2. Allison and the paragraph added to B

In support of his interpretation, Allison cites a paragraph added to the beginning of the First Analogy in the B edition of Kant’s Kritik der reinen Vernunft.Footnote ⁷ For the sake of convenience, I will follow his procedure in the first edition of Kant’s Transcendental Idealism (KTI 1) and number each sentence:

According to Allison (Reference Allison2004: 237), the argument of this paragraph falls into four parts. The first consists of (1)–(4) and ‘contends that something at least relatively persisting is required as a substratum or backdrop in relation to which change can be experienced’. The second consists of (5) and ‘argues that every change of appearances must be regarded as the change of state of this substratum’. The third consists of (6) and ‘asserts that this substratum must be absolutely, not simply relatively, persistent’. The fourth consists of (7) and ‘maintains that the quantity of this persisting substratum remains constant through all change’.

On this account, absolute persistence does not enter until (6). Upon close examination, however, it seems present in (4). Later in the First Analogy, after all, Kant equates change with arising and perishing.Footnote ⁹ Assuming that he does the same here, his meaning in (2) is that the time in which all arising and perishing of appearances must be thought does not arise or perish. The implication of (2), it thus seems, is that the time in question has not (ever) arisen and will not (ever) perish. The time in question and time in general are the same. When Kant infers in (4) that there must be a substrate in the appearances which represents time in general, it thus seems, he means that there must be a substrate in the appearances which has not (ever) arisen and will not (ever) perish, i.e. a substrate which is absolutely persistent.

On this account, moreover, the meaning of (5) is that every change of appearances must be regarded as the change of state of the backdrop or substrate which represents time in general. This does not seem like a plausible construal of (5). What that sentence states is that ‘the substrate of everything real … is substance, in which everything that belongs to existence must be thought as determination’. It says nothing of change.

Allison’s account of the passage on which he professes to base his interpretation is thus problematic. This may not entail, however, that his whole interpretation is off target. As we shall see in section 4, there are major questions with respect to Kant’s argument in the paragraph at issue. Even if Allison misconstrues parts of that paragraph, I will suggest there, key elements of his interpretation may allow for answers to those questions and thus for understanding of the relevant argument.

3. The gist of the proof that Allison ascribes to Kant

As we have already seen, Allison takes the proof in the paragraph added to B to consist of four parts. The aim of the first is to establish an initial Backdrop Thesis, he holds, while the aim of the second is to establish that every change is an alteration (1983: 203). The second also presupposes and builds upon the first, he maintains (1983: 201; 2004: 237).

The aim of the second needs further specification. In part, this is due to Allison’s account of what Kant means by a Wechsel (and thus the English term ‘change’). At A187/B230, Kant makes clear that a Wechsel (or change) is an arising or perishing. According to Allison, however, ‘ein Wechsel is the kind of change in which one item is replaced by another’ (Reference Allison1983: 204; Reference Allison2004: 240). Even on his own subsequent account of Kant’s argument, this cannot be correct.Footnote ¹⁰ Even on that account, after all, the claim that every Wechsel is an alteration is supposed to rule out the possibility of arising ex nihilo and/or perishing in nihilum. The claim that every change in which one item is replaced by another is an alteration would not do so.Footnote ¹¹

Perhaps because of his focus on the distinction between replacement change and change of some other sort(s), Allison does not emphasize the distinction that truly matters in his account of this part.Footnote ¹² Here is the start of that account:

If one has successive observations between which one notices some difference, a change takes place in apprehension. From the mere fact that a change takes place in apprehension, Allison thus takes Kant to hold, one cannot infer that a change of the sort with which Kant is concerned has occurred. A change that does not take place merely in apprehension is a change that takes place ‘in the object’. A change of the first sort is merely subjective, one might say, while a change of the second sort is objective. The distinction that truly matters, on Allison’s account of Kant’s proof, is that between these two sorts of change: subjective on the one hand and objective on the other. Kant’s aim in this part, Allison thus actually holds, is to establish that every objective change is an alteration.

Despite all that can be determined from two successive observations between which one has noticed some difference, Allison has just emphasized, one could simply be having successive representations of coexisting states of affairs. His account continues so:

If I experience or so much as believe that I experience the genuine arising or perishing of some x, Allison here takes Kant to hold, the arising or perishing of that x must take place in apprehension and I must represent it as objective. In apprehension, for instance, a house of the sort children build out of blocks is present in apprehension at time t₂ but was not present in apprehension at t₁ (or any earlier time).Footnote ¹³ At least in apprehension, this entails, the house in question has arisen. By itself, however, the fact that the house in question was not present in apprehension at t₁ (or any earlier time) does not entail that it was not in existence at t₁ (or any earlier time) and thus that the arising that has taken place in apprehension was genuine or objective. In order to represent it as such, Allison takes Kant to hold, I must refer the house and something else that was present in apprehension at t₁ (or some earlier time) to some common subject. In order to represent it as such, in other words, I must take the house and something else that was present in apprehension at t₁ (or some earlier time) to be the same subject with different determinations or in different forms. If I do this, however, I perforce view the arising as a mere alteration of something that existed prior to it and still exists when it has taken place.

According to Allison, consequently, Kant subscribes to these claims:

How does Kant get from here to the claim that every objective change is (in fact) an alteration? Allison does not explain but would surely answer on the basis of materials in chapter 2 of KTI 1.Footnote ¹⁴ ‘It is an analytic truth that any object represented must conform to the conditions under which alone it can be represented as an object’, he asserts there (Reference Allison1983: 29). There is a changed point of view involved in the recognition that ‘the cognitive structure of the human mind is the source of certain conditions which must be met by anything that is to be represented as an object by such a mind’, he also claims there (ibid.). This changed point of view brings with it a radically new conception of an object, he then infers: ‘An object is now to be understood as whatever … conforms to the mind’s conditions for the representation of it as an object’ (p. 30). An objective change is an object, he also holds.Footnote ¹⁵ Given these materials, we can discern the following answer to our question at the start of this paragraph:

1. 1. Any objective change represented must conform to the conditions under which alone it can be represented as objective.

2. 2. In order to be represented, an objective change must take place in apprehension.

3. 3. Since this is the case, a condition under which an objective change that takes place in apprehension can alone be represented as objective is a condition under which any objective change can alone be represented as objective.

4. 4. Since an objective change is an object and an object is now to be understood as whatever conforms to the mind’s conditions for the representation of it as an object, an objective change is now to be understood as whatever conforms to the mind’s conditions for the representation of it as objective.

5. 5. The concept involved in the action described in Rep-Change-as-Objective₂ is such a condition.

6. 6. Given Rep-Change-as-Objective₂, nothing that does not conform to this concept is now to be understood as an objective change.

7. 7. Given Rep-Change-as-Objective₂, therefore, every objective change conforms to this concept.

8. 8. This concept is that of an alteration of something that exists prior to it and still exists when it has taken place.

9. 9. Since every objective change conforms to the concept of such an alteration, every objective change is such an alteration.

This completes the second part of the proof that Allison ascribes to Kant. As the reader may have noticed, it does not presuppose or build upon an initial Backdrop Thesis, i.e. a separate and independently established claim that something at least relatively persisting is required to serve as a substratum or backdrop in relation to which change can be experienced.Footnote ¹⁶ Somewhat surprisingly, therefore, the proof in question could simply begin with the part that Allison takes to come second.Footnote ¹⁷

Having established (a) the claim that every objective change is an alteration of something (at least) relatively persistent, maintains Allison, Kant moves in the third part of his proof to (b) the claim that every objective change is an alteration of something absolutely persistent. The requisite argument proceeds by applying (a) to the enduring entities whose necessity has just been established, explains Allison. Take a piece of wood consumed by fire:

Given (a), this is in order. How does it follow, however, that the destruction of the wood is a mere alteration of something absolutely persistent? Kant’s answer, holds Allison, is that the matter we are constrained to presuppose must be identified with substance:

According to (a), every arising or perishing that is objective is an alteration of something that exists prior to it and still exists when it has taken place. For any x, furthermore, it follows from the claim that the arising or perishing of x is such an alteration that x is merely a way in which something else exists.Footnote ¹⁸ Given (a), this entails, anything the arising or perishing of which is objective is a way in which something else exists. For Kant, however, substance cannot be a way in which something else exists.Footnote ¹⁹ For Kant, consequently, it follows from (a) that nothing the arising or perishing of which is objective can be substance. Since the matter of which things are composed must be identified with substance, Allison thus takes him to infer, no arising or perishing of that matter can be objective. For this reason, the matter in question is absolutely persistent and every objective change (including the destruction of the wood) is an alteration of something absolutely persistent.

This completes the third part of the proof that Allison ascribes to Kant. Since nothing the arising or perishing of which is objective can be substance, Allison takes the fourth and final part to maintain, the quantity of substance remains constant through all change.

4. Initial objections of Ward

To the best of my knowledge, the most extensive previous discussion of Allison on the First Analogy is that of Andrew Ward. According to Ward, Allison’s interpretation is shared by such figures as D. P. Dryer and Paul Guyer. In his view, this ‘shared interpretation’ is based wholly on a single passage at A188/B231. For this reason, he holds, its adherents must take this passage to ‘introduce some entirely new … argument into the analogy, incongruously stuck on almost at the end’ (Ward Reference Ward2001: 387). The first thing that must strike the reader upon examination of the relevant passage, he maintains, is that ‘the’ account of it offered by Allison and the other figures in question is ‘most strained’ (p. 388). On Allison’s own admission, he points out, ‘Kant himself contributed to the almost universal misunderstanding of the argument of the First Analogy by his failure to spell out any of this [viz. any part of the shared interpretation]’ (Allison Reference Allison1983: 206; Ward Reference Ward2001: 389; bracketed interpolation by Ward).

In reality, of course, there is no interpretation shared by all of these figures. Allison, as we have seen, takes Kant to be concerned with conditions under which alone we can so much as represent a change that takes place in apprehension as objective. Dryer and Guyer, on the other hand, take him to be concerned with conditions under which alone we can know (as opposed to merely believe) that a succession (or change) that takes place in apprehension is objective.Footnote ²⁰ It is admittedly true, nonetheless, that all of them rely heavily on the passage from A188/B231 and that none of them defend their interpretations of it in great textual detail. Here is the passage:

In both editions of KTI, Allison points to the first sentence of this passage – but only to that sentence – as possible support for his account of the second part of Kant’s proof. In neither edition does he seem especially confident, however. ‘It may not be immediately evident that there is any such argument’ as that which he is about to describe, he confesses in both (Reference Allison1983: 205; Reference Allison2004: 241). Allison’s potential case here is much stronger than he makes it. The problem is his exclusive focus on the first sentence.

The passage concerns conditions under which alone we can perceive arising and perishing. One might take this to involve the representation of arising and perishing that takes place in apprehension as objective. In order to do this, one would then take Kant to assert in the third sentence, one must attach a point of time in which the x that arises was not to that which was already there. In doing the latter, Kant then clearly implies on any reading of the fourth sentence, one connects the arising of this x to things that were in existence before it arose and last (at least) until it is in being. One does so, moreover, in a way that entails that this x is only a determination of those things, i.e. a way in which those things exist.

In hopes of understanding, let us return to the example of a house composed of blocks. To represent the arising of this house as objective, implies Rep-Change-as-Objective₁, one must take the house and something else that was present in apprehension at an earlier time to be the same subject with different determinations or in different forms. Present in apprehension at an earlier time, let us say, was a set of blocks scattered on a flat surface. If one takes the house and the blocks that were scattered to be the same subject (the same set of blocks) in different forms, one takes something to be the case that would rule out the existence of the house at the earlier time. If one does this, it seems natural to say, one attaches a point of time in which the house (at least in one’s own resulting conviction) was not to that (namely the set of blocks) which was already there. In so doing, it also seems natural to say, one connects the arising of the house to things (the relevant blocks) that were in being before it arose and last (at least) until it is in being. The way in which one does this, moreover, entails that the house is only a way in which those things exist, i.e. a determination of those things.

There is thus a striking fit between Rep-Change-as-Objective₁ and the third and fourth sentences of the passage from A188/B231. In view of this fit, Allison need not make the admission upon which Ward pounces – the admission, namely, that Kant fails to spell out any of ‘this’.

Must he nonetheless admit that the passage introduces some entirely new argument into the analogy, incongruously stuck on almost at the end? Not if this would imply that the passage introduces an argument unconnected with what has come before. What the passage actually does, Allison could insist, is reveal at least some of the grounds for crucial but mysterious assertions near the start of the analogy in both its A and B forms. Consider the paragraph that comes second in both and begins with this flourish:

In apprehension, implies Kant in the first sentence of this passage, various elements of the manifold given in or through sensibility are always arising and perishing. To determine that two such elements, as objects of experience (and not merely in apprehension), follow after each other, we must determine that the perishing of the one and the arising of the other are objective. We can never do this, asserts Kant in the second half of the second sentence, where it is not the case that in the manifold something lies at the ground which is persistent. We can also never do this, he asserts in the same portion of that sentence, where it is not the case that the elements in question are merely ways in which the persistent at the ground of the manifold exists.

Kant does not proceed to explain and/or defend these assertions. In the sentence that follows, he simply draws an implication. In the next three, he points out a correspondence between the persistent on the one hand and time itself on the other. In the two after that, he proclaims that being in different parts of the temporal succession receives a magnitude through the persistent alone and provides a ground for that proclamation. The three sentences with which the paragraph then concludes are so closely related to the earlier sentence in which he simply draws an implication that they could (and perhaps should) follow directly upon it. Like that earlier sentence, however, they do not explain and/or defend the assertions with which we are concerned. The last of them is virtually identical to the Principle of Persistence that Kant aims to prove in A and begins with ‘therefore’. The implication, it seems clear, is that the proof of said principle is now complete.

Given their place in the relevant paragraph, the assertions with which we are concerned are presumably essential to that proof. Given the rest of the paragraph, however, they must rest on grounds that Kant has not (at least yet) made explicit. The passage from A188/B231 turns out to be crucial in this regard, Allison could maintain. In order to determine that the arising or perishing of some element of the manifold is objective, after all, we must represent it as objective. Any condition under which we can alone do the latter will thus be a condition under which we can alone do the former. In the relevant passage, Allison could argue, Kant spells out conditions under which we can alone do the latter. In so doing, he could conclude, Kant reveals at least some of the grounds for the assertions with which we are concerned, and thus for crucial assertions near the start of the First Analogy in A.Footnote ²²

As we have seen in section 2, there are major problems with Allison’s account of the paragraph added in B.Footnote ²³ If he were to revise that account, however, he could hold that the passage from A188/B231 plays the same basic role with respect to that paragraph. While sentences (1)–(3) seem in order, he could observe, (4) gives rise to questions. Since time cannot be perceived for itself, asserts Kant in the first half of that sentence, the substrate which represents time in general (überhaupt) must be to be met with in the objects of perception, i.e. the appearances. What substrate which represents time in general? Why must there be such a substrate?

Sentences (6) and (7) presuppose that there is such a substrate, while sentence (5) merely equates the substrate of everything real with substance. If Kant gives any answer(s) to these questions in the paragraph itself, therefore, he must do so in the second half of (4). His answer, in that case, is that all change or being at the same time can be perceived only through the relation of appearances to such a substrate. What does this mean, however, and why should we believe it?

When Kant speaks of change here, Allison could hold, he means arising and perishing that is objective. In the later passage from A188/B231, he could then note, Kant spells out conditions under which alone such arising and perishing can be perceived. Combined with other elements of the proof upon which he takes Kant to rely, the conditions in question entail that the matter of which things are composed must be absolutely persistent. This matter would be a substrate in the objects of perception, i.e. the appearances. It would also represent time in general in the sense that it has never arisen and will never perish. In the passage from A188/B231, Allison could thus conclude, Kant finally reveals some of the grounds for crucial assertions near the start of the First Analogy in B.

5. Further objections of Ward

Ward has two further objections to the ‘shared interpretation’. The first is that the argument ascribed to Kant by its adherents fails to account for the very ability with which they take him to be concerned. The second is that the argument in question would undermine Kant’s own subsequent attempt to prove the causal principle. The first is completely off target in the case of Allison. The second, however, points towards a real challenge.

Here is Ward’s summation of the first:

This question may be relevant in the cases of Dryer and Guyer. According to both of them, after all, Kant is concerned with our (alleged) ability to know (as opposed to merely believe) that there has been an objective change. According to Allison, however, the focus of Kant’s attention is our (indisputable) ability to represent a change that takes place in apprehension as objective.Footnote ²⁴ In order to do this, we need not ‘ascertain’ that two incompatible states belong to the same object. We need merely suppose that they do. Ward’s question is thus irrelevant in the case of Allison.

Now for Ward’s account of the second of these objections:

In a somewhat revised form, this does raise a question for Allison. In the Second Analogy, he holds, Kant is concerned with conditions under which alone we can represent a succession that takes place in apprehension as objective (Reference Allison1983: 221–2; Reference Allison2004: 250–1). In order to do so, he takes Kant to insist there, we must take there to be a cause of that succession (Reference Allison1983: 226; Reference Allison2004: 251). Given what he takes Kant to hold in the First Analogy, this may well seem odd. If one represents a change that takes place in apprehension as objective, one represents a succession that takes place in apprehension as objective. In order to represent this succession as objective, Allison takes Kant to hold in the First Analogy, we must refer the elements involved in it to some common subject. Yet in order to represent this same succession as objective, he then takes Kant to hold in the Second Analogy, we must take it to have a cause. Why would Kant hold both of these things? Why would he take the action invoked in the Second Analogy to be needed?

Allison does not address these questions. According to Béatrice Longuenesse, however, Kant holds that the action invoked in the Second Analogy is a necessary condition of that invoked in the First. ‘We can attribute changing marks to the same … object only if we suppose that there is a ground of change that can be stated according to the form of a hypothetical judgment’, she takes him to insist (Reference Kant and Timmermann1998: 365). To attribute changing marks to the same object is (in Allison’s somewhat different terminology) to refer elements of a succession that takes place in apprehension to some common subject. To suppose that there is a ground of change that can be stated according to the form of a hypothetical judgement is to suppose that there is a cause. In order to answer the questions with which we are presently concerned, therefore, Allison could appeal to the analysis of Longuenesse.

What is the support for that analysis, however? According to Longuenesse, Kant holds that ‘judgments … are assertions under a universal condition’ (Reference Kant and Timmermann1998: 93). ‘Kant inherits the term “condition” from Wolff and his school’, she also maintains. ‘The “sufficient marks” to know the truth or falsity of a judgment are what Wolff calls the condition of the judgment’ (95–6). When one attributes changing marks to the same object, she appears to assume, one makes a judgement, i.e. an assertion under a universal condition. In making such an assertion, however, one assumes the existence of a sufficient ‘mark’ or set of ‘marks’ to know its truth. The only possible such ‘mark’ in the case of one’s attribution of changing marks to the same object, she takes Kant to believe, is a ground of change that can be stated according to the form of a hypothetical judgement.Footnote ²⁵

A fair assessment of this analysis would far exceed the bounds of this paper.Footnote ²⁶ In possible support of it, however, one might mention a puzzle that concerns the Second Analogy alone. In apprehension, let us say, there is a ship at point A and then a ship at point B. In order to represent this succession as objective, Kant repeatedly implies there, we must take there to be something that precedes it upon which the replacement of the one state of affairs (a ship at point A) by the other (a ship at point B) follows in accordance with a rule.Footnote ²⁷ But why would he hold this? A different explanation seems at least equally plausible. Assuming that the ship at point B is very similar to the ship at point A, we may simply take it to be the same ship. If we do so, it seems, we will perforce represent the succession at issue as objective. Kant fully agrees, on the analysis of Longuenesse. Yet in order to take the ship at point A and the ship at point B to be the same ship, Kant holds on that analysis, we must take there to be something upon which the replacement of the one state of affairs (ship at point A) by the other (ship at point B) follows in accordance with a rule. This would be a cause of that replacement and thus of the succession at issue. If on target, therefore, the analysis of Longuenesse does not merely render Allison’s account of the First Analogy compatible with his account of the Second. It also resolves a serious puzzle concerning the Second itself.

6. Problems with the second part of the proof

The interpretation of Allison may thus survive the objections of Ward. Even if it does so, however, there seem to be problems with the second part of the proof that Allison ascribes to Kant. One concerns Rep-Change-as-Objective₁ and Rep-Change-as-Objective₂. Others concern the reasoning by means of which he takes Kant to move from the second of those claims to the thesis that every objective change is an alteration.

In order to see the first of these problems, we need only reflect on the response of James Van Cleve to a reading of the passage from A188/B231 suggested by Arthur Melnick. According to Melnick (Reference Melnick1973: 71–7), Kant may be concerned there with conditions under which it is verifiable that some state of affairs (S₂) came into being at time t₁. This is verifiable only if it is verifiable that S₂ did not exist anywhere at t₁. The latter is verifiable, Melnick thinks Kant may hold, only if for some S₁ there is a law that if S₂ existed anywhere at t₁, it existed where S₁ existed. If there is such a law, he also thinks Kant may hold, S₁ and S₂ are connected as states of a substance. Here is the response of Van Cleve:

There is no discussion here of any act(s) we must perform if we are to represent an arising (or perishing) that takes place in apprehension as objective. There is thus no immediate threat to Rep-Change-as-Objective₁ and Rep-Change-as-Objective₂. With a bit of adaptation, however, we can formulate such a threat.

In apprehension, let us say, there was at t₁ a flat surface with nothing on it and is at t₂ a flat surface with a house composed of blocks on it. At least in apprehension, let us further say, there was no such house prior to t₁. At least in apprehension, this entails, the house has arisen. There is no apparent difference between the surface that is present in apprehension at t₂ and the surface that was present in apprehension at t₁. For this and other reasons, we take it to be the same surface. The interval between t₁ and t₂ has been short and we have focused carefully on the vicinity of the surface and paid close attention throughout the interval. For whatever reasons, finally, some of us take it utterly for granted that items such as the house are never subject to rapid transport, i.e. transport so rapid that we would not notice the movement of an item like the house even if we focused on the relevant vicinity and paid close attention. Given that some of us do this, some of us will take it utterly for granted that the house has not moved to its present location during the interval between t₁ and t₂. Will this by itself not lead those of us who do so to represent the arising of the house as objective?

In search of a principled answer, let us return to the scenario discussed in section 4. If we take the blocks that compose a house to be the same blocks that were scattered on a flat surface at some earlier time, Allison takes Kant to hold, we will represent the arising of the house as objective. The reason, he must evidently maintain, is that we will assume with complete certainty that what we take to be the case is incompatible with the existence of the house at the earlier time. If the blocks that now compose the house are the same blocks that were scattered, we will assume with such certainty, the house cannot have existed anywhere at the earlier time and the arising of the house cannot have taken place merely in apprehension.

In the scenario with which we are now concerned, some of us take it utterly for granted that the house has not moved to its present location between t₁ and t₂. If those of us who do so also assume with complete certainty that this is incompatible with the existence of the house at t₁, the above analysis suggests, we will indeed represent the arising of the house as objective.Footnote ²⁸ We will do so, moreover, without referring something that is now present in apprehension and something else that is no longer present in apprehension to a single subject. The scenario in question casts serious doubt on Rep-Change-as-Objective₁, therefore. Since Rep-Change-as-Objective₁ is the ground of Rep-Change-as-Objective₂, it casts equal doubt on the latter.

It is possible, of course, that this doubt is not in order and that both of these claims are actually solid. Even if they are, however, there seem to be problems with the reasoning by means of which Allison takes Kant to get from the second of them to the thesis that every objective change is an alteration.Footnote ²⁹ One such problem concerns the new conception of an objective change that said reasoning invokes. Another concerns a possible difference between conforming to a concept and corresponding to it.

According to Allison, as we have seen, there is a changed point of view involved in the recognition that ‘the cognitive structure of the human mind is the source of certain conditions that must be met by anything that is to be represented as an object by such a mind’ (Reference Allison1983: 29). This recognition ‘brings with it’ a radically new conception of an object, he asserts: ‘An object is now to be understood as whatever conforms to the mind’s conditions for the representation of it as an object’ (p. 30). Since an objective change is an object and the concept involved in Rep-Change-as-Objective₂ is a condition of the sort in question, he evidently infers, an objective change is now to be understood as whatever conforms to that concept.

If this is really so, the relevant conception of an objective change should follow from this three-part supposition:

• The human mind is the source of the concept involved in the action described in Rep-Change-as-Objective₂.

• That concept is a condition that must be met by anything that is to be represented as an objective change by such a mind.

• Meeting that condition consists in conforming to that concept.

The relevant conception does not appear to follow. On our ‘old’ conception, an objective change is (or was) understood as a change that does not take place merely in apprehension. If our three-part supposition is in order, anything that is to be represented as such a change by the human mind must conform to the concept of an alteration. If Rep-Change-as-Objective₂ is in order, furthermore, we could not even have our ‘old’ conception of an objective change without the concept of an alteration. It hardly seems to follow, however, that an objective change is now to be understood as whatever conforms to that concept. Why should it not continue to be understood as a change that does not take place merely in apprehension? How does or would the recognition that concept x makes conception y possible ‘bring with it’ (i.e. entail) a transformation of conception y itself?

Without answers to these questions, the argument by means of which Allison takes Kant to move from Rep-Change-as-Objective₂ to the assertion that every objective change is an alteration hits a wall at step 4. Even if it did not, moreover, there would remain a problem with step 9. Since every objective change conforms to the concept of an alteration, proclaims this step, every objective change is an alteration. If Rep-Change-as-Objective₂ is in order, of course, we must view a change that takes place in apprehension as an alteration in order to represent it as objective. There is no apparent reason, however, why we must correctly view the change that takes place in apprehension in this way in order to represent it as objective. There is no apparent reason, in other words, why the change in question must conform to the concept of an alteration in the sense of corresponding to it and thus of being an alteration. The only sense in which the change in question must ‘conform’ to that concept, it appears, is that of allowing us to apply that concept to it, perhaps correctly but perhaps also not.

7. A problem with the third part of the proof

In Allison’s own case, there is also a problem with the third part of the proof that he ascribes to Kant. In that part, he maintains, Kant moves from the claim that every objective change is an alteration of something at least relatively persistent to the claim that every such change is an alteration of something absolutely persistent. According to Allison, the key to that move lies in the identification of substance with the matter of which things are composed. ‘This identification is necessary in order to have a subject or “substratum” of which one can predicate the changes which occur when enduring physical objects … come into or pass out of existence’, he explains (1983: 209).

At least prima facie, this appears to be false. In the case of the destruction of the wood by fire, for example, one could identify the matter of which the wood is composed at the relevant time with a large set of molecules. If one does, it seems clear, one has a subject or ‘substratum’ of which one can predicate the change that occurs when the wood passes out of existence. The change in question, one might then hold, is merely an alteration in the form or arrangement of the set of molecules. Since the relevant molecules have arisen and may perish, however, the set comprised of them cannot be identified with substance.Footnote ³⁰ In order to have a subject or ‘substratum’ of which one can predicate the changes which occur when enduring physical objects come into and pass out of existence, therefore, it is not in fact necessary (at least in the first instance) to identify substance with the matter of which things are composed.

This point might seem minor. Even though the set of molecules does not qualify as substance, one might be tempted to respond, something else surely must. The something else in question may be a set of atoms, a set of subatomic particles, vibrating strings of energy, or something even more basic. No matter what it is, it is ‘the matter’ of which the wood is composed and any arising or perishing of sets and/or items further up the chain will be an alteration of it. Although false in the first instance, on such a response, Allison’s claim that it is necessary to identify substance with the matter of which things are composed turns out to be true.

The obvious question with respect to such a response, however, is why something else must qualify as substance even though the set of molecules does not. The only possible answer, it appears, is that the chain (piece of wood, set of molecules, set of atoms, and so forth) must eventually bottom out in something that is not merely a way in which something else exists.Footnote ³¹ The claim that this is so does not seem analytic. Nor is it empirical. In order to hold that Kant is entitled to it, consequently, one must hold that he has already shown in the Transcendental Deduction of the Pure Concepts of Understanding that there is something in any item the arising or perishing of which is objective that qualifies as substance. Given his own assessments of that deduction, however, Allison cannot do so.

In KTI 1, he draws a distinction between objective validity and objective reality and takes the Deduction to show that the pure concepts of understanding have both (Reference Allison1983: 134–6 and 170). In his view, however, this entails only that those concepts have application to perceptions or ‘subjective objects’, not that they have application to items of the sort any common person means by a house composed of blocks or a piece of wood (Reference Allison1983: 167–70). Given this view and the fact that the arising and perishing of such items can be objective, he cannot take Kant to show in the Deduction that there must be something in any item the arising or perishing of which is objective that qualifies as substance.Footnote ³² At least in KTI 1, consequently, Allison should reject the argument on which he takes Kant to rely in the third part of his proof.

He should do the same in KTI 2. What he there holds about the Deduction is that it fails to show that the dynamical categories are even conditions of apprehension or perception, let alone that they are conditions of the sort of experience with which he takes the First Analogy to be concerned. The concept of substance is a dynamical category, however. This being so, Allison cannot take Kant to show in the Deduction that there must be something in any items the arising or perishing of which is objective that qualifies as substance. Just as in KTI 1, therefore, he should reject the argument on which he takes Kant to rely in the third part of his proof. Just as in KTI 1, nonetheless, he explicitly maintains that it is sound (Reference Allison1983: 200; Reference Allison2004: 237).