8 Feb 2015

Priest, (4) ‘Dialectic and Dialetheic’, section 4, “Motion: An Illustration”, 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”

4 Motion: An Illustration

Brief Summary:

One way we can illustrate how dialetheic logic can apply to dialectics is by accounting for motion in a Hegelian way. An object in motion is at a certain point at a certain instant, but since it is in motion, in that instant it is already leaving that point. Thus it is both true and false that the object is at that point in that instant.


Priest has been discussing the dialetheism of Hegel’s and Marx’s dialectics. He will now illustrate with the example of motion. If we think of an object in motion as both being in its spot and already leaving it, then the statement that it is in that spot is both true and false.


Suppose a body, b, occupies a certain spot, s, at a certain time. What is the instantaneous difference between its being in motion and its being at rest? A Russell would say “none”: being in motion is not an intrinsic, but a relational state. Hegel would say “consistency.” Let A be the sentence “b is at spot s.” Then if b is at rest, A is true, and true only (T). If b is in motion, then A is true, since b does indeed occupy the spot s; but, equally, since it is in motion, it has already started to leave that spot; hence b is not still there: ~A is true. Thus A is both true and false (T and F).

But there is a problem with this formulation. [I am not exactly sure of the situation Priest describes in the following. It seems that because we have A and ~A separated by conjunction, we are misrepresenting the fact that the opposing terms in dialectics are somehow more intimately related. This has something to do with extension and intensional contradictions. I am not sure what these are. A classical example in intensional logic is ‘the son of Jocasta is the husband of Jocasta’. The extensional meaning is the set too which the terms refer, in this case, they both refer to a set with one member, Oedipus. For the motion example to be an extension rather than an intensional contradiction, perhaps the matter is that we are speaking of two spots, the object being in those two spots, which taken apart from one another is not a contradiction but together they are. But for some reason, dialecticians would say that there is instead internal intensional contradiction. I am not sure how, but perhaps they are saying that somehow ‘the object is at point b’ is in itself already self-contradictory. Priest replies to this objection first here it seems by saying that this is such a conjunction where both parts of the conjunct need to be together for correct information to be conveyed. So in that way they already exhibit an intimate link. However, since dialecticians do not think that the conjunction can be accidental but rather somehow depend on each other, and in that way are very intimately linked, we will need to have more than just an extensional (external) conjunction. Priest will return to this in section 8, so I will quote it for now.]

Some dialecticians would argue that Hegelian contradictions cannot be of the kind illustrated here. For this contradiction is a merely extensional contradiction: a logical contradiction of the form A&~A, where there is no essential connection between the conjuncts. One can, for example, infer each of A and ~A from this contradiction and assert each independently. By contrast; dialectical contradictions are intensional. There is an internal relation between the conjuncts which is not captured by a mere extensional conjunction. Thus, dialectics | [the following is block quotation]

lays stress on the fact that this two-fold interrelation of opposites is to be conceived, not "eclectically," as ·mere. conjunction or succession, but dialectically, in· the sense that these opposites are so far intertwined that the one cannot exist without the othr. Not only do they not exclude each other, they presuppose and reciprocally condition each other. (Wetter, 1958, 340.) [from bibliography: Wetter, G. A. 1958. Dialectical Materialism. London: Routledge and Kegan Paul.]

In particular, it is not permissible to detach either conjunct from the other and assert it, without falsifying the description. (This criticism is made in Havas, 1981.) To a certain extent this objection is simply answered. Less than the whole (relevant) truth can itself be quite misleading and give a false picture of the situation. Thus, suppose your car runs out of petrol and you ask me where the nearest garage is. If I detach and assert only the first conjunct of “There is a garage around the corner but it is closed” my answer will be highly misleading. There is a conversational implicature, to use the notion of Grice (1975), that relevant information has not been omitted. But in dialectical contexts, the distinction between something’s being true (only) and its being true and false is quite crucial. Thus to assert only A when A&~A is true is equally misleading. As Hegel himself puts it (1969, Vol. I, book 1, section 1, ch. 10, 91) [from bibliography: Hegel, G. W. F. 1969 (1812). The Science of Logic. London: Allen and Unwin.]: [the following is block quoted]

The commonest injustice done to a speculative [i.e., dialectical] content is to make it one-sided, that is, to give prominence only to one of the propositions into which it can be resolved. It cannot then be denied that this proposition is asserted; but the statement is just as false as it is true, for once one of the propositions is taken out of the speculative content, the other must be equally considered and stated.

Nonetheless, as Hegel and most other dialecticians have stressed, dialectical contradictions are no mere “accidental” conjunctions. In some sense the contradictory conjuncts depend on each other, so that the one could not exist without the other. Thus, there should indeed be a more intimate relation between dialectical contradictories than mere extensional (external) conjunction. What this is, we will be in a position to see by section 8.





Citations from:

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








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