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