Summary: Critique of Pure Reason (page 5)

In fact, there already exists a discipline that catalogues and classifies the operations of reason in its functioning: logic. The starting point of the Critique is therefore an inquiry into this discipline:

General logic provides me […] with an example of how all the simple acts of reason can be fully and systematically enumerated. ¹

Through the study of this science, we will first grasp what the pure concepts of the understanding are—those fundamental concepts through which our intellect operates.

The Critique will aim to demonstrate, as well as clarify, the objective validity of these a priori concepts.

Finally, this study will allow for the creation of an inventory of all that we possess through pure reason, arranged in a systematic manner.

We must therefore begin with logic—and it is precisely with an examination of this discipline that the Preface to the second edition opens.

Logic is thus the science from which we must set out in order to grasp how the mind functions—that is, the a priori laws of the understanding.

Kant regards the logic of his time, inherited from Scholasticism, as a closed, completed, and satisfactory science—a view that would later be challenged, given the considerable advances in logic since then.

The significance of logic lies in its ability to rigorously demonstrate the formal rules of all thought. But what does this mean?

Logic does not concern itself with the content or matter of reasoning, but with its form—the way in which reasoning is conducted.

Here is an example of a logically correct form of reasoning:

A is B
But B is C
Therefore, A is C

This is purely formal because it takes no account of the content of each proposition—A, B, and C are left undefined and could refer to anything.

For example:

A cat is a feline. But a feline is a mammal. Therefore, a cat is a mammal.

Or:

Socrates is a man. But men are mortal. Therefore, Socrates is mortal.

In fact, even if we substituted absurd content into this reasoning, it would remain formally correct:

"A cat is a dog. But dogs are canaries. Therefore, cats are canaries."

This remains logically valid, even though the content—the matter—of the reasoning is false.

We now understand why Kant sees logic as the discipline in which we find the formal laws of thought. When studying it, the understanding deals with nothing other than itself and its own form.

The laws of logic, by virtue of their formal nature, are a priori laws of thought. They are not learned through experience but precede it. They do not concern our experiences of the external world but the laws of the mind itself—the laws that the understanding follows when it analyses experience.

We should therefore bear in mind that formal and a priori are necessarily linked concepts in Kant's philosophy.

Kant then shows that other sciences have followed the same path—mathematics and even physics—and that this has led to highly successful results.

Indeed, just like logic, mathematics and physics are the two theoretical forms of knowledge in which reason must determine its objects a priori.

When a mathematician reasons about a circle and draws a figure on the board, for instance, they are not reasoning about that particular figure they have just drawn, based on their experience of it—that would be an empirical approach, one that relies on experience. The drawn figure serves only as an illustration.

¹ Our translation. The references for the quotations are available in the book Kant: A Close Reading