Ontological Contradictions & Dialetheist Correspondence
I. Introduction
Quite apart from the viability
of a given system of paraconsistent logic, there is the question as
to the metaphysical import of true contradictions. Whatever this
import turns out to be, there is no doubt that it is intimately
related to the theory of truth one adopts. While deflationism's
relation to ontological contradictions is anything but clear,
it is apparent that a correspondence theory of truth must
have a viable theory thereof. In the interest of ontological
contradictions, I aim to show in this paper that the connection
between them and correspondence is not so hard to swallow as one
might suppose. To
this end, I am up against the viewpoint of Armour-Garb and Beall,
which restricts true contradictions to ungrounded, semantically
pathological sentences. A correspondence account (both Priest's and
my own) seeks to defend the view that there may be ontological
contradictions, and
not just those occurring in the course of semantic pathology. In this
paper I seek to challenge the statement of Armour-Garb and Beall,
that, “After
all, the key (and, by our lights, the only) candidates for true
contradictions are semantically paradoxical sentences—each of which
is ungrounded, or otherwise irreducibly semantic”.
While this insistence on purely semantic contradiction might not be a
necessity of deflationist dialetheism, that is perhaps a question for
another time; what I need to show in this regard is that dialetheism
admits, perhaps more easily than previously thought, of a
correspondence theory of truth.
In the second section, I will
discuss the general compatibility of dialetheism with correspondence
theory, here taken as a good example of a robust theory of truth
which thus implies the possibility of ontological contradiction. In
the third section, I will follow Priest in suggesting several
candidates for ontological contradiction and provide a broad
commentary on what those suggestions might imply if correct. In the
fourth, I will address the view, put forward by Kroon, that utter
triviality (or trivialism) is the outcome of ontological
contradiction, or at least that such an outcome is not in itself
disbarred thereby. This will be placed within the larger context of
metaphysical versus conceptual views of contradiction.
II. Dialetheism & Correspondence
The relationship of dialetheism
to deflationism has been documented (see Armour-Garb & Beall).
However, that of dialetheism to correspondence theory has not, to my
knowledge, been quite as deeply explored. In the first place, in
“Truth and Contradiction”, Graham Priest has argued (and in this
he is backed up by the aforementioned pair) that there is nothing
inherent in correspondence theory that is not accommodating to
dialetheism of some kind. While I will not rehearse the argument in
full, I will draw attention to several important points.
Priest writes, “One
should note, for a start, that if one supposes reality to be
constituted solely by (non-propositional) objects, like tables and
chairs, it makes no sense to suppose that reality is inconsistent or
consistent. This is simply a category mistake” (Truth
and Contradiction).
Our theory, then,
must allow for states of affairs and not just objects. Further, and
this is perhaps the explicitly dialetheist component, these states of
affairs must also be described by a polarity relation, that is, every
state of affairs is related to the value 1 or 0. Intuitively, 1
stands for such a state obtaining and 0 for such a state failing to
obtain. This part of the theory rests on the assumption that
something failing to obtain still has ontological status, in other
words that a “negative” state of affairs (one relating to 0)
still is.
As long as we do not confuse obtaining with being, this seems to me
an uncontroversial move to make. The non-obtaining of a certain state
of affairs, in other words, has a determinate effect on observable
reality, or better, is constitutive
of that reality, to the same degree that obtaining might. Both
obtaining and non-obtaining are part of being. For example, my
writing of this paper is the way it is because it is not
the case that I'm writing it for pleasure, because I am not
on fire, &c. We can describe reality both positively and
negatively, in what it is and in what it is not, and I don't think we
can dispense wholly with either—but that is a question for another
time.
So
here we have a definition, according to a type of correspondence
theory, of ontological
contradiction:
When a state of affairs both obtains and fails to obtain at a given
time, place, etc.; or, if we believe states of affairs to be atomic,
it is when a state of affairs obtains and at the same time another
state of affairs with exactly the same determinate qualities or
relations as the first fails
to obtain. For a contradiction to occur, I must have two states of
affairs differing in only their polarity-relations, so that the same
objects are brought into the same relations with only obtainment
differing. Of course, this model only defers the philosophical
question of whether such a contradiction could really
exist, rather than simply being compatible with the theory. The
problem would initially seem to be one of comprehension:
Our
hunch is that the difficulty in seeing how a state of affairs could
both obtain and fail to do so involves the mistake of trying to
imagine observable
states of affairs both obtaining and failing to do so—e.g., the
journal's being here in front of you and its not being here in front
of you. For what it is worth, we cannot imagine such states of
affairs both obtaining and failing to obtain, either. (Armour-Garb &
Beall)
Clearly,
the impossibility of anything observable or familiar being
contradictory would be a black mark against the theory. However, it
is my contention that this is not the case, and as such I will now
explore this possibility.
III. Contradictions in the World: Philosophical Considerations
What
would be just such an observable or otherwise familiar contradiction?
Following Graham Priest's suggestions in his book In
Contradiction,
I hold that change, including and even especially movement, is in a
broad sense is contradictory. To show this we must focus in on the
instant of change—in order to make things simple, I will focus on
the case of movement, though the extension to other types of change
follows relatively easily.
Say
we have a ball moving from point A to point B. By the orthodox
(consistent) account of motion, we might say that at each instant the
ball is not moving, as if each instant were a snapshot. Somehow, the
infinite summation of these non-moving instants yields the movement
from A to B. Though it is tempting to take the infinitesimal calculus
as a vindication of this view, such an explanation in fact leaves
many properly philosophical questions unanswered. In the first place,
it implies that movement is a mere correlation of object and position
over time, in other words, that there is no state
of change—movement itself is in this view extrinsic to the moving
object. It is not a way out to say that movement is simply change
over time, because
While
there is much more that could be said about that,
perhaps more important for our argument here is that such a
snapshot-view (what Priest calls the “cinematic view”) of motion
is highly unintuitive. It is only because the orthodox account of
motion seeks to avoid contradictions at all cost that it is forced
into such an unintuitive position. In contrast to this, a dialetheist
account of motion can help itself to contradiction and can therefore
avoid such a fate, perhaps as the following elaboration will show.
First,
it would be well to acquaint ourselves with the so-called Leibniz
Continuity Condition (henceforth LCC): “Any state of affairs that
holds at any continuous set of times holds at any temporal limit of
those times”, or, stated more intuitively, “Anything going on
arbitrarily close to a certain time is going on at that time too”
(Priest, In
Contradiction 166).
While not universally applicable, I hold with Priest that the LCC can
be fruitfully applied to a number of fields or continuums, including
space (and therefore motion). Here we return to our previous example
of a ball moving from A to B. Splitting up motion into instants once
again, we see a rater different picture from the orthodox “cinematic
view”. In particular, at each instant there is intrinsic
motion in the ball, meaning that even at a single instant, there is
an inherent difference between a ball in motion and a ball at rest,
though each be something like a snapshot. But what is the nature of
this intrinsic motion?
At
each instant, the ball is both entering the space, staying in the
space, and leaving the space, all along the arc of its motion.
Applying the LCC, we get the result that at time = 0, when the ball
begins moving, it is both at rest and already leaving its space,
already moving. This is because, being a limit, the starting-point is
subject to the subsequent state, the state of motion. But, since it
is also at rest before it begins moving (by the definition of the
problem), we have a contradiction. This analysis can be extended to
account for not just the endpoints or limits, but also to all motion
whatsoever, so that movement (or change more generally) is a
continuous contradiction. A change from p holding to ~p holding
admits of at least an instant where p & ~p holds. Therefore, a
change from one position to the next yields the result that at each
instant there is a truth
of the form p & ~p,
where p is the sentence or proposition that the object is in a
certain state (or place, &c.). This truth, that of the position
and movement of the object, is not properly semantic—it might be
either conceptual or metaphysical; I believe that there are reasons
to assume the latter, though it is not absolutely clear-cut.
One
of these reasons for the metaphysical interpretation, and perhaps the
major one, is the Spread Hypothesis (henceforth SH), a formulation
more particular to motion itself:
We
suppose that over small neighbourhoods of time it is impossible to
pin down states of affairs. The impossibility is not merely
epistemological, but ontological: nature itself is such that it is
unable to localise precisely its doings. Each instant is so
intimately connected with those around it that their contents cannot
but encroach. (Priest, In
Contradiction
213)
This
“localisation” has a clear analogue in the attempt to envision a
“snapshot” that would be consistent. Suffice it to say that the
SH is, even if philosophically controversial, at least scientifically
valid or possible, at least for the time being. I simply draw
attention to it in order to indicate that the argument presented here
is not inherently opposed to scientific understanding, as might be
supposed. In particular, the objection that contradiction makes us
unable to understand or otherwise comprehend the world can be
disposed of. Finally, this argument for change as contradiction would
seem to be a vindication of the Hegelian view whereby determination
in a broad sense is the outcome of a process of self-differentiation,
in other words of contradiction. In particular, there is not a
radical separation between what an object is now before a change and
what it is after that change. It is simply an object in a state
of change, something which is internal to what it is. The context or
processes in which an object exists (or which exist in it!) serve to
determine that object. This is but one modality of the Hegelian
rejection of atomism.
We
would now do well to consider another major objection to the theory
outlined above, namely the belief that in fact there are no instants
of time, but only intervals. If we define motion simply as distance
covered over time, it is clear that there would then be no such
instant. This is of no great consequence, however, because the
“instant” we refer to could just as well be some interval,
although usually a very very short one (even planck time!). In fact,
if we apply the LCC to time itself (the legitimacy of which is
dicussed in Priest's book), we get the result that each instant is
actually that instant and
all the instants around it.
Thus the dialetheist here has a way to capture even the insight on
time as an interval or as a flow; while I can't delve too deeply into
this question here, I hope I have shown the objection is at least not
devastating. Again, an “instant” in the context of the LCC is
only meant to imply a liminal state, and not necessarily a
metaphysical “point” of time.
IV. Conclusion: Metaphysical & Conceptual Contradiction
Earlier we asked the question as
to whether our account would be amenable to a conceptual rather than
metaphysical interpretation. To bring this into focus we turn to
Priest: “However,
it might be suggested, to say that the world is consistent is to say
that any true purely descriptive sentence about the world is
consistent” (In
Contradiction
159). This is likewise the case for inconsistency. It might be argued
that, though our best explanation of the world at any given time
might be contradictory, the world itself is not contradictory, such
that God's explanation would be totally consistent. It is to this end
that Kroon writes, “...the
paradoxes indicate that some of our concepts are deeply defective at
certain points: in particular, the rules that govern them produce
inconsistent results when applied at certain limit points” (253).
Indeed,
this question was not a problem for Hegel, whose philosophy was a
working-out of the identity (in difference) between thinking and
being. For us, however, of a more skeptical bent, the question is
more difficult. In his paper, Kroon argues that once we have
contradictions in the world there is no regulating principle, no
reason to prefer that there be fewer contradictions rather than more.
Thus there is no regulative principle which would keep us from
accepting as plausible the view that, metaphysically speaking,
everything
is in contradiction: “...what
precisely is wrong with allowing a tolerant account of entailment on
which everything
is both true and false since something
is both true and false” (Kroon 252).
Taking
this possibility alone as reason to reject ontological contradiction,
Kroon writes, “As
I said earlier, however, the thought that the truth of trivialism is
a genuine open possibility in this sense ought to strike us as
bizarre and intolerable. Unlike other incredible doctrines, it
deserves not an incredulous stare, but no stare at all” (252-253).
In the first place, we might say that, just as in Priest's more
general presentation of dialetheism, there is no reason to suppose
that such a state of universal contradiction is or even could
materially be the case (Kroon seems to acknowledge this). This aside,
there is absolutely no a
priori
reason for disbelieving metaphysical triviality—if we are
rationally led to the conclusion, so be it, although I don't see this
ever occurring. To rule it out a
priori,
as Kroon does, and then to use this “bizarre and intolerable”
position to rail against ontological contradiction as such, is on the
whole quite irresponsible.
Thus,
I hope I have shown that a dialetheist correspondence theory of truth
is not ruled out by potentially unsavory results relating to
ontological contradiction. A plan for further research in the area
might include a more in-depth look at how the LCC can be applied to
the flow of time, as well as a fuller discussion of the
conceptual-metaphysical divide (and Hegel's position thereon).
Works Cited
Armour-Garb,
Bradley and JC Beall. “Further Remarks on Truth and Contradiction.”
The
Philosophical Quarterly Vol
52. No 207 (2002): pp. 217-225. Electronic.
Kroon, Frederick. “Realism
and Dialetheism.” The
Law of Non-Contradiction. Eds.
Graham Priest, JC Beall and Bradley Armour-Garb. New York: Oxford
University Press, 2004. pp. 245-264. Print.
Priest,
Graham. In
Contradiction: A Study of the Transconsistent. Dordrecht;
Boston: Distributors for the U.S. and Canada, Kluwer Academic, 1987.
Print.
---.
“Truth and Contradiction.” The
Philosophical Quarterly Vol
50. No 200 (2000): pp. 305-319. Electronic.
