Chapter 3: The Antinomy of Pure Reason
I found this chapter to be more challenging than the previous two. There are a few areas that I am not confident I fully understand. I need to let these ideas digest before raising any questions, so only the summary is given.
Summary:
Kant uses the Antinomies to demonstrate how reason contradicts itself when thinking about certain questions. He attempts to show that there are two equally compelling but incompatible answers to each question. Kant claims that both answers to each are false and that the questions themselves rely on presuppositions derived from transcendental realism. More importantly, Kant says that the questions naturally arise from the transcendental realistic position, and so if the answers to the questions are all false (leading to a contradiction), then the questions and the presuppositions that ground them (transcendental realism) are also false, which entails that transcendental idealism is true.
Both thesis and antithesis for each question are apagogic. Kant believes that the equal success of each position in refuting each other demonstrates the impossibility of a solution to the conflict that respects the transcendental realistic (dogmatic) assumptions underlying it. These conflicts of reason arise from its demand for an absolute totality of conditions (grounds) for any conditioned (given). This “intellectual categorical imperative” is a logical requirement for a complete justification or explanation for every assertion. Every true proposition must have a ground. Kant claims that problems arise when this logical requirement to “think the whole” is applied to states of affairs, where the totality is the world of space and time.
Only the temporal aspect of the First Antinomy is discussed by Allison in his book. With respect to the world of space and time, Kant says there are two mutually exclusive options when considering its conditions: either there is some first element, limit or beginning, or the inquiry into its conditions extends ad infinitum. These are the thesis and the antithesis, respectively; the temporal world is either finite or infinite.
Allison emphasizes that Kant is focused on the world, and not space and time themselves. The world, according to Kant, is “the object of all possible experience”; it is not merely the whole of representation, but the actual representation of the whole as a united totality. It is not just the thought of an aggregate of items, but the thought of these items as constituting a whole (
Ganze).
The thesis (for the finitude of the world) is broken down by Allison into six steps:
1.) Assume the world has no beginning in time.
2.) It follows that up to the present, an eternity has elapsed.
3.) This means an infinite number of successive events has occurred, i.e. an infinite series has been completed.
4.) According to the “transcendental concept of infinitude”, an infinite series can never be completed through successive synthesis.
5.) Therefore the concept of an infinite series of events in the world that have passed away (been completed) is self-contradictory.
6.) So there must have been a beginning of the world in time, a first event.
Allison discusses various critiques of this argument, raised by philosophers like Russell and Stawson. He provides responses to these critiques, and while the issues discussed might be interesting to some, I was not particularly curious about them but was more interested in the later things that Allison brings up.
In the Second Antinomy, Kant distinguishes between a
totum syntheticum and a
totum analyticum. A totum syntheticum is a whole that presupposes its parts. The question of whether a totum syntheticum is possible is equivalent to the question of whether a complete collection of its parts is conceivable. A totum analyticum is a whole, the parts of which are only conceivable with reference to that whole. Space and time are tota analytica, but the material universe in space and time is conceived as a totum syntheticum.
The alleged contradiction of the infinitistic position is in its application of the concept of infinite to the material universe. Since it is a totum syntheticum, the thought of a complete enumeration or synthesis of its parts contradicts the thought of the inexhaustibility of the infinite. Thus there are two incompatible rules for thinking the same object, amounting to a contradiction. Because the world is taken to be a totum syntheticum, it cannot be a series extending infinitely into the past, but instead it must have a first moment.
However, the presupposition here is that the world is a totum syntheticum. This is the transcendental realist assumption that is rejected by transcendental idealism.
The antithesis asserts that the world can have no beginning in time and no limit in space. Allison breaks it down as follows:
1.) Assume the world has a beginning in time.
2.) The concept of a temporal beginning presupposes a preceding time before the thing exists.
3.) Therefore it is necessary to think of an empty time before the world existed.
4.) But such points of time cannot be distinguished from one another.
5.) A world cannot meaningfully be said to have come into existence at one time rather than another time if both times are empty.
6.) So we cannot meaningfully say the world came into being in time at all, therefore the world is infinite with respect to past time.
Step 6 is a non-sequitur and Kant recognizes it as such, but the point does follow given the fact that the world must be either finite or infinite.
As with the thesis, Allison discusses objections that have been raised by people like Strawson and Bennett. But again, as it’s clear throughout the chapter, even with the rebuttals given by Allison, neither the thesis nor the antithesis are convincingly sound. I think they are less important to the overall understanding of Kant’s transcendental idealism, so I won’t discuss them much here.
To summarize though, Allison says that the conjunction of a first event with a first time is incoherent. An event is defined as a change of state of a thing in time, so the first event designates the earliest change to have occurred in the universe. The problem is that if the first event occurred at the first time, there was no prior state in which the thing existed. An event not preceded by a time in which the world was in a different state is incoherent. Allison says that “it is a condition of the possibility of conceiving of a change of a thing in time that we are able to contrast the state of a thing at an earlier with its state at a later time.” We can say that time began with creation, but we cannot meaningfully claim that creation occurred at the first time.
Allison ends the chapter by focusing on what the consequences are for transcendental idealism with respect to the Antinomies. Because the conflict between the two positions is based on a “transcendental illusion”, it is “merely dialectical”. The conception of an absolute totality of conditions that constitutes the world in itself violates the rules of empirical synthesis. An experience of an infinite space or elapsed time, or a boundary of either, is impossible.
All forms of transcendental realism, according to Kant, must regard the absolute totality of conditions for a state of affairs as constituting a world-in-itself, “in-itself” meaning the independence of this world so conceived from the conditions of empirical synthesis. It is logically committed to the proposition that the world (the sum of all appearances) is a whole existing in itself, but it forgets the conditions of experience in which this world is given. The regulative Idea of totality, which is grounded in the intellectual categorical imperative, is conflated with the thought of an actual object (the world) - and this is the transcendental illusion.
Kant says:
“From this antinomy we can, however, obtain, not indeed a dogmatic, but a critical and doctrinal advantage. It affords indirect proof of the transcendental ideality of appearances - a proof which ought to convince any who may not be satisfied by the direct proof given in the Transcendental Aesthetic. This proof would consist in the following dilemma. If the world is a whole existing in itself, it is either finite or infinite. But both alternatives are false (as shown in the proofs of the antithesis and thesis respectively). It is therefore also false that the world (the sum of all appearances) is a whole existing in itself. From this it then follows that appearances in general are nothing outside our representations - which is just what it meant by their transcendental ideality.” — Kant
The argument here contains two suppressed premises: that the antecedent proposition (the world is a whole existing in itself, a totum syntheticum) is entailed by transcendental realism, and that transcendental realism and transcendental idealism are mutually exclusive and exhaustive positions. The negation of the antecedent entails the negation of transcendental realism, which entails the affirmation of transcendental idealism.