Hegel's science of logic in an analytic mode

• Author: Clark Butler
• Position: Professor of Philosophy, Purdue University, Indiana University-Purdue University Fort Wayne
• Pages: 173-187

Page 173

The concept of the subject, of what Hegel calls absolute negativity, already appears early in the logic of being.¹ Absolute negativity, negation of the negation, occurs throughout the logic as identity in difference understood as self-identification under different descriptions. First, the subject refers to itself merely under an incomplete description. Second, it refers to something other than itself under a second description which is logically required by the first. (For example, the description of being in general requires some determinate description of being in particular.) But this second description is dialectically excluded by the assumption that the first description is complete. Third, the subject negates its negation of the other. It discovers itself in the other, under the other description, and thus comes to refer to itself less incompletely. This is Hegel in the analytic mode.

The very concept of analytic Hegelianism may suggest that we have deformed Hegel. Perhaps it would be more honest to call my proposal something else. My reply is that I am maintaining the essential content of Hegelianism even while developing the form further. This content, the content of systematically dialectical speculative philosophy, lies in two essential theses. The first is the thesis of the whole speculative tradition up to and including Schelling: in and through human knowledge of the absolute, the absolute knows itself.² The second thesis is specifi-Page 174cally Hegelian: the absolute comes to know itself concretely by a deductively necessary dialectical thought process realized both in the history of philosophy and in world history.³

My ultimate project is to restate Hegel's dialectical logic in quantification logic. The technical aspects of it will not be my focus here.⁴ In this paper, I apply linguistic ascent by translating the central Hegelian concept of identity in difference into the Fregean language of identity under different descriptions.⁵ More particularly, I use Keith Donnel-lan's concept of successful reference under a false description (i.e., the non-attributive use of definite descriptions) to interpret identification of the absolute under descriptions that dialectically prove false. By "attributive," Donnellan means the following: all definite descriptions are referential. Some such descriptions are true. The speaker frequently attributes the description to the referent, as we might attribute to Queen Elizabeth being head of the Anglican Church. Other descriptions used in reference are non-attributive or false, as the speaker may have no intention of attributing those descriptions to the referent. For example, Spinoza makes attributive as well as referential use of the term "substance," insofar as Spinoza thought the absolute was substance. But Hegel makes purely referential use of the term "substance." For Hegel, to be the absolute is not to be merely substance.

In undertaking the proposed translation, I put philological, exeget-ical explication of Hegel's texts to the side. I myself practice such explication, but I do not think that it does enough to clarify Hegel for us today. In translating Hegel's 1831 lectures on the science of logic, I use the phrase "identity in difference," not "identity under different descriptions." But that is a translation of Hegel's words. This paper is a restatement of Hegel's concept by linguistic ascent.

My motive for restating Hegel's science of logic in an analytic mode is in part because many people find Hegel's language obscure,Page 175 while they find the Fregean language clear. Unfortunately, Hegel did not have twentieth century symbolic logic available, so he could not state himself as clearly as we can. As he was a conservative in science, it is reasonable to suppose that Hegel would use contemporary logic if he were alive today.

Do I expect to win more friends for Hegel's science of logic by my procedure? Not necessarily. Modern symbolic logic is a language for doing philosophy, not a philosophy as such. Translation of the Hegelian position into that language is not a justification of it. Many very different philosophies can be translated into symbolic logic. Frege's distinction between sense and reference has been used to make materialism clear. The mind is brain process under a different description. I would not expect that its use in making Hegelian idealism clear would, by itself, resolve disputes between idealists and materialists. At most, we might expect more widespread discussion of the issues.

If symbolic logic were a philosophy, (e.g, the philosophy of logical atomism), I would agree that translating the Hegelian position into analytic philosophy would prove impossible. But the failure of such an attempt would favor Hegel rather than logical atomism. Any logical atomist claim that "This is yellow" states a fully analyzed atomic fact can be refuted-Hegel's early demonstration in the science of logic that positive qualities imply negative qualities contains such a refutation.⁶ But since symbolic logic is only a language for doing philosophy, translation of Hegel's position into doe not necessarily fail.

Symbolic logic itself has evolved and can serve as a vehicle for restating Hegel. As Hegelians, we may adopt Frege's distinction between our rich but sometimes ambiguous ordinary language and the disambig-uated but more mechanical language of quantification logic. That there is a speculative genius to ordinary language,⁷ or that everyone assimilatesPage 176 the truth most deeply in his native tongue,⁸ does not mean that there is nothing for Hegelians to learn from regimentation in quantification logic.

Quine denied that symbolic logic is more successful in getting at the meaning of an ordinary sentence than the ordinary language original. Rather, he held that, when we are pragmatically concerned with simplicity and ontological economy, the logical language sometimes usefully replaces ordinary language. But H.P. Grice, in preserving the meaning of what is said as determined by the sentence's truth conditions,⁹ but not as determined by what the speaker intends by using the sentence, is closer to Hegel. Meaning is not use, as Wittgensteinians have thought, and economical use is not our only concern as some Quinians might suggest. Quantification logic gets at the constant semantics of an ordinary language sentence even when, pragmatically, uses of that sentence vary. Such logic gets at what the sentence says without necessarily capturing what the utterer means or intends in saying it.¹⁰ Ordinary sentences containing the verb aufheben, regardless of varying speaker intentions in uttering them, express conflicting meanings, according to Hegel.¹¹ But if this is so, symbolization by quantification logic would purge ordinary language containing that verb of its rich ambiguity. Senses are now expressed in quantification logic without ambiguity by assigning different terms to different senses. A general Gricean solution to the problem of meaning seems to accommodate, better than Wittgenstein's or Quine's solution, Hegel's respect for the sense and ambiguity of ordinary language while allowing for the possibility of quantification.Page 177

Symbolic logic does not replace ordinary language with its rich speculative spirit. Rather, symbolic logic reduces the speculative content of ordinary language to a kind of child's play, so that we can return to ordinary language with a better conscience-much as a good musician might return to the enjoyment of Paganini's caprices reassured by knowledge of the technique needed to play through them.

Despite what he says of the speculative ambiguity of German, Hegel's own systematic writing can be understood as free of ambiguity. "Being" retains the same sense at the end of the logic as it has at the beginning, where what has being is considered totally indeterminate. New predicates are added, but the sense of the old ones remains. Hegel's logical syntax predates quantification logic, but just as he would likely be a Darwinian were he alive today, he would also likely use quantification logic. An unambiguous use of terms is, of course, necessary if the dialectic is to be, as Hegel claims, deductively necessary.

Like Frege, Hegel would undoubtedly deny that there was only one correct analysis of ordinary statements. "John is Mary's father" can also be analyzed as "Mary is John's daughter," or as "x being the father of y is co-instantiated by the ordered pair John and Mary." None of these analyses gets at the one, and only one, logical structure of the English. Formal logic disambiguates an ordinary English sentence, but if the ordinary language is, as Hegel thinks, richly ambiguous, each disambiguation loses part of the sentence's meaning. Other logical expressions, however, might be added to retrieve this lost meaning.

Understanding a singular sentence does not require having the complete science of the referent, including all its properties. It does not require that we know how it is related to everything in the universe, as Russell thinks Hegelianism demands.¹² For Hegel, knowledge of the absolute begins with abstract predicates like being, determinate being, something, and something else, to the implicit exclusion of all the other predicates that follow. Even a system of prepositional thought (an sich, fur sich, etc.) as complete or concrete as Hegel achieved fails to exhaust, as he admits in his 1829 review of Goschel,¹³ the full nature of the absolute as we are acquainted with it in feeling. The most that can be said is that when negation of the negation is effected a million times, it can be effected a million times plus one, and in this sense it can be reiteratedPage 178 infinitely. To grasp the principle of dialectical cycle is to grasp prolepti-cally the infinite series of cycles necessary to fully describe the absolute.

Michael Dummett's interpretation of Frege's "contextual principle"...