Rödl on Kant's First Analogy of Experience

Here's how Kant states the First Analogy in the A-edition of KRV, where it is labelled the "Principle of Permanence": "All appearances contain the permanent (substance) as the object itself, and the transitory as its mere determination, that is, as a way in which the object exists." (A182)

In the B-edition of KRV, Kant adds a paragraph to the beginning of this section. In "Logical Form as a Relation to the Object", Sebastian Rödl goes through this paragraph sentence-by-sentence (omitting some parenthetical remarks of Kant's and the final sentence). As Rödl presents it, Kant argues as follows (following the Kemp Smith translation, B224-5; each of these is a single sentence of Kant's German):

1) All appearances are in time; and in it alone, as substratum [...], can either coexistence or succession be represented.

2) Thus the time in which all change of appearances has to be thought, remains and does not change. For it is that in which, and as determinations of which, succession or coexistence can alone be represented.

3) Now time cannot by itself be perceived.

4) Consequently there must be found in the objects of perception, that is, in the appearances, the substratum which represents time in general; and all change or coexistence must, in being apprehended, be perceived in this substratum, and through relation of the appearances to it.

5) But the substratum of all that is real [...] is substance; and all that belongs to existence can be thought only as a determination of substance.

Claim 1) is established by the Transcendental Aesthetic. See II.ss4.1, the first paragraph of the Metaphysical Exposition of the Concept of Time, for the argument; the idea is that we can't build up to a representation of time by first perceiving items as simultaneous or sequential and then abstracting "time" out of those perceptions, since perceiving them in that way requires already seeing them as in time: so the representation of time is a priori, as it is only against the background of time that we can represent things as simultaneous or sequential.

2) follows from 1): if we need to use time as a background against which to represent things as happening simultaneously or sequentially, then representing anything as changing will also require this (as changes are sequential: there is something changed from and something changed to). The background against which change is represented is not itself represented as changing, but is what makes the change intelligible as a change. As this background is time, time must be represented as remaining without change. Rödl here notes that it seems that the way to represent the logical form of thoughts of items in time is as "determinations of time", as Kant says: something like "A exists at t1", with the time "t#" being part of what the thought determines. Simultaneity would then be existence at the same t#, succession would be existence at a later or earlier t#.

3) I am sure Kant argues for somewhere, but I'm not finding a reference at the moment. That time is not itself an empirical intuition follows from the argument for 1), but I don't see where Kant actually makes that inference explicit. But it's a trivial enough point that he hardly needs to: once a distinction is noted between perceiving objects in time and perceiving time itself, it is easy to grant that we do the former and not the latter. (There's a reason we need clocks.) Rödl notes that this simple point poses a problem for the idea that the way to represent an item in time is "A exists at t1": we are trying to articulate the logical form of an appearance of something in time. So if the logical form of an item with a temporal position (simultaneous with, earlier than, or later than some other item) is "A exists at t#", then we cannot be given any items with temporal positions in perception, as perception does not provide us with a time to put for the schematic "t#".

4) From this Kant concludes that "there must be found in the objects of perception [...] the substratum which represents time in general": Rödl puts the point thusly: "what is given in intuition—appearances—as such contain something that represents time in the sense that something is conceived as a determination of time in virtue of being apprehended as a determination of it. Apprehending A and B as determinations of this thing, we apprehend A and B as succeeding, or as simultaneous with, one another." (p.365) The problem with thinking that "A exists at t1" could represent the logical form of a thought of an appearance having a temporal position was that nothing was given which could stand in for a "t#": the solution is to see A as a determination of time (as having a temporal position determined in the thinking of it) in virtue of it being represented as a determination of something which is given in perception, and which functions as a substratum against which simultaneity and succession can be represented.

5) And here Kant draws the conclusion of the Principle of Permanence: All appearances are in time, as the Transcendental Aesthetic established; this entails that they are given to us as simultaneous with one another or earlier or later than one another. To be represented in this way (which they must be to be given to us as appearances in time), there must be found in these appearances something which is grasped as a substratum against which temporal positions can be apprehended, and the various temporal positions must be represented against the background of such a substratum. But such a substratum in appearance is just what the Principle of Permanence calls "substance": there is in all appearances in time a distinction that can be made between substance and "mere determination", which Rödl calls "state". Rödl puts it this way: "We perceive that A succeeds or is simultaneous with B, as we apprehend A and B as determinations of time [by perceiving them thus]. And we apprehend A and B as determinations of time, not by predicating A and B of a time as in “[A exists at t1 and B exists at t2] ”, but by predicating A and B of a substance as in “S was A and is B” . Temporal thought bears a predicative structure. It is not articulated into a time and what is at this time, but rather into a substance and its states. It is in virtue of being thus articulated that a thought distinguishes a time from what is at this time and thus represents its object as temporal. This completes the proof." (p.365) "S was A and is B" represents a substance, 'S', which can be in different states at different times (is now B, was previously A) while remaining the same substance. Thoughts which represent substances as substances exhibit this form: the substance thought of is known as something which can bear contrary predicates at different times, as Aristotle put it; it is a perceptible item which can be seen to change or remain the same at different times. Being able to perceive such items is what enables us to have appearances which have a temporally order internal to how they are given to us: thinking thoughts of the form "S was/is F" is how we can represent some appearances as coming before, after, or alongside others. A Hume-style skeptic about substance needs to make this intelligible by thinking thoughts of the form "A exists at t1" and "B exists at t2", and this cannot be done, as time is not perceptible. Thus the proof against this sort of skepticism is complete: in all appearances substances are given, as the substrate of changeable states.

Rödl continues on to note a few things from the later pages of the Analogy, but the impression given is that the rest is a mop-up operation: the important work is already done in that first five sentences. There is a small puzzle about this, given that these sentences were added in the B-edition, and replaced a short section that doesn't contain this argument. But I think it's plausible that the argument Kant puts more clearly in those five sentences can be found in the first few paragraphs of the A-version Analogy, spread out more widely and unclearly.

There are two more puzzling things about Rödl's handling of the First Analogy. One is that it might seem that Rödl's way of handling perception of time-positions can't handle the relative positions of states of distinct substances. I will handle this indirectly, by first looking at something Rödl points out. It might be thought that one advantage of representing temporal thought by "A exists at t#" is that the various numbers which slot in for '#' will all line up of themselves: t1 is before t2, which is before t3, etc. But this is an illusion: "the things to which “t1” and “t2” refer, and the unity of these, cannot be perceived. Here nothing satisfies “the condition of the empirical unity of time” (A 188/B 231). By contrast, in “S was A and now is B”, there is no need to connect two things determined by A and B respectively, for there is only one thing, the substance, determined by both. Its unity represents the unity of time. In this way is the “condition of the empirical unity of time” satisfied." (p.366) That is, the attempt to represent temporal thought by "A exists at t1" and "B exists at t2" etc. fails to satisfy a demand established by the Transcendental Aesthetic: there is only one time, and all times are limitations of it. There is nothing in the representation of temporal appearances by "A exists at t#" which guarantees that everything which stands in for "t#" will be part of a single time. Rödl's way does meet this demand: If S was A and is now B, this can only happen in a single time through which S persists, as is represented by the single symbol 'S' in the notation.

Now, what does that have to do with the following worry: Rödl's way can't handle "S is A" and "P is B" being simultaneous, since those two thoughts don't share a substance? Here I think I see why Rödl talks of "states" and not "properties" or "determinations": it is tempting to think that there is something special about monadic properties or determinations, but it is much less tempting to think this about states. The 'A' in "S is A" can perfectly well be "near the P which is B"; this is a state a substance can be in, and the thought of it includes the time-determination of the other substance, and represents the empirical unity of the times in which these substances exist. Here I am speculating as to how Rödl handles this question; it seems like something he should address, but I haven't read anything where he takes it up. But I don't see any reason my way wouldn't do fine for him: relational states are perfectly good states, and an appearance of multiple substances in relational states will satisfy Kant's demand to respect the empirical unity of time. (The Transcendental Aesthetic can, I think, already be taken to have shown that all appearances will be related in a single time; it will thus not be necessary to further guarantee that all states of substances will be so related, as these are merely a species of the genus "appearance". That is to say, I do not need to establish that all substances will stand in relational states to one another which determine their time-relations; the Aesthetic does the needed work. What is needed is only to provide a way of presenting substances in thought which does not violate the condition of the empirical unity of time, as "A exists at t#" did. Provided that substances are in fact related to one another in time, polyadic state-variables represent them as in a single time.)

There is another puzzling thing about Rödl's way of handling the First Analogy. The five-sentence proof from Kant he looks at is only in the B-edition, but he only presents the A-edition's statement of the Principle of Permanence. Related to this, he does not discuss the last sentence of the paragraph added to the B-edition: "And as it is thus unchangeable in its existence, its quantity in nature can be neither increased nor diminished." This sentence goes along with the B-edition statement of the (slightly renamed) "Principle of Permanence of Substance", which says "In all change of appearances substance is permanent; its quantum in nature is neither increased nor diminished."

Rödl mentions this sentence only in a footnote: "We disregard the last sentence of the proof (“Da diese also im Dasein nicht wechseln kann, so kann ihr Quantum in der Natur auch weder vermehrt noch vermindert werden.”), which does not pertain to anything stated in the First Analogy in the A-edition. It is a further thought, with its own difficulties, which lie beyond the scope of this essay." (p.369)

Now, it is curious that Kant changes the statements of the principles of the Analogies in the B-edition. But he leaves so much of the argumentation unchanged in these sections that it seems hard to deny that he thought he merely reworded them, and left their substance unchanged. But I think Rödl is simply right about this much: Nothing in the First Analogy in the A-edition supports the claim that the quantity of substance in nature is constant. Substances are things which can change in various ways while remaining the same substances; Kant tells us nothing here about why "quantity in nature" is something unchangeable. More problematically, I don't think Kant has given a sense to "quantum" here: Does he mean that substance in nature does not change in total mass, or in total energy, or in total extension, or in some other quantity measured in some other way? There are many quantities of substance in nature which do change: the number of dinosaurs is a quantity in nature. As far as I've been able to tell, at this point in the Transcendental Logic Kant has no grounds whatsoever for speaking of a single quantity of any sort which is constant for all substance at all times: the Principle of Permanence is entirely compatible with an Aristotelian world of many finite substances with different natures and different ways of being. (The only thing I can find which can even pretend to be an argument otherwise is the Anticipations of Perception, with its talk of intensive magnitudes of reality -- but this section also does not establish that there is a single scale of reality-magnitude, but only that any reality given in sensation is given in a scaleable way.)

Here I suspect Kant changed the B-edition of KRV to make it line up more smoothly with his physics, which he had in the meantime laid a groundwork for in "Metaphysical Foundations of Natural Science". But this sort of move is illicit, by Kant's own standards: principles of a special science such as physics are not established before the System of Principles of the Pure Understanding, as these pure principles are used in determining the principles of the special sciences (which are partly empirical: in MFoNS Kant relies on experience for the claim that bodies have weight, if memory serves). If Kant hasn't established that the sort of substance which must be found in the appearances to make experience possible is the kind his preferred empirical science talks about, he shouldn't pretend otherwise: and viewed from our later vantage-point, we should feel welcome to jettison the supposed necessity of Kant's Newtonianish physics, and feel no compulsion at all to read it back into the Analogies -- even if Kant himself did this while revising the B-edition. It is only Kantian for us to attempt to understand the philosopher better than he understood himself.