## 9 Jun 2014

### Priest (12.4) In Contradiction, ‘… And Its Consequences’, summary

by Corry Shores
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[The following is summary. My own comments are in brackets, but please consult the original text, as I am not a logician. All boldface and underlining are my own. Proofreading is incomplete so mistakes are still present.]

Graham Priest

A Study of the Transconsistent

Part III. Applications

Ch.12. The Metaphysics of Change II:
Motion

12.4 … And Its Consequences

Brief Summary:

Priest’s dialetheic Hegelean account of motion solves many of the problems created by the Russellean orthodox (‘at-at’) account of motion. For example, the orthodox account says that motion is made up only of states of rest, which is counter-intuitive. The Hegelean account however allows us to say that the object is both in a location and not in a location at the same time, and thus always is in a state of motion. It would even seem that time itself is structurally self-contradictory. For a dialetheic account, this does not mean that it is therefore non-real. Rather, it allows time to be both inconsistent and real.

Summary

Previously Priest accomplished the following.

The Hegelean state description of a body in motion, with its notion of the spread of locations at any time, makes quite precise Hegel’s claim that to be in motion is | to occupy more than one place (in fact a continuum of places) at the same time, and hence both to be and not to be in some place. It therefore renders quite rigorous his account of change. Moreover, the important defect of the account that I mentioned at the start of the last section, namely that it is unclear how the account relates to the canonical mathematical representation of motion, is clearly overcome. An equation of motion, x=f(t), still captures the idea that at time t the object is at f(t). It is just that there is more to change than this. It might be elsewhere too!
[179-180]

Priest’s Hegelean account solved some of the problems he found with the orthodox account. Recall for example that it implies motion is constituted only by states of rest, and it is never actually in a state of motion. This seemed counter-intuitive. The Hegelean account allow for a moving body to occupy multiple locations for a single time point, so it does not have this problem. [180]

Also recall that in Zeno’s paradox of the arrow, the arrow was said to be in only one position at one time. Given the spread hypothesis, we can have the object in multiple locations for one time point. [p180]

Some things still need to be explored regarding the spread hypothesis. Nonetheless, we know it is preferable to the Russellean account. [180] Priest also notes that quantum indeterminacy might be explained using the spread hypothesis [for details see 180-181]

In fact, we might even say not only are objects in motion in two places at the same instant, but we might also say that time itself is structured as self-contradictory, with one moment occupying multiple time-points.

Let me end this chapter with one final application of the Hegelean account of change, where the change in question this time is not motion. Take any point of time, say, midnight on 1/1/2000. Then at this time ‘It is midnight on 1/1/2000’ is true. For a continuous period before and up to this time ‘It is not midnight on 1/1/2000’ is true. Hence by the LCC, this is true at midnight too. Thus, at this time it is both midnight on 1/1/2000 and not midnight on 1/1/2000. This application of the LCC is somewhat moot. It is not completely clear that ‘It is midnight’ and similar temporal claims describe states of affairs in the required sense of the word. But assuming that they do, the fact that such contradictions are produced, together with the Hegelean account of change, gives an exact and plausible sense to the obviously true and non-trivial claim that time itself is in a state of change or flux. This commonsense view has given all sorts of problems to the Russellean account of change. For, on the orthodox account, the view that time is itself in a state of change amounts to the banality that at one time it is one time, and at another, another. This has prompted a variety of responses of varying degrees of incredibility, from the view that time is not in a state of flux, to the view that there are ‘‘hypertimes’’. The contradiction theory of change solves the problem cleanly and swiftly.
[181]

[Priest then raises the question of whether the spread hypothesis applies to either or both time understood as indexical temporal ‘A series’ and as non-indexical temporal ‘B series’. For details, see p.181.]

Some philosophers have concluded that time itself is inconsistent. But they further conclude that this means time is not real. Dialetheic logic, however, allows time to be both inconsistent and real.

A number of people have argued that time in itself is inconsistent. Many of these, such as the idealists Bradley and McTaggart, thought that for this reason it should be consigned to the realm of appearances, or of non-existence—though exactly what this means is not so clear. Dialetheism allows time to be both inconsistent and real.
[181]

Citations from:

Priest, Graham. In Contradiction: A Study of the Transconsistent. Oxford/New York: Clarendon/Oxford University, 2006 [first published 1987].

#### 1 comment:

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