Kant's First Antinomy: The Beginning of the Universe

The philosopher Immanuel Kant (1724-1804) famously argued that reason is not capable of answering the question of whether the universe began to exist. Kant sought to show this by demonstrating that both the proposition that the universe began to exist and its negation (i.e., the universe did not begin to exist) admit of incontrovertible arguments in their favor, thus implying that reason leads to the conclusion that a proposition (what Kant calls the “thesis”) and its negation (what Kant calls the “antithesis”) are both true. But by the principle of non-contradiction, a proposition and its negation cannot both be true. Kant refers to such paradoxes as antinomies of pure reason. In his Critique of Pure Reason, Kant identifies four such antinomies, the first of which is the one presently under discussion. In trying to answer such cosmological questions by way of pure reason, reason itself, as Kant puts it, “soon falls into such contradictions that it is constrained, in this cosmological field, to desist from any such pretensions” (Critique of Pure Reason, Bk. II, Ch. II, pg. 385). Given the present antinomy, we must conclude that reason itself is bankrupt with respect to answering the question of whether the universe began to exist, even though the question must of logical necessity have an objective answer. As Kant writes,

For although [the respective supporters of both sides of the dispute] have failed to support their contentions by valid grounds of proof, nothing seems to be clearer than that since one of them asserts that the world has a beginning and the other that it has no beginning and is from eternity, one of the two must be in the right. But even if this be so, none the less, since the arguments on both sides are equally clear, it is impossible to decide between them (ibid., Bk. II, Ch. II, Sec. 7, pg. 445-446).

For present purposes, it will not be necessary to consider Kant’s proposed demonstration of the proposition that the universe began to exist (the thesis) since the antinomy only succeeds if contrary propositions admit of demonstrations. Instead, we will focus on Kant’s proposed demonstration that the universe did not begin to exist (the antithesis). We will show why it fails and will have thereby resolved the antinomy. Kant’s “demonstration” of the antithesis from his First Antinomy is as follows:

[L]et us assume that [the world] has a beginning. Since the beginning is an existence which is preceded by a time in which the thing is not, there must have been a preceding time in which the world was not, i.e., an empty time. Now no coming to be of a thing is possible in an empty time, because no part of such a time possesses, as compared with any other, a distinguishing condition of existence rather than of non-existence; and this applies whether the thing is supposed to arise of itself or through some other cause. In the world many series of things can, indeed, begin; but the world itself cannot have a beginning, and is therefore infinite in respect of past time (ibid., Bk. II, Ch. II, Sec. 2, pg. 397).

The argument as it stands is predicated on two primary issues: what it means to begin to exist and some version of the principle of sufficient reason. Let us begin with the former. Kant’s analysis of what it means to begin to exist seems to be something along the following lines: x begins to exist if it exists at some time t, there exists a time prior to t at which x does not exist, and x does not exist at any prior time t’ < t. Even if this is not precisely how Kant would want to cash out the analysis, at the very least, a clear necessary condition for what it means to begin to exist for Kant is the following: x begins to exist only if it exists at t and there exists a t’ < t at which x does not exist. On this analysis, the idea that time itself has a beginning is incoherent because it would entail that there exists a time at which time does not exist.

This puzzle is resolved by an alternative, more adequate, and less prejudicial analysis of what it means to begin to exist. William Lane Craig offers such an analysis as follows:

1. x begins to exist at t iff [if and only if] x comes into being at t.
2. x comes into being at t iff [if and only if] (i) x exists at t, and the actual world includes no state of affairs in which x exists timelessly, (ii) t is either the first time at which x exists or is separated from any t’ < t at which x existed by an interval during which x does not exist, and (iii) x’s existing at t is a tensed fact (The Blackwell Companion, pp. 184).

A more simplistic analysis can be given as follows: x begins to exist at t if x exists at t and there is no time t’ < t at which x existed. On such an analysis, it is perfectly coherent to say that time itself began to exist. For we can say that time began at its first moment, t. Time exists at this first moment t, and there is no time t’ < t at which time existed. Hence, time began to exist. So, the first step in Kant’s argument is false, and this blocks the inference to there being an “empty time” from which the universe sprang into being.

Although this suffices to rebut Kant’s argument, it will be instructive to consider the second part of his argument anyway. The second part of the argument, as aforementioned, appeals to some version of the principle of sufficient reason (henceforth, PSR). The basic idea of the PSR is that everything that is must have some sufficient reason for, or explanation of, why it is. The literature on the PSR is vast, and we will not delve into it here; rather, we will keep things at a very basic level, which suffices for present purposes. Kant’s argument is that if the universe began to exist in empty time, then there would be no sufficient reason for why it began when it did rather than at some other time. But then, this is a violation of the PSR. Hence, that the universe began to exist a finite time ago must be false.

From an explicitly theistic perspective, the problem can be posed in the form of the following question: Why did God not create the universe sooner? This question has been wrestled with by various thinkers over the centuries, including St. Augustine and G.W. Leibniz (cf. Time and Eternity, pg. 229-230). St. Augustine succinctly expresses his thoughts on this question as follows:

But if the roving thought of any one should wander through the images of bygone time, and wonder that You, the God Almighty, and All-creating, and All-sustaining, the Architect of heaven and earth, for innumerable ages refrained from so great a work before You would make it, let him awake and consider that he wonders at false things. For whence could innumerable ages pass by which You did not make, since You are the Author and Creator of all ages? Or what times should those be which were not made by You? Or how should they pass by if they had not been? Since, therefore, You are the Creator of all times, if any time was before You made heaven and earth, why is it said that You refrained from working? For that very time You made, nor could times pass by before You made times. But if before heaven and earth there was no time, why is it asked, What were You doing then? For there was no then when time was not (The Confessions, Bk. XI, Ch. 13).

The question, it seems to me, by the PSR, must have an answer. Yet, it seems that the question cannot have an answer if the universe began to exist at some finite time ago in empty time. Thus, what we ought to conclude is that (i) if the universe began to exist, then empty time could not have existed. William Lane Craig lays out an argument from the PSR to the necessity of time itself being finite (which implies that empty time could not have existed) as follows:

1. If the past is infinite, then at t God delayed creating until t + n.
2. If at t God delayed creating until t + n, then He must have had a good [i.e., sufficient] reason for doing so.
3. If the past is infinite, God cannot have had a good [i.e., sufficient] reason for delaying at t creating until t + n.
4. Therefore, if the past is infinite, God must have had a good [i.e., sufficient] reason for delaying at t, and God cannot have had a good [i.e., sufficient] reason for delaying at t.
5. Therefore, the past is not infinite (Time and Eternity, pg. 230).

Now, if the past cannot be infinite, then empty time could not have existed. Hence, since the past cannot be infinite, if the universe began to exist, then empty time could not have existed. Hence, (i) is established. Kant would agree with this conditional. But he would also affirm the conditional that (ii) if the universe began to exist, then empty time must have existed. Hence, the universe having a beginning would imply a logical contradiction. Therefore, Kant concludes, the universe cannot have had a beginning but must rather have an infinite past. But we’ve already seen that Kant’s argument for (ii) fails as it relies on an inadequate and prejudicial analysis of what it means to begin to exist. Hence, there is no contradiction and thus no antinomy. Therefore, Kant’s First Antinomy has been dissolved since his alleged demonstration of the antithesis fails. Kant has therefore failed to show that reason is altogether incapable of answering the question of whether the universe began to exist.