” constitutes the mere form of a cognition; that logic abstracts from all content […].’
4 Hegel Citation2015, 538.
5 Hegel Citation2015, 528/12.31.
6 Although formality appears to be inherently relative, we will significantly qualify this claim in due course when we consider Hegel’s position on the abstract universal and the category of quantity.
7 Hegel Citation2015, 24/21.29. Here Hegel points out that no absolute separation of form and content is possible: ‘since thinking and the rule of thinking are supposed to be its subject matter, in these logic already has a content specifically its own; […]’ Here Hegel clearly implies that while it is impossible for a concept to be completely formal, it is possible for concepts to be formal in some respect. Otherwise, Hegel could not in principle distinguish the standard formal logic of his day from his own dialectical logic.
8 Hegel Citation2015, 530–534/12.33–12.37. For an alternative perspective on the relation of the concept to the universal, see Trisokkas Citation2009.
9 Hegel notes that the concept is the ground of all finite determinations. Hegel writes that ‘the concept is a synthesis a priori’ and ‘contains determinateness and differentiation within itself’. Because it has content, it is not completely formal. Moreover, ‘the concept is the ground and the source of all finite determinateness and manifoldness’ which must include not only its own determinateness, but also all formal determinations, since formal determinations presuppose a difference between form and content and are thereby finite. Hegel Citation2015, 520/12.23.
10 Hegel has many ways of expressing the logical structure constitutive of self-reference. In the Encyclopedia Logic Hegel employs various terms such as ‘having turned back into itself’ (Züruckgekehrtsein in sich selbst), Hegel Citation1975, 121, paragraph 83, ‘withdrawing inwards’ (Insichgehen), ‘sinking deeper into itself’ (ein Vertiefen desselben in sich selbst), ibid, paragraph 84, ‘return into themselves’, ‘back turning into themselves’, or ‘return-into-self’ (ihrer Rückkehr in sich), ibid, paragraph 162, 225. Also see Hegel Citation1969, 274. In the concept of the Rückkehre, we find the German correlate of the Greek ‘back-turning’ or palintropos.
11 According to Hegel, ‘Being itself and the special sub-categories of it which follow, as well as those of logic in general, may be looked upon as definitions of the Absolute.’ Hegel Citation1975, paragraph 85.
12 Hegel is unequivocal that the reality is ‘derived’ from the concept itself: He writes: ‘the derivation of the real from the concept, if “derivation” is what we want to call it, consists at first essentially in this, that the concept in its formal abstraction reveals itself to be incomplete and through a dialectic immanently grounded in it passes over into reality’. Hegel Citation2015, 522/12.25. The existentially implicative aspect of the concept is further described by Hegel as a kind of ontological argument: ‘The concept of God realizes itself most fully as this universal that determines and particularizes itself – it is this activity of dividing, of particularizing and determining itself, or positing a finitude, negating this – its own finitude and being identical with itself through its negation of this finitude. This is the concept as such, the concept of God.’ Hegel Citation1984, 324.
13 See Hegel Citation2015, 535/GL 12.38, in which universality itself is a particular instance of universality.
14 Hegel Citation2015, 534–546/12.37–12.49.
15 Hegel Citation2015, 546–549/12.49–12.52.
16 See Hegel Citation2015, 529/12.32.
17 ‘On the contrary, every determination, anything concrete, every concept, is essentially a unity of distinguished and distinguishable elements which, by virtue of the determinate, essential difference, pass over into elements which are contradictory.’ Hegel Citation2015, 384/11.289.
18 One can find many senses of contradiction in Hegel’s Science of Logic. Although contradiction is more conventionally understood as a relationship between two propositions, the contradiction here is constituted by a relation of the concept with itself, i.e., the concept as universal and the concept as particular. Hence, the contradiction is more precisely the self-contradiction of the concept. Indeed, when Hegel first introduces the concept of contradiction in the Science of Logic, he describes it as ‘something self-contradictory’. See Hegel, Citation2015, 378. Although this contradiction is not yet articulated as a contradiction between two propositions or judgments, it certainly can be reformulated as such, e.g. ‘the concept is universal’ and ‘the concept is not universal’. Bordignon traces other senses of contradiction in Hegel’s text, such as the contradiction as an error of the understanding, as well as a metaphorical sense of contradiction. The contradiction elucidated here is neither merely an error, for Hegel affirms the concept to be both universal and particular, nor is it merely metaphorical. For more on the various senses of contradiction, See Bordignon Citation2013, 165.
19 Since dialetheism is the position that some contradictions are true, and Hegel holds that there are some true contradictions, I hold that Hegel is a dialetheist. For a discussion of the neologism, ‘dialetheism’, see Priest Citation1998, 416. Priest has defended the position by appealing to paradoxes of self-reference, such as the liar paradox See Priest Citation1979, Citation1985–Citation1986. Although Hegel’s dialetheism is grounded in a form of non-formal logic, and is thereby quite different from the form of dialetheism developed in conjunction with Priest’s paraconsistent logic, like Priest, the truth of contradiction in Hegel is also motivated by a form of self-referential predication. For more recent work on the dialetheic interpretation of Hegel’s approach to self-referential paradoxes, such as the liar paradox (d’Augustini and Ficara Citation2022).
20 Halfwassen Citation2016, 82. Although some commentators (such as Bordingnon) are hesitant to describe Hegel’s philosophy as dialetheist (due to a number of dissimilarities with Priest’s philosophy), many scholars in the English speaking world have recently advanced the thesis that Hegel affirms the truth of contradiction (Bordignon Citation2013, McGowan Citation2019, Ficara Citation2021, Moss Citation2020).
21 See Hegel Citation2015, 520/12.23.
22 Hegel Citation1991, 20.
23 See Robert Stern Citation2009, 111. Stern cites this passage from Hegel in Berichten seiner Zeitgenossen, ed. Guenter Nicolin, paragraph 383, 254–255.
24 Hegel Citation1975, 52.
25 Hegel writes that the concept alone is responsible for the correspondence of the concept with reality: ‘Now it must certainly be conceded that the concept is as such not yet complete, that it must rather be raised to the idea which alone is the unity of the concept and reality; and this is a result which will have to emerge in what follows from the nature of the concept alone.’ Hegel Citation2015, 518/12.21.
26 Hegel Citation2015, 101/21.117.
27 F(f) and C(c) both express the singularity of each concept. While the formula ‘Px’ expresses that some particular, x, instantiates a universal, P, C(c) expresses that the particular instantiating the predicate is the predicate itself, such that Px & x=P. Although each member of c is self-particularizing (including f and c), because each member is an instance of c, no member of c can be completely autonomous.
28 On the one hand, c specifies the feature that every concept must possess in order to belong to the domain of concepts. F is a concept, and because all concepts instantiate c, f instantiates c, such that C(f). On the other hand, every concept is a concept, but it is equally true that every concept is finite. Because c is a unique concept, and every concept is finite, c is finite. Thus, we must admit that c too falls within the domain of finitude, such that F(c). As a result, it is both true that C(f) and F(c). C is the universal that f instantiates, and f is the universal that c instantiates. Because each also the instance of the other, f is a particular in the domain of concepts, and c a particular in the domain of finitude.
29 For the full transition from finitude to infinity, see Hegel Citation2015, 108–109/21.124–125.
30 Parsons Citation2017.
31 For Aristotle’s discussion of the principles of the square from which the relations are deduced, see Aristotle Citation1975, 6–7.
32 Although one can infer that ‘not every S is P’ from ‘No S is P’, for Aristotle the O form is not existentially implicative. If one assumes that it is false that ‘some unicorns are blue’ (for there are no unicorns) then it would be true that E, namely ‘no unicorn is blue’. If E is true, then A is false, and O, ‘some unicorns are not blue’ would be true. Since there are no unicorns, it seems that O should be false. However, In Aristotle, the O form states that ‘not every S is P’ not ‘some S is not P’. Because there are no unicorns, it is trivially true that not every one of them is blue. The proposition ‘not every unicorn is blue’ does not commit Aristotle to the existence of blue unicorns. This argument follows the defence of Aristotle’s reasoning (Parsons Citation2017).
33 Aristotle’s logic of existential implication corresponds to his metaphysics, in which the Form of the thing, (articulated as a universal), is an activity that works upon material in order to generate composites (articulated as a particular) of Form and material.
34 Parsons Citation2017.
35 For further discussion of Hegel’s critique of the traditional relation between contradiction and contrariety, see Pluder Citation2022, 136. Pluder notes that for Hegel contrariety is not independent of the contradictory relation.
36 See Hegel Citation2015, 545–546.
37 See Pluder Citation2022, 137: ‘While in Hegel’s logic a single proposition has the power to overcome its isolated fixation and reveal its true nature as part of a wider context, diagrams and traditional logic do not provoke such a development.’ Pluder’s argument closely follows the argument in Hegel Citation2015, 544–545.
38 For a concise discussion of the difference between Hegel and Aristotle’s theory of categories, see Halper Citation1993. While Hegel’s categories are self-referential, Aristotle’s are not. For Aristotle, Thinghood itself is not a thing.
39 Parsons Citation2017.
40 In the Science of Logic, Hegel argues that empirical predicates such as ‘one hundred dollars’ fail to exhibit the self-referential structure. Hegel writes: ‘This so called concept of a hundred dollars is however a false concept; […] a hundred dollars is nothing self-referring’ (Hegel Citation2015, 64–65/ 21.75–21.76). From the fact that I can think the predicate ‘one-hundred dollars’, it does not follow that I have one-hundred dollars. The predicate ‘money’ is not itself money, and thereby fails to be existentially implicative. Empirical predicates generally lack the character of self-referential predication and existential implication. Finally, unlike the concept of the concept, such predicates do not apply to every concept. Consider other examples: The predicate ‘water’ is not an instance of water. Likewise, the sword cuts, but the predicate ‘sword’ is not itself a sword. Fire burns, but the predicate ‘fire’ does not burn anything – it is not itself an instance of fire. However, because empirical concepts are common terms, they are universals, and insofar as each is distinct from the others, each is a particular universal. Because they are both universal and particular, they are also singular, for singularity is the unity of both universality and particularity. Because such empirical concepts are universal, particular, and singular, yet fail to exhibit the features of the concept, Hegel will describe empirical concepts as ‘self-external’. Regarding such empirical predicates, Hegel writes that they ‘are the sides of its free self-externality […]’ (Hegel Citation2015, 282–283). Although Hegel will also use this expression for non-empirical concepts such as quantity, empirical predicates are distinguished from concepts such as quantity by failing to have an absolute extension, and as such they are defined by their own particular mode of self-externality. For more on the problem and character of empirical predicates in Hegel’s system, see Moss Citation2020, 445–481.
41 In the course of the Science of Logic Hegel considers three kinds of formal concepts: the abstraction, the class, and the genus. Each of these kinds of universals are formal to the extent that they do not differentiate the particulars that fall under them. In the sections on judgment and syllogism Hegel will make a place for each of these kinds of formality in the Doctrine. (i) A genus is a universal containing different species within itself, for example ‘quantity’ contains ‘discrete’ quantities and ‘continuous’ quantities. The ‘differentia’ differentiates these species from one another. The genus and the differentia together define the species. Genera, insofar as they contain species, have an internal relation to other universals and do not exhibit a merely external relation to other universals. Although the genus immediately contains its own differentiations, within itself, and is constituted by the totality of its species, the genus itself does not provide an account of the process by which the genus is differentiated, since the genus is only the common form of all of it species. Instead, a prior difference must be imported in order to differentiate the contents. Hence, the principle of differentiation is still missing from the genus. (ii) For Hegel the class also exhibits this formal structure. The class consists of a collection of individuals. Each particular is one member of the class, and taken all together, the class is an aggregate of individuals. As an aggregate, the universal is not distinct from the totality of the particulars, as the abstract universal is, for it is neither itself a separate member of the class, nor is it distinct from the aggregate itself. The universal simply is the totality of the particulars. Since the class only specifies that each is a member of the class, it does not specify that in virtue of which each member is different from the others. Hence, like the genus, the class does not provide any means of differentiating the particulars within itself.
42 Hegel writes: ‘Abstraction, which is the soul of singularity and so the self-reference of the negative, is, as we have seen, nothing external to the universal and the particular but is immanent in them, and these are concreted through it, they become a content, a singular’ (Hegel Citation2015, 548/12.51).
43 Hegel will speak of determinations of the understanding as the ‘unconceptualized concept’. See Hegel Citation2015, 537.
44 Hegel Citation2015, 537/12.40.
45 Even the abstract universal is universal, particular, and singular. Each abstract universal has a common content that is instantiated in each instance. It is a particular abstract universal, such that it is distinct from others. Finally, it is the unity of the universal and particular: it is a particular universal. However, the abstract universal fails to be self-particularizing, and for this reason it is the concept insofar as it is not fully commensurate with the concept or ‘outside itself’. Entäußerung (self-externality) is another term Hegel invokes to conceive of such an inverted relation.
46 One can quantify over an object without attending to what kind of thing it is. Indeed, this is one reason Hegel conceives of quantity as a quality that is ‘indifferent’ to qualitative determinations. Quantity is an ‘indifferent determinateness’ (Hegel Citation2015, 152/21.173–74).
47 As I have already indicated, I do not mean to imply that quantity is the only form of Entäußerung. The Science of Logic contains many forms of Entäußerung in addition to quantity, such as the concept of the abstract universal and mechanism, among others.
48 For a complete reconstruction of the Doctrine of the Concept and its relation to Hegel’s metaphysics, see Moss Citation2020.
49 See Bordignon Citation2012, 235. Bordignon shows the intimate link between the concept of self-reference and negativity in Hegel’s theory of determinacy and determinate negation. Also see Koch Citation2002 for a further discussion of the relation between self-reference and negation.
50 ‘Self-negation’ and ‘outside itself’ or ‘self-external’ are all self-predicative. Accordingly, the transition out of the formal dimension of particularity can be equally demonstrated with these terms.
51 For the full transition from particularity to singularity, see Hegel Citation2015, 540/12.43.
52 Hegel Citation2015, 383.
53 See Ficara Citation2021, 8.
54 Hegel Citation2015, 737/12.238.