In Kant's 1st Critique, The Critique of Pure Reason, he employs four so-called "antinomies" to show the futility of using reason to answer certain unanswerable metaphysical questions: namely is the universe limited or limitless, does time have a beginning, is space infinitely divisible, are we free and is their extrinsic intelligence in the universe (eg God). What Kant does is that with each one of these debates he actually proves both sides. In other words, he starts by proving both that the universe is limited and that the universe is limitless, showing that both sides can be logically proven. Interestingly, Kant proves both sides of the antinomies with apagogic arguments, namely indirect arguments, using reductio ad absurdums. For example, to prove that time has no beginning he says, if time had a beginning, it must have been preceded by an "empty time" (a non-time before time). But how could time have emerged out of this "empty time"? Thus, time must be without beginning. But then he says, but if we assume that time has no beginning, then we're led to the assumption that it retreats into the past infinitely, which means it's taken infinite time to get to the present. But how could we possible pass through all this infinite time to get to the present? (Personally I'm not convinced by this latter argument, but let's overlook it for now).
But the really odd one of the four antinomies is the third one, about freedom. On the one hand, there is no freedom, then all events are part of a causal chain of cause and effect, whereby each event is caused by a previous, caused by a previous, caused by a previous, ad infinitum. The explicit problem he presents with this is that it prevents us from fully determining the cause of any event, because we can't determine every antecedent cause and cause of that cause and cause of that cause, etc. On the other hand, for the other side of the antinomy, he refutes the possibility of freedom. He says that if there are free acts, then these acts must occur outside the causal chain, which means that we can't understand them using our understand by means of uniform laws. Thus, we really can't have experience of free acts.
In both cases, the argument against relies on this idea of us being able to have experience. It is somewhat sensible because the larger goal of the antinomies is the refutation of "Transcendental realism," which is the idea that the world is at it appears. He wants to say that if the world is at it appears, then we should be able to have complete experience of the world. But of course this doesn't follow because we don't see the whole world, but only small pieces of it, meaning it would take infinite time to experience the whole of it. This means that an infinite regress of causes is compatible with transcendental realism. And of course, the other side of the argument doesn't work that well either. I of course, can have experience of freedom, I just may not immediately assume it is free, since I can assume that it's part of a causal chain. The problem with proving freedom through reason is not that both sides of the argument lead to absurdity, but that neither side leads to absurdity, making the issue irresolvable.
Ultimately, Kant will want to say that freedom is provable by means of practical reason. The argument that he presents in his 2nd Critique, The Critique of Pure Practical Reason, is basically that I have awareness of moral choice via practical reason (thereby assuming I have practical reason to begin with). For me, to have moral choice requires freedom. Therefore I have freedom. Of course, to say that I have accurate awareness of moral choice is a big assumption. Might as well just assume you have freedom and avoid the smoke and mirrors of trying to create the appearance of a legitimate argument.
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'But then he says, but if we assume that time has no beginning,..how could we possible pass through all this infinite time to get to the present? (Personally I'm not convinced by this latter argument, but let's overlook it for now).'
I actually find this issue gripping, and I find Kant's point to be compelling. To review, if the past is infinite then that means the world must have gone through an infinite amount of time in order to reach the present moment; but how could something ever pass through an infinite amount of time? That seems nonsensical.
And, I agree. How can a series (of past events/states) have an end but no beginning? It is perhaps, only a purely philosophical argument, that this is inconceivable, but nevertheless, I think it is.
However, the reply that this is only a purely philosophical argument does remain. Perhaps we can tolerate self-contradictory concepts. It may, indeed, seem harder to tolerate what Kant is selling here -- the superficial gloss on that being something like that time and space are 'subjective', or, better, are not anything more than forms of experience. What Kant calls 'My doctrine of the ideality of space and of time..' I can't say enough here, probably, to make this seem likeable to many.
However, though you may declare the world infinite as to space and time, you cannot do it and say that your assertion is contained in experience. You haven't got an experience of an infinite time elapsed. This is a mere idea, as it were. Then, can a 'quantity of' the world, exist 'in the world itself', apart from all experience? This contradicts the notion of a world of sense, --a complex of the appearances whose existence and connection occur only in experience. It is the concept of an absolutely existing
world of sense, that is, for Kant, self-contradictory. the solution of the problem concerning its
'quantity' is always false.
I like to consider what may seem an easy question, as an analogy. It might seem like you can ask a physicist on this one, or go to NASA website, easily google the answer. How many stars are there? And, there are assertions to be found, about how many stars there are in the *visible* universe, which is a sphere, in which we can be found at the center. It's kind of a reversal of the copernican revolution. Like has traveled only so far, since the big bang, so in principle, we can see only so far, when we look into the sky, and there are a finite number of stars in the sky. But, what is to be found, further out than that? Green cheese? No, one speculates confidently that there are more stars/galaxies/etc. out there, beyond the 'visible' universe. And, furthermore, in the future, we'll be able to see them too. Then, how many stars, total, are there? It's hard to say, but is it at least easy to say whether the quantity of stars is finite or infinite? What would it even mean to say that there are an infinite number of stars? In that case, some simple calculations of probability would yield the point that there are an infinite number of stars that are orbited by planets that are like the planets in our solar system, including an Earth with a moon, and even, the same constellations in the sky. This merely an unlikely coincidence. In other words, it would happen an infinite number of times. And if life on earth is a coincidence, then perhaps there are an infinite number of you out there. I don't make this claim, I merely find that this would be entailed, if there are an infinite number of stars -- are there really an infinite number of things that can happen, or only a finite number? Then each thing that can happen would be currently happening in an infinite number of places right now. An infinite number of stars seems to mean an infinite number of everything conceivable, as well. So, maybe the universe is not infinite. But, it's also not finite. Does it have an edge? What is its shape? Maybe you have some answers that you prefer, here..?
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