Priest, (2) ‘Dialectic and Dialetheic’, section 2, “The Argument Against this Interpretation”, summary

 

by Corry Shores
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[The following is summary. All boldface, underlying and bracketed commentary are my own, unless otherwise indicated.]

Graham Priest

“Dialectic and Dialetheic”

2 The Argument Against this Interpretation

Brief Summary:

The main argument against reading Hegel and Marx as dialetheists is that it goes against the basic restriction of classical logic that you cannot have contradictions. But this restriction is based on an assumption and is thus not a necessary one.

Summary 

[Dialetheism is the philosophical position that true contradictions exist.] Previously Priest noted how many scholars do not think that Marx’s and Hegel’s dialectics involve a non-logical notion of contradiction or that contradiction is conceptual and does not obtain in reality. Priest stated that he will take the opposite position, that the logical sense of contradiction is fundamental to their philosophies of dialectic. In the remaining sections, Priest will defend his thesis, but for now in this current section, he will explain “why so many have rejected this view, and see why this is mistaken” (391).

Priest first notes how Hegel makes the correct distinction between dialectics and formal logic. At his time, formal logic was Aristotelian syllogistic logic, which is only applicable to the limited domain of static and changeless matters. In such cases, the law of non-contradiction holds. However, this law fails in dialectical logic, which applies more generally (391). But since Hegel’s time, formal logic “matured into modern Frege/Russell logic” (391), which rules out dialetheais. This means that if dialectic logic would like to be compatible with modern logic, which many presume gives “a definitive account of the most abstract norms of correct scientific thought,” then it cannot be dialetheic. “Thus Hegel’s and Marx’s rejections of the law of non-contradiction, and, consequently, their notion of contradiction, have had to be interpreted non-literally, on pain of a charge of being unscientific, or of irrationalism” (391).

Those that defend dialectic tried to show that Marx and Hegel did not literally mean what they said about contradiction. Popper, however, holds Hegel and Marx to their words in order to invalidate them, on the basis that their contradictions prove all statements true. (391-392) “Thus, modern dialecticians, most of whom know very little formal logic, have allowed themselves to be intimidated, and even brow-beaten, into reinterpreting dialectical contradictions” (392).

The Frege/Russell logic is a “theory of the norms of reasoning” (392). Thus its assumptions are debatable and are not themselves truths. So their belief that A&~A; therefore B [that is, from any contradiction any other statement can be proved true] is not something that is necessarily so. Therefore, dialecticians need not submit to the Frege/Russell prejudices against logical contradiction (392). In fact, many of their assumptions have already been shown untenable.

It is notable that 20th century logicians themselves – as opposed to those who merely quote it – have been under no illusions about the contentious and often shaky nature of some of the assumptions built into the Frege/Russell theory. Though the mutual exclusiveness of truth and falsity may not have been questioned (until recently), many other presuppositions have been questioned, and often rejected: that truth and falsity are exhaustive; that all terms denote; that the conditional is truth functional; that “existential quantification” has existential import; and so on.
(392)

In fact, also since Frege and Russell there have developed paraconsistent logics. Priest will give an informal explanation of one kind, dialetheic logic, in the following section (393).

Citations from:

Priest, Graham. ‘Dialectic and Dialetheiç’. Science & Society, 1989/1990, 53 (4) 388–415.