Kant's Conflicts (and Resolutions) of the Transcendental Ideas


In The Antinomy of Pure Reason, Immanuel Kant takes on some long-standing unresolved problems of philosophy. Does the world have a beginning? Is it bounded in space? Is substance infinitely divisible, or is it atomic? Are there causes through freedom? Is there a necessary being? The rationalist and empiricist camps each seemed to have clinching proof of its own views on these matters---yet the views of one side directly opposed those of the other. Kant took advantage of this debate by setting down side-by-side the most unassailable proofs of each faction---and, for each pair of opposed theories, either demolishing both statements, or showing that the opposed theses were actually compatible.

The extent of the world

The first Antinomy deals with the extent of time and space. According to the thesis, The world has a beginning in time, and in space it is also enclosed by boundaries (B454). The boundedness of time is supported with an argument from the impossibility of infinite descent: ``the infinity of a series consists precisely in the fact that it can never be completed through a successive synthesis'' (B454). Since an infinite series of past states could never be synthesised, they cannot make up the whole that is the world. Hence, the argument goes, time is finite. A similar argument demonstrates the boundedness of space: if space were not bounded, we could only think of the totality of space through an infinite synthesis; but then ``in the enumeration of all coexisting things, and infinite time would have elapsed, which is impossible''.

The antithesis of this statement is that ``The world has no beginning and no bounds in space, but is infinite with regard to both time and space'' (B455). If the world had a beginning in time, there would be a point in time preceding the universe. However, ``no arising of any sort of thing is possible in an empty time, because no part of such a time has . . . any distinguishing condition of its existence rather than its non-existence'' (B455). That is to say, the universe could not arise in time, because there would be nothing to distinguish the universe's existence from its non-existence. Likewise, the boundedness of the world in space is disproved by considering what lies beyond it. If the universe sits within a larger space, it must be related to space itself. Since there is nothing outside the universe that could ground intuition, there is ``no correlate of the world to which the world could stand in relation'' (B457). Hence ``the relation of the world to empty space would be a relation of the world to no object'' (B457), and the boundedness of the world would be nothing.

According the ``System of cosmological ideas'', the first antinomy concerns the ``Absolute completeness of the composition of a given whole of all appearances.'' (B443). A marginal note in Kant's copy of the Critique expands on this: ```Absolute totality' signifies the totality of the manifold of a thing in itself and is something contradictory in respect of appearances as mere representations'' (A417). This is expounded further in the remark on the antithesis. According to Kant, ``space taken absolutely (simply by itself) alone cannot occur as something determining the existence of things'' (B459), and space ``may well be bounded by appearances, but appearances cannot be bounded by an empty space outside themselves'' (B460-461). Here is the beginning of a resolution of the paradox.

The basic form of the solution to the first antinomy comes in ``The regulative principle of pure reason''. If we are given the whole in intuition, we can thereby regress infinitely. However, if we are merely given a single member of a series, ``only an indeterminate kind of regress (in indefinitum) takes place'' (B540). the full solution comes in Section IX, ``On the empirical se of the regulative principle]''. According to this section, ``in the empirical regress there can be encountered no experience of an absolute boundary'' (B545). The world is not infinite because the empirical concept of infinity is ``absolutely impossible in regard to the world as an object of sense'' (B548). Likewise, the world is not bounded because ``an absolute boundary is likewise empirically impossible'' (B548). Kant's final answer is that ``the world of sense has no absolute magnitudes'' (B549). Thus Kant shows both the rationalists, with their bounded world; and the empiricists, with their infinite world, to be wrong. His solution, however, leans much closer to the empiricist view: ``infinite'' is simply changed to ``indefinite''


The second Antinomy, like the first, is a ``mathematical-transcendental idea'' (B556). It deals with the divisibility of substance. The thesis states that ``Every composite substance in the world consists of simple parts, and nothing exists anywhere except the simple or what is composed of simples'' (B462). It is opposed to the antithesis, that ``No composite thing in the world consists of simple parts, and nowhere in it does there exist anything simple'' (B463). The thesis holds, with the atomists, that there is a limit to the division of matter; Kant refers to Leibniz in calling this ``the dialectical principle of monadology'' (B470). The second, ``for which the ground of proof is merely mathematical'' (B467), claims that space and matter are infinitely divisible.

In Kant's architectonic system, this conflict concerns the idea of ``The absolute completeness of the division of a given whole in appearance'' (B433). The regulation of this idea is given in part II of Section IX of the Antinomy. A composite whole is a ``conditioned'', and its parts are its conditions. This, in dividing the whole, we perform ``a regress in the series of these conditions'' (B551). Kant concludes that, just like the regress associated with the first antinomy, we must consider the regress indefinite but not infinite. That one can decompose objects to infinity ``is something that cannot be thought at all'' (B554); an infinite regress is nonsensical. Likewise will we never reach an end to our division; the regress we make towards the quantum discretum is indefinite.


The existence of free causes, subject of the third Conflict of the Transcendental Ideas, is of a different type from the preceding two. Whereas they dealt with ``mathematical . . . synthesis of appearances'' (B556), here we have a dynamical synthesis. Thus Kant will, rather than proving both sides of the argument false (as he did in the first two Conflicts), will ``make good the defects . . . that have been misconstrued on both sides'' (B558), and reconcile the two claims. The opposed theses are themselves quite simple. The first is that ``Causality in accordance with laws of nature is not the only one from which all the appearances of the world can be derived. It is also necessary to assume another causality through freedom in order to explain them'' (B472). The opposed antithesis is that ``There is no freedom, but everything in the world happens solely in accordance with laws of nature''.

The question of freedom and determinism refers, according to the System of Cosmological Ideas, to ``The absolute completeness of the arising of an appearance in general'' (B443). In the Remarks, Kant connects it to the first antinomy. As the first antinomy considered the existence of things ``mathematically first in the world as far as time is concerned'', the third considers things ``dynamically first in the world as far as causality is concerned'' (B477). The empiricist of the antitheses holds that ``no first beginning, whether mathematical or dynamical, need be sought'' (B477).

In Section IX, Kant (as mentioned previously) proposes to unify the two ways of thinking about causality. Kant admits that ``if all causality in the world of sense were mere nature, then . . . the abolition of transcendental freedom would also simultaneously eliminate all practical freedom''. However, Kant argues, we need not abolish transcendental freedom. For ``If appearances were things in themselves . . . then the conditions would always belong to one and the same series as the conditioned'' (B564). Since this is not the case, there are other possibilities: we can ask ``whether every effect in the world must arise either from nature or freedom, or whether instead both, each in a different relation, might be able to take place simultaneously in one and the same occurrence'' (B564). If, as Kant has held throughout the Critique, appearances are ``mere representations connected in accordance with physical laws'' (B565), they ``must have grounds that are not appearances'' (B565). Since these intelligible grounds are not appearances, they are not bound by natural law, and ``The effect can therefore be regarded as free in regard to its intelligible cause'' while at the same time being, in the world of appearance, produced by necessary natural laws. It is important to note that Kant does not prove or claim to prove the existence of freedom, and in fact does not ``even [try] to prove the possibility of freedom'' (B586), for such a task lies outside the scope of pure reason. Rather, he shows that ``nature at least does not conflict with causality through freedom''. This, however, is enough to allow us to think of ourselves as free, and thus consider ourselves as subject to a moral law of the ``ought'' (B575-576).

A necessary cause

Kant's final Conflict of the Transcendental Ideas deals with the existence of a necessary being. The rationalistic thesis states that ``To the world there belongs something that, either as a part of it or as its cause, is an absolutely necessary being'' (B480). Its competing claim is the antithesis that ``There is no absolutely necessary being existing anywhere, either in the world or outside the world as its cause''. This is a question of ``The absolute completeness of the dependence of the existence of the alterable in appearance'' (B443). In the thesis, Kant considers only the cosmological proof of the existence of a necessary being; the ontological proof ``belongs to another principle of reason'' (B484), and will be discussed later, in the Ideal of Pure Reason.

Much like with the previous dynamical principle, that of freedom, Kant does not reach a definite conclusion in his resolution of the fourth antinomy (holding, in fact, that such a definite conclusion is impossible). Rather, he establishes that ``the entire series [of cause and effect] could be grounded in some intelligible being``. Two things are important to note here. First of all, the being (whom we shall henceforth call ``God'') does not exist within the world of sense; for if God did, e would be ``subjected to the law of the contingency and dependence of all appearances'' (B589). Secondly, for such a being we cannot prove necessary or even possible existence; we can only show (as we did with freedom) that God's existence is compatible with the contingency of appearance. Thus Kant has made room for faith by clearing out the weeds of specious transcendent metaphysics.


It must be said that Kant's resolution of the first two Conflicts is not particularly satisfying. He sets the bounded finite regress of the rationalists (whether to atoms, monads, or a creation) against the infinite regress of the empiricists' infinite and infinitely divisible universe; he then claims that both are false, and the truth lies in an indefinite, but not infinite, regress. However, he states in the proof of the thesis of the first antinomy that ``the infinity of a series consists precisely in the fact that it can never be completed through a successive synthesis'' (B454). Does not this perfectly describe his ``indefinite regress''? It seems that, by equivocating on the word ``infinite'', Kant is trying to avoid labelling himself as a pure empiricist.

The second pair of Conflicts, the dynamical ones, show Kant in a much more favourable light. The resolutions of these opposed views is precisely the kind of synthesis of rationalism and empiricism that underlies much of Kant's fame. By showing that metaphysics (regulative metaphysics, as opposed to false transcendent metaphysics) and science do not conflict with free will or with the existence of a deity, Kant opens the way for the peaceful coƫxistence of science and moral theory (it is worth noting that Kant wrote both The Metaphysical Foundations of Nature Science and The Metaphysics of Morals). Kant made religion a matter of faith and science a matter of empirical evidence---to the improvement of both.

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