Kant on Causality and Time

Introduction

David Hume, in A Treatise of Human Nature (Bk. I, Pt. III, § III), argues that we cannot derive the necessity of a cause from ``knowledge or any scientific reasoning''. Thus, according to Hume, our belief in such a necessity must arise from experience. We must therefore, he claims, ask ourselves two questions: ``how experience gives rise to such a principle [viz. necessary causality]?'' and ``why we conclude that such particular causes must necessarily have such particular effects, and why we form an inference from one to another?''. As for the first question, Sections VI (``Of Probability'') and VII (``Of the Idea of a Necessary Connection'') of An Enquiry Concerning Human Understanding argue that experience cannot give rise to such an apodictic certainty. We are thus led to conclude that necessary causality is an illusion.

Immanuel Kant's Critique of Pure Reason provides the framework for a response to Hume's argument. In particular, Kant develops the idea of synthetic a priori knowledge and judgement---one which has a priori certainty, yet is more than a simple analysis of concepts. Thus he sidesteps Hume's first question by providing a third possible form of judgement, one which allows causality to have a priori certainty while still applying to objects. The Second Analogy of Experience (B232--56), in particular, is an attempt to prove that causality is necessary to our perception of objective reality.

The Second Analogy

Kant begins (B235) by distinguishing an appearance (what we might, in a fit of terminological laziness, call an ``thing''---not to be confused with a ``thing-in-itself'') from its representation in apprehension. In particular, apprehension is always successive, even when it concerns an appearance that is not so (for example, a house standing before me). Thus there is something, which Kant terms the ``object'' (Object), which ties together different apprehensions into a single appearance, while excluding other unrelated apprehensions. This definition of ``object'' is similar to the definition in the Transcendental Deduction (§17, B137):

An object (Object) . . . is that in the concept of which the manifold of a given intuition is united.
As in the Deduction, Kant is concerned with conditions for the existence of such an object. In particular, without a objective sequence of appearances, Kant claims that ``no appearance would be distinguished from any other'' (B238). How, then, do we have such an objective sequence? That is, how can we say that one appearance follows another, rather than that one of my apprehensions follows another? For in the latter case, I determine nothing about the object; the order of my apprehensions is entirely arbitrary (well, almost entirely---see ``Problems and Alternatives'' below). Such an objective sequence, according to B238, occurs only when apprehensions follow one another ``in accordance with a rule''. That is, given any event, there must be a rule that, from what precedes, is able to derive that event. This rule is the cause of the event.

Not only is a causal relation necessary for the existence of objects: it is necessary for each object (B247). That is, every object of experience falls under a relationship of cause and effect, and such a relationship is valid for every object. This is because cognition requires a synthesis of the manifold of appearance, which (because it is of appearance rather than of mere apprehension) has determined an order in the object (B246). Thus experience, which requires cognition, thereby requires causality; and any object of experience falls under relations of causality.

This conception of causality, of course, is somewhat counterintuitive. It claims that, for us to be able to speak of an object, we must already have related our apprehensions of that object through necessary causality. We normally think of things differently: we form the idea of a causal relationship after observing many sequences of events (B240-1). This, in fact, is Hume's conception of causality; Hume has demonstrated well enough that such a concept would be ``merely empirical'', and hence incapable of certainty. Thus we need Kant's objective causality. However, even with objective causality, we must make use of the causal relation through experience before we can obtain ``logical clarity of this representation of a rule''. That is, although we use certain relations of cause and effect to determine the objects of our experience, we must analyse the objects before we can intellectually state what those relations actually are. This is Kant's answer to Hume's second question: we empirically rediscover, so to speak, the causal relationships that we already intuitively grasped.

Problems and Alternatives

In the Second Analogy, Kant continually refers to the need for an objective sequence of appearances. For example, without an objective sequence, ``no appearance would be distinguished from any other'' (B238). Or, later, if occurrences did not have necessary causes, ``we would have only a play of representations'' and, again, ``no appearance would be distinguished from any other as far as the temporal relation is concerned'' (B239). Why is this the case? It seems that Kant is suggesting that a mere subjective sequence of apprehensions is too fragmentary to yield distinct appearances (and thus objects).

From a Humean perspective, it seems that Kant's argument begins with an assumption that a necessary sequence underlies the unity of appearance. From there, he establishes that causality is precisely the kind of sequentiality needed. Of course, Hume would argue, this is begging the question: the necessary ``objective sequence'' which Kant assumes is precisely that of which he is trying to prove the existence.

Suppose we grant that an objective time-determination is needed for the possibility of experience. Kant claims that time is the necessary condition of all inner experience. In particular, we perceive our own internal states within time. We thus have a subjective order of events, based on when they reach our mind; this is Kant's subjective order of apprehension. Add to this subjective order, then, the fact that we perceive time ``backwards''. That is, a thought can concern events occurring before, but not after, that thought. Given this constraint, the order of apprehension is not entirely arbitrary---we apprehend X before we apprehend an apprehension of X, for example. This is a rule, in accordance with which the apprehension of one thing follows another. According to Kant's criteria, this allows for an objective sequence of appearances. Thus, without cause and effect, but rather with the internal ordering of memory, we can separate appearances. Causality is then not a necessary condition of objects; it, in fact, does not necessarily exist at all.

Kant and Special Relativity

Interestingly, we can find a parallel to Kant's Second Analogy in a twentieth-century theory: that of Albert Einstein's and Herman Minkowski's special relativity (SR). A discussion of the origins and results of SR is outside the scope of this paper; we restrict ourselves to discussing light cones and simultaneity.

The fundamental object in SR is an event---simply a spacetime coordinate. Each event has a light cone, a double cone centred at that event. The forward half (the future-cone) contains the set of points reachable by a light flash at that event. The other half (the past-cone) consists of those points from which a light flash could reach the event in question. Because the speed of light provides an upper bound on the transfer of information, an event A can causally influence event B only if B lies within A's future-cone (or A lies within B's past-cone---the two conditions are equivalent).

Also important to the Kant--SR connection is relativistic simultaneity. According to SR, there is no such thing as absolute simultaneity; rather, each event has a ``plane of simultaneity'' in spacetime: a set of events which an observer at that event would measure as simultaneous with him- or herself. Any event occurring above that plane will be measured by the observer as in the future; any event occurring below the plane will be measured to be in the past. The angle of the plane becomes steeper as the speed of the observer increases; at the speed of light, the plane would be tangent to the light cone. Thus, by changing one's velocity, one alters the apparent order of events from one's perspective.

Let A and B be events. It can be demonstrated that:

  1. If A lies within B's future-cone (i.e., B lies within A's past-cone), an observer will necessarily measure A as occurring after B.
  2. If A lies within B's past-cone (i.e., B lies within A's future-cone), an observer will necessarily measure A as occurring before B.
  3. If A does not lie within B's light-cone, there exists frames of reference (observers) in which A follows B, and others in which B follows A.

Interpreting light cones as domains of causality, we see that there is a necessary, observer-independent order between A and B only if one of A and B could cause the other. This conclusion is very similar to that reached by Kant in the Second Analogy: that we can only order events by virtue of causal relationships. The parallel is not exact, of course: SR speaks of ``possible causality'' while Kant speaks of ``necessary causality''. However, it is interesting to observe Kant's ``Copernican'' philosophy as the first step towards another revolutionary model of the universe over a hundred years later.

Conclusion

The Second Analogy has been set up to do a very difficult task: dispel Hume's scepticism concerning cause and effect. It is thus not at all surprising that it not succeed in this task. That failure, though, is not a total one: Kant has provided a persuasive argument for the possibility of a priori causality, and has thus partially answered Hume's first question. Kant's answer to the second question, however, is unsatisfactory: the suggestion that science works to find causal relationships that we, deep down, already know is naïve, if not slightly offensive. On the whole, though, the Second Analogy has contributed much to metaphysics and science---not only does it provide an alternative to Humean scepticism, but it lays the groundwork for one of the most important scientific theories of the twentieth century.

---Neil Moore

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