Kant and the Critique of Pure Reason

A shorter version of this article can be found here.

---

A) Presentation

The starting point of the Critique of Pure Reason—what it takes for granted, without any need for criticism—is that mathematics and physics are established as true sciences, advancing with certainty and enjoying the universality by which a science deserves such a name (it is not a matter of criteria or opposing schools of thought, but rather they are the same for all people, regardless of their creed or cultural background). And the problem essentially posed is related to this: whether it is possible to establish metaphysics with the same certainty and universality enjoyed by those sciences. To this end, he will investigate how scientific knowledge is possible, how it has formed its judgments, and from where it has drawn its truth, in order to see whether the same is possible—and under what conditions—in metaphysics.

To this end, Kant begins by examining the different types of judgments. He classifies them, according to their relationship to experience, into hindsight y preconceived notions, depending on whether they precede or follow experience—that is, whether they follow from some observation of experience, or whether they have been formed independently of it. If I say “this body is heavy,” it is because I have experienced it, but if I say that 123 plus 241 equals 364, this is a judgment that precedes experience, since I did not need to gather so many objects together with so many others and then count them together afterward. Since a characteristic feature of science is its universality—its propositions are universally accepted—it is necessary that the judgments appearing within it be a priori; for if they were derived from particular experiences, their truth would depend on those experiences and they would not enjoy universality.

According to another criterion, Kant divides judgments into analytic and synthetic. Analytical judgments These are judgments formed by analyzing the terms involved in them; for example, “all bodies are extended.” Analytic judgments do not reveal anything truly new, since it was already implied in the definition of their terms. Synthetic judgments are those that cannot be formed by analyzing the terms but rather establish a truly new link or connection (hence their name “synthetic”) between those terms. For example, “bodies are heavy” or “iron expands with heat,” or 2+5=7, since the fact that the sum is 7 is not mentioned in the definition of 2 (the number following 1) nor in that of 5 (the number following 4). It is clear that science needs synthetic judgments, since analytic ones do not truly expand knowledge.  

In short, for something to be considered science—that is, an advance in knowledge that is universally accepted—it must contain judgments that are both synthetic (so that they constitute new knowledge) and a priori (so that they are universally valid). Synthetic a priori judgments include, for example, “2+5=7,” “through two points passes a straight line and only one” (a fact independent of experience, since even a blind person understands it, and a fact that cannot be deduced from the definitions of a point and a straight line). Or also: “every change has a cause.” Thus, if metaphysics is to constitute true knowledge of universal validity, synthetic a priori judgments must be possible within it. 

Since it is an indisputable fact that mathematics and physics are well-established sciences with universal validity, it is certain, then, that synthetic a priori judgments exist within them, and in fact some examples have already been identified. We are interested in knowing whether this is also possible in metaphysics, and to that end we examine where these synthetic a priori judgments in mathematics and physics derive their truth: do they derive it from experience? No, for they precede it. Do they derive it from the analysis of their terms? No, for they are not analytic but synthetic. They must therefore derive it from a priori principles that are present in our own faculty of cognition. This is how Kant comes to know that there are a priori principles in our knowledge, even before he has discovered them in the study of knowledge, at the various levels, into which he subsequently delves.

The first level he examines is the lowest one, the one we share with animals: the level of sensibility. He calls this study Transcendental Aesthetics, since αεστετοσ means “sensible.” It involves studying the formation of our intuitions, what in scholastic philosophy are called perceptions, and what Kant calls phenomena, that is, what appears in our sensibility (ϕαινω = to appear, ϕαινομενον = that which appears). His first observation is that there are two pure intuitions that appear mixed together in all phenomena: I can think of a room that is familiar to me and strip it of furniture, ceiling, walls, and even floor, but there is something I cannot take away from it—space. This is a sign that this intuition, space, was already present in my faculty of cognition (I can think of a space empty of bodies, but never of a body without space). Similarly, every event occurs in time, and I can imagine it stripped of all its characteristics except for the duration of time (I can imagine, however, an empty time in which nothing happens, but I cannot imagine an event occurring without time). 

These two concepts—space and time—enable us to organize the data that reaches our senses into different categories, assigning them different time frames as well, so that what has impressed my senses remains unknown in its original form (since we know it only as it is clothed in space and time). That is why he calls it the ignotum X, or “the thing-in-itself,” or νοουμενον (the thought, even though it does not appear to us in knowledge), as opposed to the φαινομενον, the phenomenon (what appears in knowledge). Thus, in summary, in every phenomenon (what appears in sensory knowledge) or sensory intuition there is a component that comes from outside, through our senses, and another internal component: space and time, the pure intuitions. 

Geometry studies a pure intuition—space—and derives its truth from it, articulated in propositions that are truly synthetic (they express a new truth) and a priori (they derive that truth from the a priori nature of our sensibility, which is space). Mathematics studies not only space but also time and the relationship between the two in motion (in time, that is, in iteration, Kant sees the origin of numbers, and thus of arithmetic). It is for this reason that mathematics is a synthetic a priori form of knowledge. 

The next part of the *Critique of Pure Reason* is the *Transcendental Analytic*. It examines the formation of concepts and judgments in our understanding. This faculty is no longer shared with animals, but is unique to humans. It consists in the capacity to think phenomena, that is, to form intelligible concepts from the intuitions received through our senses, so that they may become part of our judgments; and also in the faculty of forming these judgments, that is, propositions that link the concepts formed in this faculty (judgments such as “this body is extended” or “every body is extended,” “this body is heavy” or “every body is heavy.” The most common form is the attribution of a predicate to a subject, but there are other forms of judgments)

Just as, in order to intuit the “thing-in-itself,” we needed the a priori forms of space and time—pure intuitions—so too, in order to think about the intuition thus formed, so that we may form a concept from it, we need certain pure concepts. These are a priori forms of our understanding to which Kant also gives the noble name of categories, for they play a role in his theory of knowledge analogous to that of the Aristotelian categories, that is, the predicaments which in Aristotle correspond to the modes of being, which we well recall: substance and accidents, the latter divided into quantity, quality, relation, ubi, quando, action, and passion. (Kant demonstrates that there is a priori knowledge in our understanding in a manner similar to how he demonstrated that there are a priori elements in sensibility: “if in your empirical concept of any object, corporeal or incorporeal, you disregard all the properties that experience teaches you, you cannot, however, suppress that property by which you conceive it as a substance or as adhering to a substance”) 

Kant classifies a priori concepts, pure concepts, or categories according to the different modes of judgment, since these correspond to the various ways in which a concept has appeared as the term of a judgment and, therefore, the various ways in which it has been categorized. The result is the following “table of categories.” Of quantity: Unity, plurality, totality. Of quality: Reality, negation, limitation. Of relation: Inherence and subsistence (Substantia et accidens), causality and dependence (cause and effect), community (reciprocal action between agent and patient). Regarding modality: Possibility-impossibility, existence-nonexistence, necessity, contingency.” What interests us most here is that substance and accident appear as categories, as does causality, and therefore these are, for Kant, mere a priori forms of our understanding! Of course, he considers that we have many more pure concepts than those appearing in this table, but we derive them from these elementary ones by combining them with one another and also with the two pure intuitions (which is why he has not needed to include the Aristotelian ubi and quando here). 

In the faculty of understanding, as the faculty responsible for forming judgments about concepts, there are also innate judgments—a priori principles of the faculty itself. He calls them a priori principles, because they play the role of first principles in Aristotelian philosophy—and in fact their enumeration is similar—but with the important difference that here they are seen as innate, whereas in Aristotle they were intellectual habits, that is, habits acquired by the intellect in its faculty of judgment.  (These are the principle of contradiction, which he states in the classical manner; the principle of the permanence of substance in all phenomenal change; the principle of causality—“all alterations occur according to the law of the connection between cause and effect”—that is, “nothing happens by blind chance”; just as “no necessity in nature is blind, but rather conditioned and therefore comprehensible,” that is, there is no “fatum” in nature.  He also considers the principle of continuity in time, that is, in the temporal series of phenomena—“there are no leaps in the world”—and continuity in space—“there are no gaps in the world.” Taken together, the principle states: “in mundo non datur casus, non datur fatum, non datur saltus, non datur hiatus.”

Just as transcendental aesthetics—the study of pure intuitions—enabled us to understand the a priori synthetic nature of geometry, and of mathematics in general, this study of transcendental analytics—of the pure concepts of the understanding—enables us to understand the a priori synthetic nature of physics, since physics is defined as the study of natural phenomena through their causes, and it is here, in transcendental analytics, that cause has emerged as an a priori concept of the understanding, and the principle of causality as an a priori principle of this faculty as well. Thus, the object under study in physics is an a priori studied in transcendental analytics, which means that what we study in physics, in our study of nature, is in reality what we impose upon it when we come to know it. This is incredibly powerful!

We thus arrive at the highest level of our knowledge: our capacity for reasoning, or reason. Here we are concerned, without explicit mention, solely with reason in its speculative use (asking how things are), leaving for a later work the critique of reason in its practical use, that is, as the guide of our behavior (asking how things ought to be). This knowledge is articulated through concepts that he will call ideas, thus distinguishing the concepts of reason from the concepts of our understanding that we have discussed in the Transcendental Analytic (Ideas are not concepts of any object, such as the concept of a man, but rather are concepts without an object, such as that of virtue. The phenomenon considered in the former might be a man we have just seen on the street, a phenomenon that does not appear in the latter: no one has seen a virtue walking down the street, nor anywhere else; it is simply not an idea of any phenomenon) Here, too, we will find a priori principles—that is, transcendental ideas—which must be understood as pure ideas or a priori principles of reason, and their study will be called transcendental dialectic (this is the section that gives the work its title: Critique of Pure Reason). 

The three antinomies of reason will help us discover the pure ideas of reason. By antinomy or “opposition,” Immanuel Kant refers to well-founded, well-constructed arguments—both “laden with reason”—but contradictory, which is why they have been the subject of endless debate among people, particularly in the field of philosophy. Regarding the world, there is the question of whether it is limited in space and time or not. He sets forth the reasons given for and against, both of which are convincing. And there is also the antinomy of continuity: whether the substances of the world are composed of indivisible parts. Regarding the self, the knowing subject, there is the antinomy of freedom: whether or not we are free, and therefore responsible for our actions. And there is the antinomy of the existence of God, the necessary being who is the cause of everything. 

Of particular interest is his analysis of the proofs of God’s existence that have been put forward throughout the history of philosophy: The ontological proof, which, in reality, only leads to a conceived existence, since it starts from a conceived essence (he compares it to the merchant who believes he is becoming immensely rich by adding zeros to the right of the numbers in his ledger). He also rejects the ontological proof (there must be a cause because the world is contingent) because he sees it as essentially the same as the previous one, deducing an existence from mere concepts. And he rejects the proof from order because it would lead us not to a creator but to an organizer. But he likewise finds the contrary assertions to be objectionable: “The very same proofs that demonstrate the impotence of human reason in relation to the assertion of the existence of such a Being are also sufficient to demonstrate the presumption of any contrary assertion.”

Neither these arguments nor their opposites are conclusive. What, then, is the matter?  Kant sees the reason for these causes of centuries-old human perplexity in the fact that they treat as real ideas—corresponding to beings that truly exist independently of us—what are in reality nothing but pure representations in our mind—representations that represent nothing—; they are pure ideas of reason: the world, the self, God. In each of these arguments, these ideas have been reified; they have been attributed—whether to affirm or to refute—an existence external to reason itself, when in reality they are pure ideas, a priori principles, which our reason possesses to stimulate and order its activity. (However, “there is, strictly speaking, no controversy in the realm of pure reason. The two contending parties strike at thin air and fight against shadows, since they go beyond the limits of nature“). 

The World, as the totality and unity of all phenomena—something we have always taken for granted, yet have never seen, but without which we cannot even reason. 

The Self, as an internal psychological unit, is something that has never appeared before us, for we do not perceive it with our senses—neither internal nor external— any noumenon—in particular, we do not perceive the Self—but only phenomena (“To know oneself as a noumenon is, however, impossible, since internal empirical intuition is sensory and provides nothing but phenomena.“) 

God, who would serve as the guarantor—in the Cartesian vein—of the ultimate unity between that external unity which is the world and that external unity which is myself. “This object, which is the ideal [of reason], resides simply in reason and is also called the original being (ens originarium); and since there is no being above it, it is called the supreme being (ens summum), and insofar as everything is subject to it as conditioned, it is called the being of beings (ens entium).” This threefold consideration of unity, necessary for the regulation of our reasoning (which always seeks to find unity in what is apparently diverse), is expressed thus by the author: “Transcendental ideas are reduced to three. The first will contain the absolute (unconditioned) unity of the thinking subject [I]; the second, the absolute unity of the series of conditions of the phenomenon [World]; and the third, the absolute unity of the condition of all objects of thought in general [God]” 

He adds: “Thus, pure reason provides the basis for a transcendental doctrine of the soul (psychologia rationalis), for a transcendental science of the world (cosmologia rationalis), and finally for a transcendental knowledge of God (theologia transcendentalis) [let us recall that by “transcendental” he means “a priori”]” For Kant, cosmology, theology, and psychology—properly understood and free from antinomies—study these three great themes of philosophy, but they study them for what they are: pure ideas of reason, serving a regulative function for our reasoning. They are thus transcendental sciences—they study the a priori principles of our reason—always prescribing their merely regulative use, in contrast to their corresponding “dogmatic” sciences that claim for these ideas a reality external to our mind. Thus Kant points out that there is a correct, good, and healthy metaphysics, which establishes itself as the tribunal of pure reason to ensure that it makes of its pure ideas the purely “regulatory” use that corresponds to them, and denounces any “dogmatic” use of them. In this way, as a study of the a priori ideas of our reason—the Self, the World, God—metaphysics is constituted as a synthetic a priori knowledge, just as geometry or physics may be, and is therefore knowledge of universal validity. It thus answers the question posed at the beginning

One final observation: Kant is by no means an atheist. It is true that he regards the Self, the World, and God as hidden from our speculative reason, since they do not originate in phenomenal experience. But it is also true that they remain as possibilities, which will be revealed as realities in practical experience—a point that will form the basis of his later “Critique of Practical Reason,” already outlined toward the end of this work: “It is always to pure reason, but only in its practical use, that the merit belongs of linking to our supreme interest a knowledge that mere speculation can only imagine…I believe infallibly in the existence of God and in a future life, and I am certain that nothing can shake this faith, since it would bring down with it my own moral principles, which I cannot renounce without making myself worthy of contempt in my own eyes… But are you perhaps going to demand that a knowledge which concerns all men should be above common sense and revealed only to philosophers?”

B) Texts

Forewords 

Reason undertakes its most difficult task—that of self-knowledge—and establishes a tribunal to uphold its legitimate claims and, in turn, put an end to all unfounded arrogance… This tribunal is none other than the Critique of Pure Reason.

What and how much can understanding and reason know independently of all experience?

Mathematics and physics are the two theoretical disciplines of reason that must determine their a priori objects; 

The first person to study the isosceles triangle… saw a new light; for he found that he did not have to inquire into what he saw in the figure or even in the mere concept of it and learn its properties from it, but rather that he had to produce it by means of what, according to concepts, he himself had conceived and laid out in it a priori.

When Galileo rolled the balls down the inclined plane—whose weight he had determined himself—he realized that reason knows nothing more than what it produces according to its own design… Reason must approach nature holding in one hand its principles, according to which only concordant phenomena can have the force of laws; and in the other, the experiment, thinking in accordance with those principles.

Physics itself owes this fruitful revolution in its thinking to the insight to seek (not imagine) in nature what reason itself has placed there.

Metaphysics—the speculative knowledge of reason, entirely isolated, which rises above the teachings of experience through mere concepts…—has not yet had the good fortune to embark on the sure path of a science. 

The aim of this critique of speculative reason is to attempt to transform the approach that metaphysics has followed thus far, undertaking a complete revolution within it, following the example of geometers and physicists.

We cannot know an object as a thing in itself, but only insofar as the thing is the object of sensory intuition—that is, as a phenomenon.

I cannot even accept God, freedom, and immortality for the necessary practical use of my reason unless I simultaneously curtail speculative reason in its claim to transcendent knowledge.

I HAD TO CANCEL THE KNOW, TO RESERVE A PLACE FOR FAITH [the italics are his, the capital letters are ours: the Christian speaks, for his ultimate goal is faith; but the Lutheran Christian, for in order to attain faith he must suspend reason: and this is because, in Luther’s conception, human nature was not merely marred by original sin, but utterly corrupted.

Introduction 

It may well be that our empirical knowledge consists of what we receive through impressions and of what our own faculty of cognition (based solely on sensory impressions) provides on its own, without our distinguishing this addition from that fundamental material until long practice has made us pay close attention to it and has enabled us to separate the two

In what follows, then, we shall understand a priori knowledge not as that which exists independently of this or that experience, but absolutely independent of all experience. This stands in contrast to empirical knowledge—that is, knowledge that is possible only a posteriori, that is, through experience. Among a priori knowledge, that which contains no empirical element is called pure… If a proposition is conceived at the same time as its necessity, then it is an a priori judgment.

Every change must have a cause. In this example, the concept of cause so clearly encompasses the necessity of a link to an effect and the strict universality of the rule that it would be completely lost if one were to derive it, as Hume did, from a frequent conjunction between what occurs and what precedes it and from a custom arising from that. 

Gradually set aside, in the concept that experience provides you of a body, everything that is empirical about it—color, hardness or softness, weight, impenetrability; the space that body occupied (a body that has now completely disappeared) always remains; you cannot set this aside. Similarly, if in your empirical concept of any object, whether corporeal or incorporeal, you dispense with all the properties that experience teaches you, you cannot, however, suppress that property by which you conceive of it as a substance or as attached to a substance.

Either the predicate B belongs to the subject A as something implicitly contained within the concept A; or B lies entirely outside the concept A, though it is connected to it. In the first case, I call the judgment analytic; in the other, synthetic… For example, if I say: all bodies are extended, this is an analytic judgment… On the other hand, if I say: all bodies are heavy… it is a synthetic judgment. 

In a priori synthetic judgments… if I must move from concept A to understand another concept B, as linked to it, on what do I rely? What makes the synthesis possible, since here I do not have the advantage of turning to the realm of experience to find it? 

Mathematical propositions proper are always a priori and non-empirical judgments, for they entail necessity, which cannot be derived from experience… The science of nature (Physica) contains synthetic a priori judgments as principles… In metaphysics… there must be synthetic a priori knowledge… We wish to expand our a priori knowledge. For example, the proposition: the world must have a first beginning. And others besides. And thus metaphysics consists, at least according to its purpose, of synthetic a priori propositions.

How is pure mathematics possible? How is pure physics possible? Since these sciences actually exist, one might ask: how are they possible?

How is metaphysics possible as a science? A critical examination of reason necessarily leads to science; the dogmatic use of reason, without such criticism, leads instead to unfounded assertions… The undeniable contradictions within reason—which are also untenable in its dogmatic use—have long since stripped metaphysics of its authority.

From all this follows the idea of a particular science that might be called the Critique of Pure Reason… Its usefulness [for speculation] would in fact be purely negative, serving not to expand but to refine our reason

I call transcendental any knowledge that deals not with objects but with the way we know them, insofar as this must be possible a priori. 

Transcendental Aesthetics

The representation of space cannot be derived from experience… rather, external experience is possible only through such representation

Space is nothing more than pure intuition.

The fact that, in a triangle, the sum of two sides is greater than the third is never deduced from the universal concepts of a line and a triangle, but rather from intuition; and this is a priori, with apodictic certainty.

Space is nothing other than the form of all phenomena of external sensation. 

This predicate is attributed to things only insofar as they appear to us, that is, insofar as they are objects of the senses… Objects can be intuited as existing outside of us, and, if we abstract from those objects, what remains is a pure intuition known as space. 

Space is not the form of things in themselves; rather, things in themselves are unknown to us, and what we call external objects are nothing more than mere representations of our sensibility, whose form is space, but whose true correlate—that is, the thing in itself—is not known and cannot be known. 

As for phenomena in general, time cannot be separated from them, although phenomena can certainly be separated from time. 

Time is nothing… but a pure form of sensuous intuition… A representation that can be given only by a single object is intuition. 

Time is a prior condition of all phenomena in general and is an immediate condition of internal phenomena (of our soul); and precisely for this reason, it is also an immediate condition of external phenomena.

We deny that time has any claim to absolute reality.

Space and time are, therefore, two sources of knowledge from which we can derive various synthetic a priori insights; pure mathematics provides a brilliant example of this, particularly with regard to knowledge of space and its relationships. Taken together, they are pure forms of all sensible intuition and thus make a priori synthetic propositions possible. 

All our intuition is nothing more than a representation of the phenomenon; the things we intuit are not in themselves what we intuit in them. 

We have no knowledge other than that of phenomena… The transcendental object, however, remains unknown to us. 

Since the propositions of geometry are known a priori and with apodictic certainty, I am fully justified in asking this question: Where do you derive such propositions from?

Transcendental analysis

All knowledge, at least human knowledge, is conceptual knowledge—not intuitive but discursive.

We can reduce all the operations of the understanding to judgments, so that the understanding in general can be conceived of as a faculty of judgment. For, according to what has been said above, it is a faculty of thinking. To think is to know through concepts. Concepts, however, refer—as predicates of possible judgments—to some representation of a particular object. 

Regarding the pure concepts of the understanding, or categories… Synthesis in general is, as we shall see later, merely the effect of the imagination… But reducing that synthesis to concepts is a function that belongs to the understanding.

There are as many pure concepts of the understanding—which refer a priori to objects of intuition in general—as there are logical functions in all the possible judgments listed in the table above

Table of Categories. Regarding quantity: Unity, plurality, totality. Regarding quality: Reality, negation, limitation. Regarding relation: Inherence and subsistence (Substantia et accidens), causality and dependence (cause and effect), community (reciprocal action between agent and patient). Regarding modality: Possibility-impossibility, existence-nonexistence, necessity-contingency.

Categories, as the true root concepts of pure understanding, also have their own derived pure concepts… Allow me to call these pure concepts (though derived) of understanding the predicables of pure understanding… The aforementioned table contains all the elementary concepts of understanding.

The connection (conjunctio) of a multiple in general can never be apprehended by us through the senses, and therefore cannot, at the same time, be contained in the pure form of sensible intuition…Every conjunction, whether we are aware of it or not, whether it is a conjunction of the multiple in intuition or of various concepts, and, in the first case, of empirical or non-empirical intuition, is an act of the understanding, which we shall designate by the general term summary. 

The connection does not lie in the objects and cannot be derived from them—for example, through perception—and thus apprehended by the understanding; rather, it is the work of the understanding, which is nothing other than the faculty of connecting a priori and reducing the multiplicity of given representations to the unity of apperception. 

A judgment is nothing other than a way of reducing given knowledge to the objective unity of apperception. That is the purpose of the copula “is.”.

Categories are merely rules for understanding, whose faculty consists in thinking—that is, in the act of reducing the synthesis of the manifold, which is given to it through intuition, to the unity of apperception. 

The category has no other use in the knowledge of things than its application to objects of experience. Thinking of an object and knowing an object are not the same thing. Knowledge consists of two parts: first, the concept, through which an object is generally thought of (the category); and second, the intuition through which the object is given.

Can understanding, as spontaneity, determine inner meaning through the multiplicity of given representations, in accordance with the synthetic unity of apperception?.

One must explain the possibility of knowing a priori, through categories, the objects that may present themselves to our senses—not according to the form of their intuition, but according to the laws of their connection—that is, the possibility of prescribing the law to Nature and even making it possible. For without this capacity of ours, it would be impossible to explain how everything that can present itself to our senses must fall under laws that originate a priori in the understanding alone.

 The pure faculty of understanding, which prescribes laws for phenomena a priori through mere categories, can establish no laws other than those in which nature in general is grounded as the regularity of phenomena in space and time.

Transcendental Doctrine of Judgment (or Analytic of Principles). On the Schematism of the Pure Concepts of the Understanding… Concepts are entirely impossible and cannot have any meaning if an object is not given in them… Pure a priori concepts, in addition to the function of understanding in the category, must contain a priori formal conditions of sensibility (especially of the inner sense), which encompass the universal condition under which the category can be applied to an object. Let us call that formal and pure condition of sensibility, to which the concept of understanding is restricted in its use, the schema of that concept of understanding, and let us call the proceeding of understanding with these schemas the schematism of pure understanding… This schematism of our understanding, with respect to phenomena and with respect to their mere form, is an art hidden in the depths of the human soul, whose true workings we can scarcely guess at in nature or bring to light. 

System of All the Principles of Pure Understanding… A priori principles are so named not only because they contain the foundations of other judgments but also because they are not grounded in other higher and more general forms of knowledge…. The proposition “no thing has a predicate that contradicts it” is called the principle of contradiction… We must accord the principle of contradiction the status of a universal and fully sufficient principle… Principle of the permanence of substance: in every change of phenomena, substance remains… Principle of succession according to the law of causality: all alterations occur according to the law of the connection between cause and effect… And here is the concept of the relationship between cause and effect. 

A Refutation of Idealism. Theorem: The mere, empirically established awareness of my own existence demonstrates the existence of objects in space outside of me.

The principle of continuity ruled out any discontinuity in the series of phenomena (changes) (in mundo non datur saltus), but also any gap or void between two phenomena, within the totality of all empirical intuitions in space (non datus hiatus) … The proposition “nothing happens by blind chance” (in mundo non datur casus) is an a priori law of nature; the same holds true of the proposition “no necessity in nature is blind, but rather conditioned and therefore comprehensible” (non datur fatum)… We could easily present these four principles in order (in mundo non datur hiatus, non datur saltus, non datur casus, non datur fatum), like all principles of transcendental origin, according to the order of the categories, and assign each its proper place.

Transcendental Dialectic

Reason (subjectively regarded as a human faculty of cognition) has fundamental rules and maxims governing its use, which carry the authority of objective principles.

Let us give the concepts of pure reason a new name, just as we did with the pure concepts of the understanding when we called them categories. And that name will be “transcendental ideas.”. 

On ideas in general… I urge those who love philosophy… to take the word “idea” in its original sense [the Platonic sense]

The form of reasoning, when applied to the synthetic unity of intuitions in accordance with the categories, will contain the origin of certain a priori particular concepts that we may call pure concepts of reason or transcendental ideas.

By "idea," I mean a concept that is necessarily a product of reason and does not correspond to any object given in the senses. Thus, the pure concepts of reason that we are now examining are transcendental ideas. 

Thus, one could say that the totality of phenomena is merely an idea; for we can never form a picture of that totality… [he will call this idea “the world”]

System of Transcendental Ideas. Every relationship among representations from which we can form either a concept or an idea falls into one of these three categories: 1) a relationship with the subject; 2) a relationship with the multiplicity of the object in the phenomenon; 3) a relationship with all things in general.

Transcendental ideas can be divided into three categories. The first encompasses the absolute (unconditioned) unity of the thinking subject; the second, the absolute unity of the series of conditions of phenomena; and the third, the absolute unity of the condition of all objects of thought in general. 

The thinking subject is the object of psychology. The totality of all phenomena (the world) is the object of cosmology. That which contains the supreme condition of possibility for everything that can be thought (the being of all beings) is the object of theology. Thus, pure reason provides the basis for a transcendental doctrine of the soul (psychologia rationalis), for a transcendental science of the world (cosmologia rationalis), and finally for a transcendental knowledge of God (theologia transcendentalis) [let us recall that by “transcendental” Kant means “a priori”]

On the dialectical processes of pure reason. There are thus three types of these dialectical processes, corresponding to the number of ideas to which their conclusions lead. 

That the perceiving self is, in every thought, a singular entity that cannot be dissolved into a plurality of subjects… is implicit in the very act of thinking.

However, it is impossible to know oneself as a noumenon, since internal empirical intuition is sensory and provides nothing but phenomena. 

 The term “world” refers to the mathematical whole [that is, the set] of all phenomena and the totality of their synthesis…

First Antinomy of the Transcendental Ideas. Thesis: The world has a beginning in time and is also bounded in space. Antithesis: The world has neither a beginning nor boundaries in space, but is infinite in both time and space. 

Second Antinomy of the Transcendental Ideas. Thesis: Every composite substance in the world is composed of simple parts; and there is nothing in the world other than the simple or that which is composed of the simple. Antithesis: No composite thing in the world is composed of simple parts; and there is nothing simple in the world. 

Third Antinomy of the Transcendental Ideas: Causality according to the laws of nature is not the only basis from which the phenomena of the world can be deduced. It is also necessary to admit, for the explanation of these phenomena, a causality based on freedom. Antithesis: There is no freedom; rather, everything in the world occurs according to the laws of nature. 

Fourth Antinomy of the Transcendental Ideas. Does there exist in the world something that, as a part of it or as its cause, is an absolutely necessary being? Antithesis: There exists nowhere, neither in the world nor outside the world, an absolutely necessary being that is the cause of the world. 

Transcendental Idealism as the Key to Solving the Cosmological Dialectic. Space in itself, as well as time, and all phenomena, are not things in themselves, but rather, on the contrary, are representations that cannot exist outside our mind, and likewise the inner, sensible intuition of our mind… is not either the true self existing in itself

This object, which is the ideal [of reason], resides solely in reason and is also called the original being (ens originarium); insofar as there is no being above it, it is called the supreme being (ens summum); and insofar as everything is subject to it as conditioned by it, it is called the being of beings (ens entium)

Consequently, the famous (Cartesian) ontological argument, which seeks to demonstrate the existence of a supreme Being through concepts, is a futile endeavor that achieves nothing; no man will become richer in knowledge through mere ideas, any more than a merchant will increase his wealth if, to grow his fortune, he were to devote himself to adding zeros to his cash balance. 

On the impossibility of a cosmological proof of God’s existence. It is this proof that Leibniz calls “a contingentia mundi”… Absolute necessity is, in fact, an existence derived from mere concepts… The proof that purports to be a cosmological proof thus has no greater force than that of the ontological proof.

On the Impossibility of Physical-Theological Proof… [The question is] whether a particular experience—that of the things of this world, their nature and order—provides us with proof or not…. Such proof could demonstrate the existence of an architect of the world… but not a creator of the world, to whose will everything would be subject. 

The very same arguments that demonstrate the inability of human reason to affirm the existence of such a Being are also sufficient to demonstrate the presumption of any contrary assertion. 

On the regulative use of the ideas of pure reason. The ideas of speculative reason are not constitutive principles governing the extension of our knowledge to objects that experience cannot provide, but rather regulative principles governing the systematic unity of the diversity of empirical knowledge in general, which is precisely regulated.

The psychological idea can mean nothing more than the outline of a regulative principle, so the question “Is the soul spiritual in nature?” makes no sense… The second regulative idea of purely speculative reason is the concept of the world in general. … If we do not have this assumption merely as a regulative principle, we may make mistakes…If this idea is not restricted to merely regulatory use, reason goes astray, since it departs from the foundation of experience that must contain the blueprints for a path and ventures beyond this terrain into the incomprehensible and the unfathomable… When the idea of a Supreme Being is not used merely as a regulator (but also as a constitutive element)—which is contrary to the nature of an idea—the vagaries of reason then arise.

Strictly speaking, therefore, there is no controversy in the realm of pure reason. The two opposing sides are striking at thin air and fighting shadows, since they have gone beyond the bounds of nature.

Any synthetic knowledge of pure reason in its speculative use is, in light of the evidence that has been presented, absolutely impossible

All the concerns of my reason (both speculative and practical) are contained in these three questions: WHAT CAN I KNOW? WHAT SHOULD I DO? WHAT MAY I HOPE FOR? [capitalization ours].

It is always pure reason—but only in its practical application—that deserves the credit for linking to our highest interest a knowledge that mere speculation can only imagine.

I believe unwaveringly in the existence of God and in an afterlife, and I am certain that nothing can shake this faith, for to do so would undermine my own moral principles—principles I cannot renounce without making myself worthy of contempt in my own eyes…

Are you really going to insist that knowledge which is of interest to all people should take precedence over common sense, and that it should be revealed to you only because you are philosophers?

C) Critique

There is a standard critique of the Critique of Pure Reason that was soon put forward, known as F. Jacobi’s critique: the thing-in-itself, the noumenon, stimulates my sensibility by producing impressions in me—impressions that my sensibility arranges according to space and time. But to excite my sensibility is to produce something in it, is to be the cause of a certain change in its state of rest, when causality has been presented as a mere a priori principle of my understanding. There is, therefore, a flagrant contradiction here. Later philosophy has addressed this contradiction and has resolved it essentially in two ways that point to the two natural paths of further development of the line opened up by Kant. 

Schopenhauer’s approach consists in presenting everything around me as a representation that occurs within me, albeit a mediated representation, since only the representations I have through my own senses are immediate. Those seemingly “external” representations of the world around me are mediated because they “cause” in my senses the representations that are immediate to me: impressions. In this way, Schopenhauer restores coherence to Kant, for it no longer matters that causality is a mere representation, that it does not actually exist, since it proceeds from a representation—the mediated representation—and not from reality itself, as Kant claims.  But the price Schopenhauer will pay for this solution is very high: it is a significant step toward idealism, having viewed the world as representation (“The World as Will and Representation” is the title of his philosophical work).

The path taken by Fichte, Schelling, and Hegel is to abandon themselves unscrupulously to idealism, eliminating reality—what Kant calls “the thing-in-itself”—from the Kantian framework, since it is the ugly duckling of the marvelous Kantian edifice, that about which we can say nothing, remaining in itself as “ignotum X,” as something unknown to us. Fichte will retain the Self here, and nothing outside, with the Self being the one that goes out to objectify itself, so as to become the object of its own knowledge. This is not the time to recount the development of this philosophy, but only to say that Schelling’s philosophy will begin with the Absolute Spirit, and finally, Hegel’s philosophy will begin with Being (“God,” in religious terms, to use his own language), a Being that is Nothing—nothing to say, for it is the emptiest and most abstract idea, since it conceives of Being as an idea. 

The idea itself that it will come to know itself, just as in religious imagery the Father begets the Son—the idea already known, which contains within itself all truths, as in St. Augustine: The Idea in Itself. And this, in an act of freedom, will burst forth, an exhalation of the Spirit (as in St. Augustine), which in a pantheist thinker like Hegel will coincide with the creation of the world: The Idea gone wild.  

Cartesian philosophy evolved into Kant’s work, after which the stream of philosophical evolution continued on to Hegel’s pantheistic idealism (And this, in turn, to Marx’s dialectical materialism, for the author himself states in “The Philosophy of Poverty” that to say everything is an idea in dialectical evolution is the same as saying everything is matter in dialectical evolution—a matter of nomenclature). Hegel was right in saying that history—which for him is the history of philosophy—always ends up realizing the implications inherent in the idea: pantheism was implicit in the Cartesian idea (if I attempt, with my eyes closed, from universal doubt, to deduce reality rather than observe it, it is because everything necessarily exists, which is the very definition of God: the Necessary Being) And idealism was implied, for the Self that appears to Descartes in doubt is not the thinking self, but a thought self, from which first hangs the existence of God and then the existence of the world. A God, then, that is thought, and a world that is thought. As Vernaux says: “from a painted nail on the wall, only a painted chain can hang.”.

So far, this is the standard criticism, the one leveled by Kant’s own followers. My personal criticism is that Kant based his philosophy on science too early, when it was still underdeveloped (only a century after the publication of “Philosophiae Naturalis Principia Mathematica,” with which Newton began the journey of mechanics in 1687). For that reason, he could not be sufficiently critical of Hume, whose arguments against causality do not hold up under current science; for example: fire—a glow and a yellow color—causes the carbonization of paper, a causality that we do not see and that science will never see. Today we know that fire or an incandescent body—not a glow and a yellow color but “something that” (substance, denied by Hume) possesses those accidents and also possesses others that science has now discovered, such as the number of electrons in the outermost shell of its atoms, responsible for any chemical reaction and in particular for the carbonization of paper. Disarmed by Hume’s philosophy, he found for causality—which had vanished within it—that lifeboat of salvation that was apriorism, a lifeboat that would also serve to bring back to life the other drowned corpses of that philosophy, in particular substance and accidents. 

Second, my criticism is directed at the fact that Kant held a Euclidean conception of space and time, whereas today we know that together they form a four-dimensional manifold whose curvature manifests itself in gravity—a Lorentzian manifold. This is not the time to explain the central idea of Albert Einstein’s general theory of relativity, but it is the time to say that space-time as understood by science in Kant’s time—which he took as a priori assumptions of our sensibility—is very different from space-time as we conceive it now, and it is unthinkable that its curvature could be part of our a priori assumptions, since it has taken us centuries to come to understand it.

Third, Kant regarded Newtonian science as definitive and absolute knowledge, before it underwent three drastic revolutions: quantum mechanics, special relativity, and general relativity. In particular, no one now regards our natural science as definitive and absolute, but rather as provisional and approximate, albeit increasingly accurate.  According to Popper’s description of scientific theory, it has two phases: the creation of the experimental basis, in which experiments are conducted whose results are generalized into experimental laws; and the deduction of scientific theory from a few axioms or postulates—some experimental laws or certain propositions that imply them. In the first phase, the laws are clearly a posteriori, and in the second phase the propositions are clearly analytic since they are deduced from the analysis of the definition of the object under study, that is, from the analysis of the axioms. Thus, synthetic a priori judgments never occur, for these would be only the axioms if they were judgments, but they are not; they are merely hypotheses (In fact, none of Kant’s examples of synthetic a priori judgments drawn from science are such in light of current science: all are facts that we can deduce from the axioms of the theory in which they are framed). Simply put, There are no synthetic a priori judgments in science, as we currently understand it. But the existence of these judgments in science was the foundation—the very bedrock—of Kant’s grand edifice, which now appears as a giant with feet of clay!

Finally, I would like to draw attention to the issue of “schematisms,” a strange and mysterious aspect of Kant’s work, where he seems to concede defeat in the face of the central problem: Why do we apply certain categories to a given object rather than others? How does our understanding know which ones to apply? This could be resolved by asserting that the information he has considered “a priori” may not be merely “a priori” but also “a posteriori,” derived from the phenomenon, but this would be tantamount to shooting himself in the foot.  He resolves it by saying that “pure a priori concepts, in addition to the function of the understanding in the category, must contain a priori formal conditions of sensibility (especially of the inner sense), which enclose the universal condition under which alone the category can be applied to the object. That formal and pure condition of sensibility, to which the concept of understanding in its use is restricted, we shall call the schema of that concept of understanding, and we shall call the procedure of understanding with these schemas the schematism of pure understanding.” That the problem is not fully resolved, leaving a significant gap in his theory of apriorism, we can infer from his own words: “This schematism of our understanding, with respect to phenomena and with respect to their mere form, is an art hidden in the depths of the human soul, whose true workings we can scarcely guess at or bring to light.”.