Does Kant Provide an Indirect Proof?

Here’s one of the written exam question answers I just wrote out over the weekend toward my M.A.  While it isn’t a complete in-depth examination of Kant’s Antinomies as a whole (of which one could probably write an entire book), I do think I answer the question posed fully.


Kant claims that the ultimate argument for transcendental idealism has to be “indirect”. What does he mean? Why indirect and how does the argument proceed?

Kant’s indirect proofs for transcendental idealism come as a result of the arguments he lays down in the Antinomies of Pure Reason chapter of the Transcendental Dialectic division of the Critique of Pure Reason.  The purpose of this chapter is to show that through the use of pure reason one can argue successfully for both the thesis and antithesis of certain arguments of rational cosmology.  The resulting arguments show that neither position is tenable as they lead to contradiction and the only way to come to a satisfactory conclusion is by assuming transcendental idealism is true and thus proving it indirectly.  There are four antinomies in total with the first two being mathematical in nature and the second pair being dynamic; however there is an underlying issue amongst the set concerned with the status of an unconditioned condition which serves as the determining point for all subsequent conditioned conditions which proceed from it within a series.  Put another way, does the series of conditioned conditions terminate in an unconditioned first member that is unlike all its other members, or does the series continue on into infinity.  Either answer comes with serious issues that Kant wants to highlight as red flags to the type of reasoning being employed:  If one takes the route of infinity (i.e. each conditioned condition is presupposed by a further condition without limit) then this seems to suggest that the series in question will always be incomplete which means there will always be a condition lacking the conditioned condition it is presupposed by.  Alternatively the unconditioned could also somehow be contained within the infinite series itself which seems to be in line with Kant’s statement that “if the conditioned is given, then the whole sum of conditions, and hence the absolutely unconditioned, is also given.” (B436)  On the other hand, to posit an unconditioned condition completely unique from every condition that follows it is to say there is some entity existent outside the laws of nature from which everything else follows.  Neither of these solutions (an infinite regress or a finite beginning) is very palatable for Kant as he tells us of the former that it would be too small and the latter too big for every concept of the understanding. (B514)  With this I will now turn to each antinomy and lay out the arguments for the finite/infinite solutions.

The first antinomy asks if the world has a beginning in time and space.  Kant argues by reductio (as he does in all four antinomies) for a positive answer in both directions.  The thesis (i.e. the argument for a finite beginning in time) goes as follows:

  1. Assume the world has no beginning in time.
  2. Then for each point in time an infinite series of states of things in the world has passed.
  3. But an infinite series can never be completed through a successive synthesis.
  4. Therefore, an infinitely elapsed world-series is impossible.

And the argument for space:

  1. Assume the world is infinite. (unbounded).
  2. Then the spatial world would be an infinite given whole of simultaneously existing things.
  3. We can only think of objects not given to us in experience as a synthesis of its parts.
  4. The world as a whole is not given to us in experience.
  5. Therefore we can only cognize the world as a synthesis of its parts.
  6. If the world were infinite then it would take an infinite amount of time to cognize.
  7. But time is not infinite.
  8. Therefore the world is not infinite (bounded).

The main difference in these two arguments is that with the argument for the finitude time Kant is focused on the conceptual contradiction that can be pulled out of infinity while in the argument for the finitude of space is concerned with the cognitive capabilities of the human knower.  Now for the antithetical arguments for infinite time and space:

  1. Assume the world has a beginning in time.
  2. The beginning point must be something that precedes time. (Kant calls this “empty time”)
  3. But nothing can proceed temporally outside of time.
  4. Therefore, time must extend infinitely into the past.

And the argument for space:

  1. Assume the world is finite.
  2. Then the spatial world exists in empty space.
  3. This entails a relation of things to space.
  4. The world is an absolute whole outside of which there is no object of intuition to which the world is related.
  5. Therefore the world is not related to empty space.
  6. Therefore the world is infinite.

By empty space I take Kant to mean that if space is not infinite then it is an empty void and the world cannot stand in relation to an empty void.  I suppose this could mean that anything that is not an object of some sort is pure nothingness.  However, in the interest of brevity I shall avoid any possible objections and press onward.

The second antinomy asks whether composite substances (i.e. matter) are composed of simple substances or are infinitely divisible.  First the proof for the thesis:

  1. Assume composite substances do not consist of simple parts.
  2. Then if all composition is removed in thought then nothing would remain.
  3. Thus either removing composition in thought is impossible or a simple substance remains.
  4. The first choice in (3) entails that the composite does not consist of substances which contradicts (1).
  5. Therefore only the second choice in (3) that simple substances exist remains.

This argument turns on our inability to be able to deconstruct a substance in our minds and end up with anything other than the simple parts which compose it.  Suppose we take a red block of wood and mentally deconstruct it.  What we end up with are certain qualities which compose it (e.g. color, shape, and matter).  Here is the antithesis:

  1. Assume composite substances consist of simple parts.
  2. Every external relation between substances exists in space.
  3. Therefore there must be as many parts of space as there are of the parts of composite things occupying it.
  4. Composite things are made of simple parts.
  5. Therefore all simple parts occupy space.
  6. Everything real that occupies a space contains a manifold of elements within it that are external to one another.
  7. Therefore simple parts are really composite.

The thought running through this argument is material substances occupy space, and since space is continuous and infinite so too it must be the same of any parts of matter that are within it.  Therefore mater is infinitely divisible.

The third antinomy sees a shift from the mathematically themed arguments we saw in the first two antinomies to arguments focused on causality.  Here Kant argues both sides of the traditional free will debate –does causality other than the deterministic nature of the universe exist?  Here is the thesis:

  1. Assume determinism is true.
  2. Everything that happens presupposes a previous state which it follows without exception according to a rule.
  3. This deterministic line of causation stretches back into infinity.
  4. If the deterministic line stretches back to infinity, then there will never be a first cause which provides the grounding for the entire deterministic line.
  5. If there will never be a first cause which provides the grounding for the entire deterministic line, then determinism cannot be true.
  6. Determinism cannot be true.

Even though this argument is strictly speaking concerned with causation, we can see the important role infinity plays in the argument.  If the line of determinism stretches back to infinity, then there will never be a first cause by which the subsequent line is grounded.  Therefore there must be some sort of first cause which stands outside of nature to provide that grounding.  Here is the antithesis:

  1. Assume free will is true.
  2. Then not only will a series begin spontaneously, but also the will to produce that series will be spontaneous.
  3. But every beginning of action presupposes a state with no causal connection with any previous state.
  4. Thus freedom is contrary to natural causal laws for it combines successive states of effective causes where no unity of experience is possible, which relegates free will to an empty thought-entity.

The line of argument here is that if we assume free will is true, then what we seem to get are different chains of causation popping up spontaneously all over the place.  However, since we observe causation only in terms of the natural laws, this notion of freedom ultimately ends up an empty concept.

The last of the antinomies asks whether nature (or any part of it) necessarily exists.  It might be tempting here to think that Kant is referring to God, but the argument speaks of nature itself as being necessary.  To think of God on this line would be more along the line of how Spinoza conceives of God.  Here is the thesis:

  1. The sensory world contains a series of alterations.
  2. Every alteration is the necessarily the consequent of its prior condition.
  3. Every condition presupposes a complete set of prior conditions leading to a first unconditioned condition.
  4. This unconditioned condition is absolutely necessary.
  5. This unconditioned condition belongs to the world of sense for if it stood outside of the world of sense then it would be unable to cause the series of alterations due to it standing outside of space and time.
  6. Therefore the unconditioned condition exists in the world of sense.

Here Kant is appealing to what a human observer can know through sense data to argue to the conclusion that the necessary being has to exist in space and time.  It would be another matter entirely to try and make the argument that the necessary being stands outside of space and time yet still somehow causes alterations within it.  Those sorts of cosmological arguments Kant criticizes in the third chapter of the Dialectic.  Also note that this is the only argument that does not proceed from reductio.  Here is the antithesis:

  1. Suppose either the world or something within it is a necessary being.
  2. Then either the series of alterations would proceed from an unconditioned first cause or the series itself would be without any beginning and itself be unconditioned.
  3. The first option in (2) means there is an uncaused first cause which violates the laws of nature and the second means that a series of alteration is both conditioned and unconditioned at the same time which is a contradiction.
  4. Therefore the world or something within it cannot be a necessary being.

As in the other antithetical antinomies Kant is appealing to the notion of infinity to make his argument.  First causes (whether they are in the world or outside of it) are strange notions for they break with the laws of causation which stretch back infinitely through history.

Now that we have seen how the arguments run I want to make a couple of general statements about Kant’s strategy.  First I want to note that while my formulations of Kant’s arguments are faithful to his meaning, there were a few spots where I reworded things to make the arguments run as smoothly as possible.  That said, the question that can be asked here is what Kant has attempted to show and what are the consequences of his overarching thesis.  The goal of the antinomies is to show the flaw of rational metaphysics.  Specifically, this dichotomy in cosmological arguments between trying to find a finite source to explain different aspects of the universe, and letting things run unchecked out to infinity.  In instances of the former we end up having to posit weird metaphysical entities to halt lines causation or expansions of space and time; and with the latter we end up in a limitless world where nothing seems to end.  So then, how do we escape this conundrum?  Kant believes the answer is transcendental idealism.  With transcendental idealism a distinction is made between appearances and things-in-themselves that are not present in the antinomies.  Those arguments above are not concerned with the appearances of space and time, or causation; rather they are trying to figure out the nature of those things as real entities or things-in-themselves.  What Kant offers is a way to distinguish between those things we can argue about (the phenomenal world) and those we can say nothing about (the noumenal realm).  Thus it is not a question of the finite or infinite nature of space and time, but a question of in what way they appear to us quite separately from how they are in-themselves, and the same can be said of the rest.  As Kant tells us in § VII on the critical discussion of the cosmological conflict, “If the world is a whole existing in itself, then it is either finite or infinite.  Now the first as well as the second alternative is false…Thus it is also false that the world…is a whole existing in itself.  From which it follows that appearances in general are nothing outside our representations, which is just what we mean by their transcendental ideality.” (B534/B535)


Kant, Immanuel, Paul Guyer, and Allen W. Wood.Critique of Pure Reason. New York: Cambridge UP, 1998.

Guyer, Paul ed. The Cambridge Companion to Kant’s Critique of Pure Reason. New York: Cambridge UP, 2010


Have something to say?

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: