The claim was that the time-order of the states of an object cannot be determined through the order of the occurrence of perceptions (the subjective succession does not by itself determine the objective succession). Something more is needed to show that the subjective succession is not arbitrary, not generated by the imagination. This something more is a rule according to which states succeed one another in objects. Such a rule, Kant claimed, must be subject to on exceptions, so that given that an object is in state a at a time, that (and the states of other objects at the same time) is sufficient to bring state b about. In this way, the succession of a perception of a by a perception of b is bound to an objective succession of states a and b in the object.
A rule which specifies for a given state, what state must follow it, is a causal law. Thus causal laws are necessary conditions for the determination of the order of succession of objects. Since a determination of the order of succession is required for us (non-arbitrarily) to represent an object as changing, if any change in an object is to be represented, the states of the object must be brought under causal laws.
Note that this argument hinges entirely upon how objects must be represented and says nothing about their status independently of the way they are represented. In Kant's terminology, the category of causality applies to appearances only, not to things in themselves. It is the assumption that in representing change we represent things in themselves which led Hume to his skeptical conclusion. For under that assumption, the only way in which change could be known is a posteriori, through experience. One cannot find necessity there: the fact that we must represent change in a certain way is irrelevant to the occurrence of change in the objects in themselves. However, if an appearance must be brought under causal laws in order to become an object of experience, it is bound by those laws.
It should also be pointed out that Hume assumed that the only way in which causal laws can be known to hold a priori is if one could apply them to objects encountered for the first time. His argument depends on the fact that we have no idea how an object will behave on first encounter. (See the entry on Hume.) Kant's argument gets around this stricture by claiming that we need not be able to predict how an object will behave, but only that we must be able to bring the object under some law or other.
I will now move ahead to Kant's discussion of the modal categories in the "Postulates of Empirical Thought in General." There are three pairs of modal categories: possibility/impossibility, existence/non-existence, and necessity/contingency. In class, I took these up in reverse order.
Kant's discussion of the categories marks a break with the tradition from Leibniz through Wolff. In both cases, there is a crucial distinction between a necessary being, one whose non-existence is impossible, and contingent beings, which might not exist. God is the unique necessary being, while both the world as a whole and the things in the world are contingent. Their existence depend upon the will of God, who could have created some possible world other than the actual world which was in fact created. That there are alternative uncreated worlds allows us to attribute freedom to God in the act of creation. It also allows attribution of freedom to human acts. I am now sitting. I might be standing now, had a student come in the door (in fact, in another possible world I am so standing). So my sitting now is not necessitated by my previous state.
The fact that in another possible world I am standing means that my sitting now is not absolutely necessary. On the other hand, my sitting is conditionally or hypothetically necessary. The present set of conditions is sufficient for my sitting, so given them, I must be sitting. Only God exists absolutely necessarily; any of my states exists hypothetically necessarily.
Kant claimed that the only sense in which anything exists necessarily is hypothetically. And in fact, all objects of experience are subject to hypothetical necessity, as falling under causal laws. The attempts to extend the category to absolute necessity are ostensibly refuted in the Transcendental Dialectic, in the Fourth Antinomy and the criticism of the Cosmological Argument (in the Transcendental Ideal). If we try to claim that the contingency of the world demands an absolutely necessary being, we are extending the category of causality beyond experience. In objects of experience, the only kind of necessity we may attribute to objects is hypothetical.
The metaphysics of Wolff explained the necessity of God's existence by appeal to a version of the ontological argument. The concept of God is that of the most real being, and a being with all reality must exist. The most real being is complete with respect to all possible properties, and the Wolffians regarded existence itself as the completion of possibility. To illustrate this idea, I will suppose that I have just walked into this room. It is possible for me to sit down or to remain standing. My sitting down completes the possibility, in the sense that the other option is closed off. If there is a being whose essence is so complete in itself that it requires nothing more for its completion, then that object exists.
Kant utterly rejected this sort of reasoning. A concept, he held, can be ever so complete without anything about its existence being determined thereby. Existence is not to be found in concepts, but in perception. Thus we can say that something exists when it is perceived or is connected by causal laws with what is perceived, e.g. as magnetism is attributed to an object toward which iron filings move. The category of existence is thus limited to objects of possible experience.
Finally, the Wolffian treatment of possibility allows the postulation of many possibilities that are unactualized. To be possible, in the absolute sense, a concept must be free from contradiction. The Wolffians also employed a notion of relative or conditional possibility. Something is possible conditionally when the given conditions leave its existence open. Kant's category of possibility is akin to this kind of conditional possibility. The condition is the relation to the subject, so a possible object is one which can be represented as an object of experience. And what can be so represented is precisely what falls under the forms of intuition and categories. Thus a two-sided figure is absolutely possible, but it can never become an object of experience, while a triangle can be, since there is a way to construct it in space. Similarly, a substance which is in space without filling it is absolutely possible but is not possible relative to the conditions of experience.