Metaphysics

The basic concepts of metaphysics are non-empirical (Soul, world, being as such, God, etc.) Therefore, Kant sets out to examine the possibility of metaphysics, which he cannot do within metaphysical thinking. He needs something new, a "propaedeutic," something that precedes metaphysical thinking in order to determine its validity. This leads to a new kind of philosophy, which he calls “transcendental philosophy.”
Transcendental philosophy represents the topic is not a specific class of objects or their mode of being, but rather the possibility of a priori reference: “What is the ground of that in us which we call ‘representation’ to the object?”
In this sense, Kant's philosophy becomes a science of reason. He makes a fundamental distinction between nature and freedom. This leads to a distinction and division between science and morality. Philosophy is not speculative, it is reductive-analytic, and it examines the rational framework that enables science to understand nature.
During the times of Kant, Newton's laws of nature (see below) were provable scientific discoveries, but they create a causal-mechanical foundation that makes it difficult to interpret the phenomena of life. Kant's philosophy tries to integrate the idea of human subjectivity with a Newtonian view of nature, which is a difficult project. (See a short summary of Newton's three laws at the bottom.)
Kant starts with the analysis of reason, ("Analyse des Verstandes.") What distinguishes him from Descartes? Descartes subtracts the experience of the world to reach the certainty of the subject's self-relation, and then examines the objects of consciousness. But for Kant, the subject-object relationship is first: his transcendental analysis reflects on the process of knowing in terms of its categorical constitution. What is the condition of the possibility of empirical experiences? How do we have to think the subject, and the world itself, before any real experience takes place?
How does Kant integrate Aristotle into his philosophy? He uses the concept of categories, but in a different way: They mediate between pure reason and external reality. The Kantian subject-object relation reflects Aristotle's distinction between matter and form: the thing in itself is pure matter, and the mind is pure form. Where they come together, they form the possible experience of the world that we can know.
The Critique of Reason (KrV) (1781) defines the rules by which we can comprehend nature, and then thinks about how the human subject fits into it. The Critique of Practical Reason (KpV) thinks how nature must be organized in order to make an autonomous subject possible.

Analytic and Synthetic Statements

See more about this distinction here.

The distinction between analytic and synthetic statements can be combined with empirical validation. Again, two options exist: propositions based on logical truth alone, and those grounded in experience. A priori propositions are propositions whose justification does not rely upon experience; they are logically necessary. The truth of a posteriori propositions relies on experience.

Kant argues that if it is impossible to determine which synthetic a priori propositions are true, then metaphysics as a discipline is impossible.

Debates about the nature and usefulness of the distinction continue to this day in the philosophy of language.

Reason and Metaphysics according to Kant

There will always be some sort of metaphysics. Driven by its nature, human reason is irresistibly led beyond the limits of the sensible world and asks metaphysical questions. Why is reason driven to these questions?
Never satisfied with what is conditioned, because it does not fulfill its search for explanation, reason seeks out what is unconditioned or absolute. Reason is thus inherently metaphysical, and humans are destined to pursue metaphysical questions. But are these aspirations legitimate? Are there any specific metaphysical forms of knowledge? This is Kant’s most important question.
Naturally inclined to metaphysics, pure reason necessarily develops ideas such as the soul, freedom, or God. In the first case, the soul is the ultimate substrate of thought, in the second, freedom is the unconditioned principle of action, and finally, God is the ultimate principle of reality. Kant insists that the ultimate aim of reason pertains exclusively to these three objects: the freedom of the will, the immortality of the soul, and the existence of God.
As a propaedeutic to metaphysics, the Critique of Pure Reason’s intention is to answer one specific question: How is metaphysics possible? Or rather, since metaphysics is a real disposition: is metaphysics possible as science?
But what does he mean by “science”? Unfortunately, Kant never states it clearly when discussing the possibility of metaphysics being a science. Today, the idea of a science is commonly associated with experimental and verifiable forms of systematic knowledge. But this cannot be the case here, because metaphysics by definition exceeds the confines of experience.
So what does Kant mean by “pure reason”? It is reason seeking knowledge without any recourse to experience.
He thinks pure reason can indeed justify its search for "a priori knowledge" (universal and necessary knowledge): Reason finds it in mathematics (which is based on axioms and demonstrations derived from an a priori intuition) and in physics, which formalizes the principles that account for the general laws of nature. These laws universal and necessary, and must therefore be of rational origin. In both cases, however, pure reason is shackled to possible experience only.
Nevertheless, the Critique of Pure Reason was evidently written to make metaphysics possible. In this book, Kant defines metaphysics as “nothing but the inventory of all we possess through pure reason, systematically arranged.”
"The starting point for such an inventory is the basic question of how it is possible for a priori representations to refer veridically to their putative objects. In order to answer that question we must first determine whether we really even have such representations, and if so, how many and of what kind they are. Thus our first step must be to inquire whether our cognitive faculty contains a priori representations. Since according to Kant we possess three such faculties—namely, sensibility, understanding, and reason—a rough initial division of the investigation will result in three sections: the transcendental aesthetic (for sensibility), the transcendental analytic (for the understanding), and the transcendental dialectic (for reason). Each of these sections will have to contain an investigation revealing which “pure” or a priori representations are proper to each faculty. Let us call this investigation a “metaphysical deduction.” As we know, Kant has concluded that sensibility contains two such representations (the representations of time and space), the understanding twelve (the categories), and reason three (the ideas). In a second step, the investigation must also show that for each of these faculties we possess no further a priori representations and hence that the metaphysical deductions are complete." (Förster, Eckart. The Twenty-Five Years of Philosophy (p. 6). Harvard University Press. Slightly altered highlights by me.)
Space: Kant argues first that it is not a concept abstracted from outer experiences since it must be presupposed for me to distinguish anything from myself. Secondly, space is a necessary representation a priori since I can only represent something as outside of myself by representing it as spatial, while I can represent space itself as void of objects. Thirdly, space is a pure intuition, not a universal concept, for space contains spaces within it, whereas a concept’s subordinate concepts fall under it. Finally, we represent space as an infinite given magnitude since no limits are set to the progress of intuition. Space is thus nothing other than the subjective condition of human sensibility, under which alone an intuition of something as distinct from myself is possible. (Based on: Förster, Eckart: The Twenty-Five Years of Philosophy (pp. 17-18). Harvard University Press.)
Metaphysics, Kant says, is essentially the inventory of reason’s a priori capacities for synthesis. And such an inventory may be called a system, because everything belonging to reason, regulated as it is by the idea of a synthesis and unity, obeys a certain order, a certain architecture. He also creates a name for this new system of metaphysics: “transcendental philosophy.”

Phenomena and Noumena, or: the Thing in itself.

We have to distinguish between experiences and the categories we use to classify them. For Kant, the universal concepts of things stem from the mental machine that transforms reality into categories of reason and experience. These categories are not the universal predicates of “things in themselves.” Reality as such, the things-in-themselves are unknowable since we know of them only insofar as they are known — that is, conceptualized with the aid of our mind’s categories. Hence the Kantian distinction between phenomena and the things-in-themselves: we cannot know (or speak of) the true nature of reality, we only know things as they appear to us by applying our mind’s (“a priori”) categories to them.
The reason for this limit is particular to Kant’s epistemology: In the act of knowing, our sensory apparatus only gives us access to a disorganized “manifold” of sensible impressions. Kant thinks that these impressions become orderly only through our concepts’ active synthesis of them. Since they arise within the mind, these concepts are necessarily a priori and impose their structural laws (order, unity, coherence and causality) to phenomena. “Thus the order and regularity in the appearances, which we entitle ‘nature’, we ourselves introduce. We could never find them in appearances, had not we ourselves, or the nature of our mind, originally set them there.”
These determinations (or categories) can be known a priori because they are immanent to reason itself. And since objects are known only through the categories, these categories are the “a priori principles of possible experience,” meaning it is through them that objects can be known. Therefore, what can be known a priori are not the a priori principles of things or Being, but only the “conditions of possibility of objects of experience.”
“Ontology is the first part that actually belongs to metaphysics. The word itself … just means the science of beings, or properly according to the sense of the words, the general doctrine of Being. Ontology is the doctrine of elements of all my concepts my understanding can have only a priori.” (Jean Grondin: Introduction to Metaphysics. p.19) This characterization of ontology agrees on all points with the Kantian project of a transcendental philosophy identified with metaphysics. Kant proposes to systematize our understanding’s a priori determination to organize experience. Such a metaphysics of our reason’s “legislative” faculty is therefore possible for Kant.
Categories by themselves don't produce knowledge yet. Categories are based on concepts, and concepts are rules that allow me us to unite certain representations and to bring them under even higher (more abstract) representations.
The basic form of judgment appears in a subject-predicate form, and it allows us to refer to actual objects (S is P, etc.) We can reduce other forms of sentences, like questions or commands, to this kind of representation concepts with experiences. For instance, a question is a judgment with a question operator (Is it the case that) (s is p), a command is a judgment with a command operator (Make it happen that) (s is p), and so on.
Classical Logic has already systematized the different forms of statements by abstracting from the content and considering only their form. According to Kant, we discover twelve fundamental forms (i.e. forms which are neither derivable from nor composed of others): With respect to their quantity, judgments are either universal, particular, or singular; with respect to their quality either affirmative, negative, or infinite; with respect to their relation categorical, hypothetical or disjunctive; and with respect to their modality either problematic, assertoric, or apodictic.
Kant uses the very important concept of "conditions of possibility" in two ways. (1) Obviously, the first Critique pertains to the “conditions of possibility” for metaphysics itself, since the credibility of metaphysics has been called into question by the empiricists. (2) Transcendental philosophy is an inquiry into the conditions of possibility of all objects, and accordingly inquires into our mind’s a priori determinations (our categories), which are the same for all phenomena.
The two projects will ultimately merge into one since the critical reflection into metaphysics’ conditions of possibility leads Kant to claim that metaphysics has no other task than to clarify the conditions of possibility for the experience of objects in general.

Critique of Practical Reason

What makes moral obligation real for us, what makes it valid as a basic determination of practical reason, is not an external system of justice or a pre-existing body of law, and also not individual experience. It is a pre-existing condition that determines what it means to be a person: You stand under a moral law. There is a sharp difference between legality and morality.

Critique of Judgment

"Kritik der Urteilskraft" (Critique of Judgment) is a philosophical work by Immanuel Kant, published in 1790. The book is divided into two parts: the first deals with aesthetics, specifically with the nature of beauty and how we judge things to be beautiful or not; the second part deals with teleology, which is the study of purpose or design in nature.

Kant argues that the judgment of beauty is different from other types of judgments, because it involves a subjective feeling of pleasure or satisfaction that is not based on any particular concept or rule. He also argues that judgments of taste are universal, in the sense that they are not influenced by personal preferences or cultural differences.

In the second part of the book, Kant examines the concept of teleology, which he defines as the study of the purpose or design in nature. He argues that we cannot explain the natural world solely in terms of efficient causes (i.e. cause and effect relationships), but that we also need to consider the idea of final causes (i.e. the purpose or end goal of a thing). He proposes the idea of a "purposiveness without a purpose," which he uses to explain the apparent design we see in nature even though there may not be a conscious designer.

Overall, "Kritik der Urteilskraft" is an important work in the history of philosophy, as it attempts to bridge the gap between the objective and subjective aspects of our experience of the world. It also raises important questions about the nature of beauty, the relationship between nature and design, and the limits of human understanding.

Kant's Idea of the Subject

There are three approaches to the concept of subjectivity in Kant:

The empirical subject: this is our self-aware everyday self and our subjective experience.
The transcendental subject is the place of "transcendental apperception". It generates the categories that organize reality for us. The two main principles are proximity and sequence: Space and time become the fundamental categories that unify in an act of a-priori synthesis the subject with raw experience and leads to the recognition of reality as we know it. The transcendental subject is a necessary "condition for the possibility" of science. It is not an individualized subject.
The subject as "Ding an sich," (thing in itself), the real subject.
- As humans, we are embodied, so we live in a dimension of freedom, even though we are also determined by the laws of physics and by Newtonian logic. The human being is a thing-in-itself, which also means that it is hidden from itself.
- Freedom coincides with morality because only a free subject can act according to ethical rules.
- Because of the discordance between what is, and what ought to be, we are by reason compelled to accept two ideas. They are speculative, but necessary: The assumption of a highest good, which is God, and also the belief in the immortality of the soul. These two concepts are the necessary postulates for practical reason.
- For Kant, freedom is as fundamental as existence. These two terms belong together, and in this regard, we are not living pre-determined lives.

Summary of Transcendental Philosophy

Immanuel Kant's transcendental philosophy is one of the most influential philosophical systems in history. In this system, Kant sought to explain how knowledge is possible and how we can have knowledge of the world around us. Here are the main steps in Kant's transcendental philosophy:

The distinction between analytic and synthetic judgments: Kant begins by distinguishing between two types of judgments: analytic and synthetic. Analytic judgments are those in which the predicate is contained within the subject (e.g., "All bachelors are unmarried"). Synthetic judgments, on the other hand, add something to the subject that is not already contained within it (e.g., "The apple is red").
The distinction between a priori and a posteriori knowledge: Kant also distinguishes between two types of knowledge: a priori and a posteriori. A priori knowledge is knowledge that is independent of experience, while a posteriori knowledge is knowledge that is based on experience.
The transcendental aesthetic: In the Transcendental Aesthetic, Kant argues that space and time are not properties of objects in themselves, but rather are the necessary forms of our intuition. This means that space and time are a priori conditions for our experience of the world.
The transcendental analytic: In the Transcendental Analytic, Kant examines the nature of our concepts and argues that they are not derived from experience but rather are necessary conditions for the possibility of experience. Kant calls these necessary conditions "categories," and he argues that they are a priori concepts that enable us to make sense of our experience.
The distinction between phenomena and noumena: Kant argues that we can only have knowledge of phenomena, which are the objects of our experience. We cannot have knowledge of noumena, which are things in themselves that exist independently of our experience.
The transcendental dialectic: In the Transcendental Dialectic, Kant examines the limits of our knowledge and argues that there are certain questions that we cannot answer, such as questions about the nature of God, the soul, and the world as a whole. He calls these questions "antinomies" and argues that they arise from the limitations of our concepts and our inability to have knowledge of noumena.
The moral philosophy: In his moral philosophy, Kant argues that morality is based on reason and that moral principles are a priori. He argues that the moral law is a categorical imperative, which means that it is an unconditional command that we must obey regardless of our desires or interests.

Overall, Kant's transcendental philosophy seeks to explain how we can have knowledge of the world despite our limited perspective and the limitations of our concepts. By distinguishing between different types of judgments and knowledge, examining the nature of our concepts and their relationship to experience, and exploring the limits of our knowledge, Kant provides a comprehensive account of how we can know anything at all. His moral philosophy also provides a framework for understanding the nature of morality and the basis for ethical behavior.

Quotes

Transcendental philosophy is the propaedeutic of metaphysics proper. Reason determines nothing here, but rather speaks always of only its own faculty … No one has had a true transcendental philosophy. The word has been used and understood as ontology, but (as it is easy to make out) this is not how we are using it. In ontology one speaks of things in general … one treated things in general directly—without investigating whether such cognitions of pure understanding or pure reason or pure science were even possible … But I cannot speak this way in the Critique … In transcendental philosophy we consider not objects, but reason itself … One could therefore also call transcendental philosophy transcendental logic. It is concerned with the sources, the extent, and the bounds of pure reason, and pays no regard to objects. Hence it is wrong to call it ontology. For there we do indeed consider things according to their universal properties. Transcendental logic abstracts from all that; it is a kind of self-knowledge (Kant’s Gesammelte Schriften, Akademie Ausgabe, Volume 29752, 756)

Metaphysics

Metaphysics, on the view which we are adopting, is the only one of all the sciences which dare promise that through a small but concentrated effort it will attain, and this in a short time, such a completion as will leave no task to our successors save that of adapting it in a didactic manner according to their own preferences, without their being able to add anything whatsoever to its content. For it is nothing but the inventory of all our possessions through pure reason, systematically arranged.… Such a system of pure (speculative) reason I hope myself to produce under the title Metaphysics of Nature. It will be not half as large, yet incomparably richer in content than this present Critique, which has as its first task to discover the sources and conditions of the possibility of such criticism, clearing, as it were, and leveling what has hitherto been a waste-ground. ~ Preface to his 1781 Critique

Causality and Experience

Let us take, for instance, the concept of cause, which signifies a special kind of synthesis, whereby upon something, A, there is posited something quite different, B, according to a rule. It is not manifest a priori why appearances should contain anything of this kind (experiences cannot be cited in its proof, for what has to be established is the objective validity of a concept that is a priori); and it is therefore a priori doubtful whether such a concept be not perhaps altogether empty, and have no object anywhere among appearances … Appearances might very well be so constituted that the understanding should not find them to be in accordance with the conditions of its unity. Everything might be in such confusion that, for instance, in the series of appearances nothing presented itself which might yield a rule of synthesis and so answer to the concept of cause and effect (Critique of Pure Reason, A90, cp. 100–1).

The Limits of Reason

It is humiliating to human reason that it achieves nothing in its pure [i.e. theoretical] employment, and indeed stands in need of a discipline to check its extravagancies, and to guard it against the deceptions which arise therefrom … The greatest and perhaps the sole use of all philosophy of pure reason is therefore only negative; since it serves not as an organon for the extension but as a discipline for the limitation of pure reason, and, instead of discovering truth, has only the modest merit of guarding against error” (A795).

Questions

There are problems with the concept of the "thing-in-itself":

Does it not require also a form of causality, because it affect our senses and leads to the manifestation of objects for us, even before the transcendental subject can configure them through the categories of understanding?
Isn't there an object knowledge in us, even before science and conceptual understanding arises?
Isn't there the need for a deeper foundational principle that Kant missed, who defines the conditions of science in an almost recursive way? A principle that generates even the possibility of science?
It was inevitable in the history of philosophy that the concept of a "thing an sich" in a Kantian sense gets eliminated. Hegel completed this job.

How does Kant use the concept of reason? Are there alternative ways of using this concept?
Space and time: These two concepts play an important role in Kant's philosophy. Why?
Kant recreates metaphysics as a metaphysics of freedom, which manifests itself through a moral law. The next generation of philosophers seizes only the idea of a transcendental subject and turns it into something absolute. German idealists also fuse the idea of freedom with the idea of the absolute spirit, claiming, like Hegel, that the desire for freedom drives history. Kant tries to create a synthesis of philosophy and science, but does he not inadvertently open the door to speculative philosophies ever since?

Newton's Laws

Quoted from Wikipedia:

Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. More precisely, the first law defines the force qualitatively, the second law offers a quantitative measure of the force, and the third asserts that a single isolated force doesn't exist. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows:

First law

In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.

Second law

In an inertial frame of reference, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma. (It is assumed here that the mass m is constant – see below.)

Third law

When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687. Newton used them to explain and investigate the motion of many physical objects and systems. For example, in the third volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation, explained Kepler's laws of planetary motion.

Some also describe a fourth law which states that forces add up like vectors, that is, that forces obey the principle of superposition.