In this post we plan to explore parallels between the argumentation in Hegel's Logic and those in Sextus' Outlines. Our first observation will concern the section on 'syllogism' in the Subjective Notion and its comparison to Sextus' analyses of proof and deduction in book II of the Outlines. Hegel argues for the infinite regress and insufficiency of the syllogism of the form IPU and concludes that it is the individual that must mediate between the particular and the universal PIU. Sextus argues that this same syllogism is circular because if the conclusion can be reached from the premise(s), the major premise could only have been reached by taking into account the conclusion (Socrates is mortal): for to arrive at 'all men are mortal' it was necessary - by induction - to consider the case of the man Socrates and having ascertained that the man Socrates is mortal. Also Hegel and Sextus invoke in a similar way the infinite regress which results from further demanding a proof of the major premise and so on.
One of Sextus' rather dubious arguments against genera and species is actually already found in the Aristotle's Topics serving anti-platonic purposes. This involves how the differentia demarcating different species can subsist in the genus: all at once, none at all, only potentially ? Hegel's whole theory of Notion seems to be a development of an answer to these objections (see also Sextus's arugment against common predicates whereby seemingly all predicates become inseparably individuated - this suggests a connection to Hegel's theory of individuality in the Notion).
This is a theme which merits extensive developments. In particular one is struck by the profound connection between Sextus' arguments and both Hegel and Husserl. In particular Hegel's critique of Kant or the fact that the main components of Husserl's theory of epokhê are found in book II of the Outlines. We can consider thought and appearance without conceding the claim-to-reality.
The 'scepticism' of Sextus is perhaps the most distorted and misunderstood 'ism' in all philosophy. It has nothing in common with either Hume or post-modernism. Sextus is not a theory of relativism and it is not any kind of nihilism. Rather we must leave Western philosophy altogether to find an analogue. In a previous post we outlined a kind of formal logic version of Pyrrhonism. We do not claim that this is compatible with Sextus either, but it does share some methodological principles. Basically it is dubious if Sextus can be considered philosophy, rather we are in the presence of pure methodology and a methodic challenge which might be described as a transposition of Hilbert’s program to the analysis and critique of philosophical systems. On the most basic level the challenge is this: formalize your axioms, deductive system, definitions and proofs - and analyse consistency and completeness. But then the whole story starts again at a meta-level - yet there is one main strategy open to Sextus : produce concrete proofs in an agreed upon system $D$ of both $A$ and $\neg A$ where $A$ is, for instance, some philosophically relevant sentence. Sextus ultimately has no other weapon besides formal logic including metalogical methodology. However we must also analyse negation, paraconsistency, etc. Contradictions are sometimes resolved by refining concepts and predicates, by relativization and specialization (a monadic predicate, for instance, is refined to a relation, or multivalued logic is considered, and thus a cat can be black and white).
In order to suggest the unity of the Sextus-Hegel-Husserl triad, we present here a quote from Husserl's Introduction to Logic and Theory of Knowledge (tr. C. Ortiz Hill, pp.189 et seq.)
After we have made clear the meaning of epistemological skepticism as a methodological precondition of the beginnings of a theory of knowledge, the question however arises as to how theory of knowledge is still possible afterward, and how it can unfold as a scientific discipline in a series of progressive cognitions without slipping back into the prohibited psychologism. If we adopt the position-taking of the absolute epoché required, if we make use of no preestablished knowledge, if we hold each and every thing in abeyance, then we obviously do not fail to do something, but we do not retain anything either. We do not have a single bit of knowledge. And, shall we have any, be able to acquire any? The epoché is surely not itself already a method. It is at best a piece of a method. How is an actual, complete method of knowledge to be established here? We must obtain clarity about this. The possibility of a method first ensures the possibility of the discipline. The situation at first appears rather desperate. All knowledge is to be problematical. But, the epistemological knowledge we are seeking is indeed knowledge. It therefore seems that theory of knowledge is needed in order to obtain theory of knowledge, which seems to show that theory of knowledge is impossible in principle. Let us reflect. The precious core of Cartesian doubt may help us a bit further. Before we enter into it, we shall, however, be able to say the following: Theory of knowledge does not mean to be anything more than self-understanding on the part of knowledge. It is now obvious that we cannot assume a position outside of knowledge in order to throw light on dark areas of knowledge and to solve problems that it itself raises for us. Only by knowing are we able to shed light on knowledge. If all knowledge then becomes problematical for us, or, if knowledge in general becomes a problem for us, then some knowledge is already implied in this, and absolutely indubitable knowledge, namely that knowledge in general is problematical, or that knowledge in general harbors one obscurity or another and for this reason becomes a problem. It is also further an Evidenz that it can only be in knowing that the problem is solved, that the meaning of the knowledge sought unveils itself. Consequently, it is certainly unquestionable, and again completely evident, that questions concerning all knowledge also affect the knowledge in which, as already in that just realized, these reflections about knowledge itself lie. Nevertheless, this is not to say that those kinds of reflections about the meaning and possibility of knowledge are meaningless and must remain fruitless, that, say, the Evidenzen with which the reflections begin, and in which they advance, are not Evidenzen, not knowledge, something doubtful. The necessary referring back of the elucidation of knowledge to itself is manifestly something belonging to the essence of knowledge as such.
And now Hegel in the introduction to the Encyclopedia:
But with the rise of this thinking study of things, it soon becomes evident that thought will be satisfied with nothing short of showing the necessity of its facts, of demonstrating the existence of its objects, as well as their nature and qualities. Our original acquaintance with them is thus discovered to be inadequate. We can assume nothing and assert nothing dogmatically; nor can we accept the assertions and assumptions of others. And yet we must make a beginning: and a beginning, as primary and underived, makes an assumption, or rather is an assumption. It seems as if it were impossible to make a beginning at all.
Hegel thus is in dialogue with Sextus. He is also a phenomenologist in the sense of Husserl:
In other words, every man, when he thinks and considers his thoughts, will discover by the experience of his consciousness that they possess the character of universality as well as the other aspects of thought to be afterwards enumerated. We assume of course that his powers of attention and abstraction have undergone a previous training, enabling him to observe correctly the evidence of his consciousness and his conceptions.
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