One summary of the great Kant's view, to the extent that it can be summed up, is that he takes determinism to be a kind of fact, and indeterminism to be another kind of fact, and our freedom to be a fact too -- but takes this situation to have nothing to do with the kind of compatibility of determinism and freedom proclaimed by such Compatibilists as Hobbes and Hume. Thus Kant does not make freedom consistent with determinism by taking up a definition of freedom as voluntariness -- at bottom, being able to do what you want. This he dismisses as a wretched subterfuge, quibbling about words. Rather, the freedom he seeks to make consistent with determinism does indeed seem to be the freedom of the Incompatibilists -- origination. Is he then an Incompatibilist? Well, against that, it can be said he does not allow the existence of origination in what can be called the world we know, as Incompatibilists certainly do.
Kant's main idea, whatever sense can finally be made of it, depends on his fundamental two-worlds doctrine. He locates determinism in the empirical world or world of appearances, and freedom in the world of things-in-themselves, the world of reason. It is important that the latter world is not in time.
So he is a determinist of a kind, opposed to the tradition of Compatibilism, not really in the Incompatibilist tradition, but tries to make his determinism and freedom-as-origination consistent by his own private means. You may well wonder if he can succeed in all this -- and suspect too, at the beginning of the 21st Century, that something so radical as his view is actually needed.
The first excerpt below comes from The Critique of Pure Reason. The second excerpt, along the same lines, but maybe clearer, is from The Critique of Practical Reason. I have improved on Kant's paragraphing.
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Excerpt (1) from The Critique of Pure Reason:
...every human being has an empirical character for his power of choice, which is nothing other than a certain causality of his reason, insofar as in its effects in appearance this reason exhibits a rule, in accordance with which one could derive the rational grounds and the actions themselves according to their kind and degree, and estimate the subjective principles of his power of choice. Because this empirical character itself must be drawn from appearances as effect, and from the rule which experience provides, all the actions of the human being in appearance are determined in accord with the order of nature by his empirical character and the other cooperating causes; and if we could investigate all the appearances of his power of choice down to their basis, then there would be no human action that we could not predict with certainty, and recognize as necessary given its preceding conditions. Thus in regard to this empirical character there is no freedom, and according to this character we can consider the human being solely by observing, and, as happens in anthropology, by trying to investigate the moving causes of his actions physiologically
But if we consider the very same actions in relation to reason, not, to be sure, in relation to speculative reason, in order to explain them as regards their origin, but insofar as reason is the cause of producing them by themselves — in a word, if we compare them with reason in a practical respect — then we find a rule and order that is entirely other than the natural order. For perhaps everything that has happened in the course of nature, and on empirical grounds inevitably had to happen, nevertheless ought not to have happened. At times, however, we find, or at least believe we have found, that the ideas of reason have actually proved their causality in regard to the actions of human beings as appearances, and that therefore these actions have occurred not through empirical causes, no, but because they were determined by grounds of reason.
Suppose now that one could say reason has causality in regard to appearance; could reason’s action then be called free even though in its empirical character (in the mode of sense) it is all precisely determined and necessary? The empirical character is once again determined in the intelligible character (in the mode of thought). We are not acquainted with the latter, but it is indicated through appearances, which really give only the mode of sense (the empirical character) for immediate cognition. Now the action, insofar as it is to be attributed to the mode of thought as its cause, nevertheless does not follow from it in accord with empirical laws, i.e. in such a way that it is preceded by the conditions of pure reason, but only their effects in the appearance of inner sense precede it. Pure reason, as a merely intelligible faculty, is not subject to the form of time, and hence not subject to the conditions of the temporal sequence. The causality of reason in the intelligible character does not arise or start working at a certain time in producing an effect. For then it would itself be subject to the natural law of appearances, to the extent that this law determines causal series in time, and its causality would then be nature and not freedom.
Thus we could say that if reason can have causality in regard to appearances, then it is a faculty through which the sensible condition of an empirical series of effects first begins. For the condition that lies in reason is not sensible and does not itself begin. Accordingly, there takes place here what we did not find in any empirical series: that the condition of a successive series of occurrences could itself be empirically unconditioned. For here the condition is outside the series of appearances (in the intelligible) and hence not subject to any sensible condition or to any determination of time through any passing cause.
Nevertheless, this very same cause in another relation also belongs to the series of appearances. The human being himself is an appearance. His power of choice has an empirical character, which is the (empirical) cause of all his actions. There is not one of these conditions determining human beings according to this character which is not contained in the series of natural effects and does not obey the laws of nature according to which no empirically unconditioned causality is present among the things that happen in time. Hence no given action (since it can be perceived only as appearance) can begin absolutely from itself. But of reason one cannot say that before the state in which it determines the power of choice, another state precedes in which this state itself is determined. For since reason itself is not an appearance and is not subject at all to any conditions of sensibility, no temporal sequence takes place in it even as to its causality, and thus the dynamical law of nature, which determines the temporal sequence according to rules, cannot be applied to it.
Reason is thus the persisting condition of all voluntary actions under which the human being appears. Even before it happens, every one of these actions is determined beforehand in the empirical character of the human being. In regard to the intelligible character, of which the empirical one is only the sensible schema, no before or after applies, and every action, irrespective of the temporal relation in which it stands to other appearances, is the immediate effect of the intelligible character of pure reason; reason therefore acts freely, without being determined dynamically by external or internal grounds temporally preceding it in the chain of natural causes, and this freedom of reason can not only be regarded negatively, as independence from empirical conditions (for then the faculty of reason would cease to be a cause of appearances), but also indicated positively by a faculty of beginning a series of occurrences from itself, in such a way that in reason itself nothing begins, but as the unconditioned condition of every voluntary action, it allows of no condition prior to it in time, whereas its effect begins in the series of appearances, but can never constitute an absolutely first beginning in this series.