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[¶7] It took natural science much longer to find the highway of science; for it is only about one and a half centuries since the suggestion of the ingenious Francis Bacon partly occasioned this discovery and partly further stimulated it, since one was already on its tracks - which discovery, therefore, can just as much be explained by a sudden revolution in the way of thinking. Here I will consider natural science only insofar as it is grounded on empirical principles.
[¶8] When Galileo rolled balls of a weight chosen by himself down an inclined plane, or when Torricelli made the air bear a weight that he had previously thought to be equal to that of a known column of water, or when in a later time Stahl changed metals into calx and then changed the latter back into metal by first removing something and then putting it back again,* a light dawned on all those who study nature. They comprehended that reason has insight only into what it itself produces according to its own design; that it must take the lead with principles for its judgments according to constant laws and compel nature to answer its questions, rather than letting nature guide its movements by keeping reason, as it were, in leading-strings; for otherwise accidental observations, made according to no previously designed plan, can never connect up into a necessary law, which is yet what reason seeks and requires. Reason, in order to be taught by nature, must approach nature with its principles in one hand, according to which alone the agreement among appearances can count as laws, and, in the other hand, the experiments thought out in accordance with these principles - yet in order to be instructed by nature not like a pupil, who has recited to him whatever the teacher wants to say, but like an appointed judge who compels witnesses to answer the questions he puts to them. Thus even physics owes the advantageous revolution in its way of thinking to the inspiration that what reason would not be able to know of itself and has to learn from nature, it has to seek in the latter (though not merely ascribe to it) in accordance with what reason itself puts into nature. This is how natural science was first brought to the secure course of a science after groping about for so many centuries.
* Here I am not following exactly the thread of the history of the experimental method, whose first beginnings are also not precisely known.
Summary
Natural science has also attained security as mathematics has by recognizing that progress can only be made by guiding or structuring observations in advance (a priori) rather than on the basis of chance perceptions. We can see this when looking at experiments within the study of nature.
Commentary
Natural science deploys concepts that are drawn from experience and must apply in experience while mathematics, on the other hand, constructs its concepts. Just as mathematics became secure by actively introducing its own principles, natural science's security is tied to our active participation in the process of knowing. This includes developing theories, hypotheses, and controls so we have a reference point that we understand in advance; these are so many elements of experiment and observation that we have not had to revise even as our knowledge of nature advances.
If we consider what Kant emphasizes in his examples, it is the active role that the scientists have in their experiments. We can certainly see that things fall, and even that things fall at different speeds (a feather falls relatively slowly), but if we do not experiment we cannot isolate what features are the cause of the difference in the rate objects fall. Kant means to emphasize this by mentioning Galileo's fabled experiment where there was an attempt to observe the movement of objects of different weights in a manner in which the weight of the objects was more likely to be the only contributing factor. If one didn't try to control the experiment, then any result we observe may not give us information since we don't know what things are kept the same or allowed to be different, and so we do not know what the different outcomes are tied to.
As the topic of natural science and nature arises here, it would be prudent to explain Kant's understanding of nature. Many modern readers, but not all, may have a tendency to think of natural science as studying nature as it is in itself. If this is the approach to the study of nature, then Kant would designate it as dogmatic metaphysics rather than natural science. Of course, modern physics is not dogmatic metaphysics and so cannot be a study of things in themselves. Just as in Kant, the study of nature is a study of objects so far as they can appear, directly or indirectly, so as to be observed. Our observations are possible because we are active - we run experiments, we have hypotheses and theories that anticipate what will happen, etc. An important takeaway from this is that in our model of natural science we design and apply the law to nature. It will be important to keep this aspect of the laws of nature in mind: we are the lawgivers in the sense that we design and apply the laws, and continue to adjust them as we are further instructed by experience.
Natural laws - or laws of any kind - are not observable per se: we can only observe singular or particular objects, while laws are universal and necessary. Instead, we observe the conformity of objects in nature to a law that we have given, or, in more general terms, we observe that our concept can be applied in experience. For example, we do not observe universal gravitation for the same reason we can't observe anything universal. However, we observe that objects conform to this law (our concept finds application in experience).
Kant will argue that any order of nature, and so all possible law for nature, is determined through the manner in which we construct experience. This is a point that will need to be developed further in the future, but which we should bear in mind.
The study of nature must not be confused with the study of things in themselves. Instead, the association we make with nature in Kant should be with the sum total of appearances. Appearances have a dimension that is provided from our sensible faculty, which is receptive, and which provides a relation we can think back to the object per se.
Questions
If we give the law to nature, how is it that natural science is discovered rather than invented?
The brief response to this is that even though we apply the law to nature, it isn't any law that will apply, ultimately we are looking around for something we can use to generally describe the behavior of nature which is considered something other than us. We may feel inclined to believe we are slowly approximating to the way nature is in itself, but we never leave the realm of appearances and the way we structure them so we never have an opportunity to see how close or far we have approached to knowing things themselves. It is always possible that nature, in itself, is completely lawless and that we provide any semblance of order we find in nature. However, whether nature in itself is ordered or not is a speculative proposition that exceeds our capacity.
Terminology
empirical principles (empirische Prinzipien)
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