Kant’s Third Analogy: On the Coexistence (or Dynamic Community) of Substances

An experience many readers have doubtless had going through the pages of the Critique of Pure Reason is that Kant often later clarifies ideas he has presented in earlier sections. This impression may be due to Kant’s way of proceeding. He begins with the most general (as well as primary) concepts before proceeding to discuss their application. To a certain extent, the Critique may be reminiscent of reading Spinoza’s Ethics in this respect. But it may also be similar to getting lost in the woods before finding a way out: the simultaneous breadth and precision of his system building often yields hazy doubts for many readers amid an unfolding series of revelations. Nevertheless, the systematicity of the Critique is one of its most extraordinary features, and surely reflects the aspirations and even idealism toward system building of his age.

Perhaps the most important general topic subject to ongoing analytical resolution is his discussion of transcendental idealism underlying his “Copernican revolution.” Ultimately, he is attempting to show that a transcendental approach to understanding reality may be taken on as a way of overcoming the skeptical arguments leveled against the very attempt to understand the world about us that arose in the lineage of empiricist thinkers. The Third Analogy is an example of a section of the Critique where he begins to face that challenge more directly.

Contents:

1. Kant’s Use of Reductio Ad Absurdum to Arrive at Transcendental Principles
   • An Example of RAA in Locke’s Essay Concerning Human Understanding
   • For Those Interested in the Problem of Lockean Substance
   • Kant’s Use of RAA
   • Substituting T for E
2. Kantian “Objective Reality”
3. The Way Up/Down

Kant’s Use of Reductio Ad Absurdum to Arrive at Transcendental Principles

RAA (an abbreviation used for the reductio ad absurdum technique in symbolic logic) involves an attempt to deny the veracity of a particular claim by showing that what follows from it is absurd. In more procedural terms, it involves beginning with a claim one wishes to argue against as the premise of an argument in order to draw ridiculous, obviously false conclusions that necessarily follow. From this result, it can be claimed with some warrant that the premise is itself questionable because of the way it conflicts with other commonly held beliefs that are regarded as having greater soundness than the premise one wishes to attack. What a successful use of RAA accomplishes, is in effect, the creation of a dilemma in the reader’s mind that will be favorable to the falsification of one claim in favor of another: either (a) the premise one wishes to argue against is true and what necessarily follows from it is absurd or (b) the conclusion is true and the premise is false. If the conclusion appears more obviously true than the premise under attack, then some warrant can be given for considering it false. (An example of RAA Locke’s Essay follows. Those who wish to proceed directly to the argument of the Third Analogy may do so by clicking here)

An Example of RAA in Locke’s Essay Concerning Human Understanding

One prominent example appears in Locke’s Essay in II.xxiii.23 where we find him arguing against the Cartesian position that the “substance” of complex substances is their extension in space. Such a claim, the one Locke argues against, follows from Descartes’ substance dualism, according to which he recognizes two fundamental kinds of entities, those whose substance is extended (objects existing in space and time) and those without extension, our souls. This kind of answer may seem straightforward enough. But the claim that what makes material substances material substances as such is the fact that they are extended in space brings up the problem of what accounts for their extension.

One answer was that it that it is the influence of external pressure upon each individual material substance, imagined being exerted upon material substances by further substantial particles in the surrounding air. But this solution brings up the problem of what can be said to account for the coherence of the surrounding particles themselves. If the answer is a further set of particles, the problem is not solved but only reiterated at a more microscopic level. The solution, leads, in other words, to a regress that leaves the original problem unresolved. For our present purposes, it may be noticed that we have a premise Locke wished to argue against and an absurd conclusion that follows necessarily from it.

This example of RAA can be restated in outline as follows: (1) the premises: “substance” is really the extension of each material object, the amount of space it takes up at any particular time and (2) coherence of the extension of such substances can be explained by the action of particles in the surrounding air upon it. However, (3) this solution leads to an infinite regress (the conclusion). This sets up a dilemma: either the regress does not follow or one or both of the two premises is false. It is easier to point to the second premise than the first as a candidate for falsification, but if this is done, it immediately places the first in doubt since it forces the re-emergence of the original problem, “What accounts for the coherence of substance?”

Kant’s Use of RAA

Kant’s way of proceeding in the Third Analogy follows a suitably predictable pattern when it is assessed in terms of RAA. It may be stated in a shorthand form as follows: (1) Kant gives us what might be called an “empiricist thesis” (E), the thesis he intends to argue against; then, (2) he reveals the absurd consequence’s that conflict with the basic way in which we experience the world.

Let’s see how this works in practice. In the Third Analogy, the empiricist thesis Kant wishes to argue against emerges in B258 (at the point where A212 begins) as follows:

1. E: In a manifold of substances, each substance must be considered to be completely causally isolated from any other substance. (i.e. no one substance “acts on any other and receives reciprocal influences in return”).

However, as he points out,

2. It follows that “their coexistence would not be an object of a possible perception and that the existence of one [substance] could not lead by any path of empirical synthesis to the existence of another.” [RAA]

Two options are possible: either 1 is false or 2, but both cannot be true as long as 2 necessarily follows from 1. For Kant, accepting the conclusion leads to the denial of the empiricist’s premise. This provides the reader with a rationale for giving up E in favor of a transcendental thesis that states the conditions necessary for the possibility of the simultaneous coexistence of any two substances in time.

Substituting T for E

In order to fully appreciate Kant’s transcendental move, his point about coexistence (see 2 above) should be briefly unpacked before we can move forward. His point is really about our capacity to experience and comprehend simultaneity as such. In the first analogy, his transcendental argument in favor of the reality of substance was aimed at making duration possible: something must exist for a relatively extended period of time in order for our understanding of change to be possible; in the second analogy, his aim was to argue in favor of the necessity of causation if our experience of succession is to have any intelligibility. His argument in the third analogy in favor of the reality of simultaneity/coexistence builds upon the a priori necessity of accepting the reality of duration and succession.

In B257, Kant asks us to consider someone who looks at the moon and then at the earth. Unless we accept the reality of coexistence, our experience of the two must be considered to be disconnected in a fundamental sense: I cannot possibly infer from my perception first of the earth and then the moon their simultaneous existence–or even more bluntly, the possibility of their existence at the same time. I cannot possibly therefore infer from the existence of the moon its causal relationship with the earth and vice versa. Kant’s example is an excellent one for his purposes, since the causal relationship between the two must work both ways, or as he puts it,

There must, therefore, besides the existence of A and B be something through which A determines B, and also reversewise B determines for A, its position in time, because only on this condition can these substances be empirically represented as coexisting.

B259

The “something” Kant has in mind is what he calls a “dynamical community” wherein each substance stands in a causal relationship with another, where each plays a role in determining the properties of another (see B260). If the Newtonian concept of gravity, for example, is thought of as the basis for the dynamical relationship between the earth and moon, the two can be thought of as co-determining not only each other’s position in space, but also in time since the notion of an attractive force between the two only makes sense if they exist at the same time. Furthermore, giving up simultaneity would mean giving up the possibility of a dynamical community between any two objects, leading us to the impossibility of understanding the connectedness of objects in our experience, thus making a unified, coherent conception of our experience impossible.

Kantian “Objective Reality”

Lastly, a word on Kant’s use of the term “objective reality” in this context. In B267-B268 he applies the term not to objects, but to concepts. Those concepts that make a coherent experience of reality possible contain the possibility of being coherently related to some object in the world, to an object or series of objects that appear in our actual experience. The concept of simultaneity is one such concept. Now, if such a concept can also be tied to the form of our experience in general, it can be considered an a priori condition, necessary for such an experience to occur. Here is Kant’s description of such a condition:

The impossibility [of enclosing a figure with only two straight lines] arises not from the concept in itself, but in connection with its construction in space, that is, from the conditions of space and of its determination. And since these contain a priori in themselves the form of experience in general, they have objective reality; that is, they apply to possible things.

B268

This example shows Kant proceeding toward a transcendental concept. Only on the assumption that the concept in question (such as simultaneity or duration) can be applied to experience in general may it stand as a concept through which the mind can perform any sort of objective synthesis of its experience.

The Way Up/Down

Skeptical arguments that serve to make any such synthesis impossible can be countered by transcendental arguments to the effect that unless we admit concepts such as duration and simultaneity our experience of the world would itself be impossible. This is at any rate Kant’s basic strategy in the Critique. By “experience” he intends us to understand not only our perception of the world, but our capacity to understand it at all. It is in this sense that Kant’s way of proceeding might be seen as analogous to the “way up” Plato describes in relation to his famous allegory of the cave. Kant’s breakthrough was to see that the Forms that make it possible to overcome skepticism are belong to the form our capacity to experience reality itself takes in relation to the objects of our experience.