Gorgias, Sextus Empiricus and Intuitionism: Rhetoric and Logic

(First draft)

Maria Cecília de Miranda N. Coelho

(PUCSP-Brazil)

Gorgias’ Treatise On Not-Being or On Nature is summarized by the anonymous author of De Melissus, Xenophanes, Gorgias or MXG, included in the Aristotelian corpus, and also in Sextus Empiricus´ so-called Adversus Mathematicos, the latter being the source most quoted1.

There is one crucial aspect of Sextus´ eleven books I would like to draw your attention to, which, I believe, is not a simple detail of denomination. Five of the books are concerned with the “dogmatic” or “philosophers” and six with the “mathematicians” or “professors”. It is important to point out that the text of Gorgias is presented in the first two books of “Against the Logicians”, which, together with the two books of Against the Physicists, and another one Against the Ethicists, make up the treatise Against the Dogmatics. The other treatise, Adversus Mathematicos, is composed of six books: the Grammarians, Rhetoricians, Geometers, Arithmeticians, Astrologers and Musicians. Usually, the two books of Against the Logicians are named Adversus Mathematicosvii and viii, but this process of naming can sometimes be more distracting than helpful. It is worth remembering that the references to Gorgias (in addition to those which are made in Hipotiposis Pirronians) appear only in the treatise Against the Logicians. Thus there are no references to him in the book Against the Rhetoricians, although this treatise begins by discussing Plato’s Gorgias and making a reference to beauty as one of the instruments of persuasion (and Sextus quotes Helen of Troy). Why, when dealing exhaustively with rhetoric as the art of persuasion, does Sextus not say anything about Gorgias? This fact seems remarkable to me.

Let us pay attention to where and how Sextus talks about Gorgias. Against the Logicians begins with a discussion of the meaning of “philosophy” (I, 2) and deals with the various forms into which this discipline can be divided, assuming that the best classification is that which considers Logic, Physics and Ethics its main branches (I, 16). Later in the text, the existence of a criterion of truth is discussed (I, 27-28) and the meanings of “criterion” (I, 28-37) and “ truth” (I, 38-46), questions which, together with a proof theory, are the objects of Logic. Keeping the problems of Logic in mind, Sextus presents the philosophers who studied them. Xenophanes, Protagoras and Gorgias, in this order, are some of the philosophers presented2

It is interesting to observe that even the scholars who defend the importance of Gorgias as a profound thinker– either for the value of his criticism of ontology, for his contributions to the development of Rhetoric, or for the study of the language as an autonomous subject – when attempting to interpret the concept of truth always arrive (implicitly or not) at one of the two conclusions3:

  1. Truth does exist and is relative (to the individual or group): Dupreel (1948, 68), Adrados (1981,46), Kerferd (1981), Guthrie (1971), Mourelatos (1985)
  2. There is no sense in speaking about truth because everything is true – i.e. truth is an empty term4. Cassin (1980), Bett (1984), Paes (1989).

Let us consider the first conclusion.

The most common way to characterize Gorgias as a relativist is to establish a relationship between him and Protagoras. Probably, one of the stimuli for this type of characterization is a commentary made by Sextus immediately before his presentation of Gorgias’ Treatise. Speaking about Disionidoro and Eutidemo, soon after his discussion about Protagoras, Sextus says: “for they too consider both, the being and the truth as relative things” ( pros ti, A.L., I, 64)5. Even knowing that Sextus claimed that Gorgias denied the existence of a criterion of truth in a different way than that of Protagoras, it seems to me that this process of listing them one after the other leads to a conceptual proximity greater than that which should exist. A curious example of this practice can be found in a paper by J. Mansfeld6. When investigating to what extent the arguments of the Treatise, in both versions, can indeed be attributed to Gorgias, Mansfeld not only suggests that the echo from the doctrine of man-measure can be identified in the third part of the Gorgias’ Treatise, but also that the most interesting aspects of Gorgias’ arguments are what they imply for the discussion of public and private knowledge and their consequences in the question of “consensus”. Neverthless, Mansfeld adds, “it is very safe, however, to assume that he [Gorgias] is hardly original and that his arguments would be much less interesting if more of Protagoras had survived” (p. 258).

I understand that the man-measure thesis7 is neither compatible with the thesis of the Treatise nor with that of the Encomium of Helen. My position is to partially agree with the ideas of Bett, who argues that there is no basis to infer, from both versions of the Treatise, that Gorgias was a relativist8.

Let us consider now the second conclusion: the word truth is an empty term.

Thinking about On Not-Being, but also about other important works of Gorgias and their unity, my first objection to this statement is that we have in the Encomium of Helen and inthe Palamedes Apology the use of the word “truth” (aletheia), and in both texts it does seem to have a meaning. It seems to me that these elements are sufficient to further complicate conclusion 29 .

When interpreting these texts, Kerferd (1981, 79; 81) claims that we should not affirm that Protagoras and Gorgias had the same conception of truth, for the former, by using the concept of ‘deceit’ (apate), necessarily accepted that there exists that “which actually is true”. I think we can accept the idea of truth without having to accept the existence of an objective reality independent of ourselves. How, then, can we find meaning in the word truth?

Let us now return to On Not-Being. My interpretation of this treatise was influenced by a contemporary trend in the philosophy of mathematics initiated by Luitzen Brower at the beginning of 20th century - Intuitionism10. I believe it is important to give an explanation for this approach. What motivated me to attempt to establish this analogy were some similarities between the way the Intuitionists were received by other philosophers of mathematics, and the way Gorgias’ ideas have been received since Plato.11

It seems to me that the intuitionists have challenged non-intuitionist mathematicians 12 (mainly the realists or platonists), insofar as the former have cut off many mathematical achievements by denying the dogmatic aspirations of the latter. In a similar way Gorgias’ ideas concerning the limitation of our possibility of knowledge have produced a great strangeness and troublesomeness for other philosophers, to such an extent that he was (and still is) regarded as a “non-serious” thinker, or euphemistically, as only a rhetorician13.The conceptions of truth for Gorgias and for the intuitionists have a particularly interesting resemblance. Let me present schematically the main characteristics of Intuitionism and, simultaneously, indicate their similitude with some of Gorgias’ ideas14:

  1. The intuitionist conception of mathematics as a socio-biological activity, whose aim is to satisfy a few human necessities, or as a “social enterprise” (Tieszen, 1994, 589, Heyting, 1956, 75), could be analogous to the rhetorical practice of Gorgias. Gorgias believes in the possibility of speech to persuade others is similar to the intuitionists belief that some elementary notions (that of natural numbers, for instance) are familiar to “every thinking creature”.
  2. Intuitionists deny the actual infinite, and as a consequence, they limit the scope of the law of excluded middle15, because for them this platonic conception, “requires us to have an understanding of quantification over infinite domains, but this transcends our capacity to recognize statements which quantify over infinite domains as true” (Tieszen, 584, 590). When Gorgias denies the possibility of teaching virtue (Meno, 71e-72b) or, more generally, discusses the instability of our knowledge (EH, 11) and the inexistence of a criterion of knowledge (Treatise), we have the same sort of doubt about the universal validity of certain principles.
  3. Since a proposition is a hypothesis which can or cannot be proved constructively, “a proof is not an object, but an act” (Martin-Loef, apud Tieszen, 581), it is quite important to consider the performance of the mathematician. In a similar way, gorgianic persuasion is a process in which the truth is constructed and presented by speech (deixas kai epideixas, EH, 3).
  4. Intuitionists believe that they should avoid the illusions of mathematical platonists (Brower, 1912, 81; 1948, 90). Like Gorgias, they believe that “we know far less about objects than we can reason about, on a classical model of reasoning”16

I will try, from now on, to give a plausible argument, which will support my claim that Gorgias was not a relativist, though he was an anti-realist, in a sense that I would like to explain17. The use of terms like anti-realist and realist is recent, but I do not think this use is an anachronism that obscures my argumentation, for it is not less problematic than the use of the term relativism18. Let us now consider one central aspect of the realistic position on truth19 Roughly speaking, for a realist, the truth or falsehood of a proposition depends on whether such a proposition is in agreement or disagreement, respectively, with a reality that exists independently of us. This is valid for mathematical statements, whose truth for a realist mathematician does not depend on whether they were demonstrated or not, for statements about the physical world, whose truth for a scientific realist does not depend on the observation that they could be verifiable and, also, for moral statements, which for a moral realist have their truth or falsehood determined not by subjectiveconsiderations, but by the fact that they do or do not correspond to reality.

In opposition to the realistic conception of truth there are a large number of antirealist doctrines, and relativism is only one of them. I insist that transforming the truth of a sentence into a subjective question is not the only way to deny that this truth is a function of some reality which does exist independently of us. It is possible, for instance, to make compatible objective judgments denying the universal validity of some logical principles. Let us consider, for instance, the intuitionist critique of mathematical realism. For the intuitionists, a mathematical proposition is true only if there exists a demonstration of this proposition. For the realists, giving a demonstration of a proposition only reveals the truth which this proposition already has, by reason that it corresponds to reality (this revelatory task is, of course, extremely important, but it should not be confused with the truth which belongs to the proposition). For the intuitionists, the demonstration itself is what establishes, not only reveals, the truth of a proposition20. The intuitionists are constructivist mathematicians. As Dummett said: “constructivists….do not deny that there are mathematical propositions but hold that they relate to our mental operations; their truth therefore can not outstrip our ability to prove them (1991, 5)”21.

Let me take as an example the famous Goldbach conjecture, which affirms that every even number greater than 2 is a sum of two primes. Until now, this conjecture has not been either refuted or demonstrated. Consequently, for the intuitionists the conjecture is neither false nor true. It is not the case that we do not know if it is true or false22, but, indeed, that the conjecture is not, until now, either false or true. Despite the fact that the intuitionist critique has a strong foundation - even the realists do not deny its depth – platonists do not accept intuitionism, on the grounds that it mutilates mathematics; that is, it does not prove several theorems of the classical mathematics.23 Something similar occurs in relation to the refutation of gorgianic ideas: the “pars construens” of the Treatise is regarded by many scholars as much less effective than the “pars destruens”. It is not my intention to increase the list of labels which have been attributed to Gorgias by calling him intuitionist. However, I think it is possible to make an analogy between the intuitionist concept of truth for mathematical propositions and the conception of truth which I believe appears in the Treatise On Not-Being and, also, in the Encomium of Helen and Palamedes Apology.

Let us consider now the two apparently contradictory assertions :

  1. In the Treatise and Palamedes Apology, language is incapable of communicating exterior objects (85-7, Sextus; 21-25, MXG, 980a20-b20)
  2. The power of logos is soundly praised in the Encomium of Helen (8-15).

Another alternative, besides relativism, that can reconcile 1 and 2 is to ascribe to Gorgias a constructivist conception of truth, that is, speech would be, for him, the instrument by which the truth of a proposition would be established. This perspective is perfectly compatible with the most vigorous exaltation of the logos. For Gorgias, speech would not reveal the truth of a proposition in the same way that for the intuitionists proofs would not have the function of revealing the truth of mathematical propositions. The conception of truth as a discursive construction is also compatible with the impossibility of words to communicate (in an essentialist or foundational sense) exterior things and, rather more, it implies that this incapacity is not a limitation. We could have, consequently, with this concept of truth as a discursive construction, a reconciliation between 1 and 2, which are apparently antagonistic. I believe that reconciling 1 and 2 is more interesting than trying to defend Gorgias as a relativist. If an anti-realist conception of truth is tenable (and convincing), we do not need to conclude, for instance, that there is no meaning in talking about truth or falsehood24

Let us make a digression, connecting Gorgias and Euripides, which is a good example for the relation between epistemological and moral anti-realists in fifth-century Greek thought. Considering Euripides´ drama, we observe, in Cassandra’s scene in The Trojan Women and in Theonoe’s scene in Helen, a similar situation. Both prophetesses know what could be understood as the truth of the events. However, while Cassandra is not believed by anyone, that is, none can grasp the meaning of her words, Theonoe has to lie (to her brother) to accomplish what she thinks is the right decision (this is curious, because her name was chosen by her parents so that it could reveal her inner self, for she was endowed with the ability to know the designs of the gods). It seems to me that these two examples help to indicate how Euripides is committed to a vision similar to Gorgias’. Even if being exists, we cannot understand it. Nonetheless this does not imply that we cannot talk about truth25.

It is important to point out that there are a plethora of derogatory assessments of the works of Gorgias and Euripides, related to the concept of rhetoric. It is worth quoting two of them. One was made by Dodds (1958, p. 9) in the introduction to his edition of Plato’s Gorgias. He denied the seriousness of Gorgias by quoting the commentary of Denniston regarding the Encomium of Helen: “starting with the initial advantage of having nothing in particular to say, he was able to concentrate all his energy upon saying it”. The other was made by Kitto (1961, p. 315), when analyzing Euripides’ Helen. “Therefore the dramatist, for the first time, is free to attend entirely to his ‘form’... it is when the poet has nothing in particular to say that he must be most elegant and attractive.”

“To have nothing in particular to say”... I do not believe that this judgment about the two authors is only a coincidence. It seems to me that there are two reasons for it. First, it is a sort of ad hominem fallacy26, for I believe it is related to a moralist conception about the character of Helen. Second, the fact that the drama Helen and Encomium of Helen are related to the thesis presented in Gorgias’ TreatiseOn Not Being.27

Concerning the analogy with intuitionism, which contributes a great deal to the concept of truth as discursive construction, it is worth clarifying one last point. When the intuitionists reject that a mathematical proposition is true or false, independently of its proof or refutation, they deny the universal validity of the law of excluded middle. Gorgias, indeed, utilizes some instances of this law in his Treatise, for instance, when he affirms “it is necessary, for something to exist, to be generated or non-generated” (MXG, 12), or “if something exists, is one or multiple” (MXG, 13). But, even when he utilizes instances of the law of excluded middle, this does not make the analogy to intuitionism weaker, for what the intuitionists reject is the universal validity of this principle; they accept instances which deal with finite domains. Regarding the law of non-contradiction, which is fundamental to many criticisms on relativism, Gorgias, as we can infer from his texts (and that of intuitionists) also accepts it.

Considering now the Encomium of Helen – the most famous “piece of rhetoric” – we can infer that Gorgias is using results presented in the Treatise: he maintains that Helen cannot be considered guilty, unless we establish, through speech, her responsibility, and the same is valid for the negation of guilt. And this fact is independent of the capacity of words to indicate reality, for there would be no independent reality, with which the sentences “Helen made an error” or “ Helen did not make an error” could be compared, in order to decide which of them is true by the fact that it corresponds to that reality. If we argue that it is possible to say that a person believes that Helen made an error and another person believes that she did not, we would be faced with a relativistic perspective concerning morality. But according to my interpretation, for Gorgias, Helen would have made an error, or not, in the exact moment in which one can construct a speech proving one of these possibilities. Therefore, persuasion seems to be a consequence of the construction of the innocence of Helen. He did not, I believe, want only to persuade others of the innocence of Helen, but rather, to construct her innocence, and, in this process, to persuade others.