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Human reason, in one sphere of its cognition, is called upon to consider questions, which it cannot decline, as they are presented by its own nature, but which it cannot answer, as they transcend every faculty of the mind.

Pure Reason

Kant introduecd two distinctions, the first was Analytic and Synthetic propositions:

1. Analytic proposition: a proposition whose predicate concept is contained in its subject concept, we require only analysis of the subject itself to understand this proposition (True by virtue of Meaning and if true then it is self evident) - "All bachelors are unmarried".
2. Synthetic proposition: a proposition whose predicate concept is not contained in its subject concept, we require something outside of the analysis of the subject. (True by how their meaning relates to the world and if true then it tells us something new about the world) - "All bachelors are happy"

Kant contrasts this distinction with another one which is a priori and a posteriori propositions:

1. A priori proposition: a proposition whose justification does not rely upon experience. Therefore, it is logically necessary.
2. A posteriori proposition: a proposition whose justification does rely upon experience. Therefore, it is logically contingent.

Of course, as Kant would grant, experience is required to understand the concepts "bachelor," "unmarried," "7", "+" and so forth. However, the a priori/a posteriori distinction as employed here by Kant refers not to the origins of the concepts but to the justification of the propositions. Once we have the concepts, experience is no longer necessary. The analytic/synthetic distinction and the a priori/a posteriori distinction together yield four types of propositions:

1. Analytic a priori
2. Synthetic a priori
3. Analytic a posteriori
4. Synthetic a posteriori

We can know analytic propositions by consulting our concepts in order to determine that they are true. Analysis of the subjects by our kowledge of concepts through previous experience. Kant says the Analytic a posteriori propositions is self-contradictory, so there are no analytic a posteriori propositions. So all analytic propositions are a priori. We can know Synthetic a posteriori by experience of the world. That leaves only the question of how knowledge of synthetic a priori propositions is possible. How understanding a proposition requires something outside of the analysis of the subject yet its justification doesn't rely upon experience.

This question is exceedingly important, Kant maintains, because all important metaphysical knowledge is of synthetic a priori propositions. If it is impossible to determine which synthetic a priori propositions are true, he argues, then metaphysics as a discipline is impossible. Before Kant's first Critique, empiricists and rationalists assumed that all synthetic statements required experience to be known. Hume's skepticism rested on that basic principles such as causality cannot be derived from sense experience only: experience shows only that one event regularly succeeds another, not that it is caused by it.  Kant's goal was to find some way to derive cause and effect without relying on empirical knowledge. Kant rejects analytical methods for this, arguing that analytic reasoning cannot tell us anything that is not already self-evident. Instead, Kant argued that it would be necessary to use synthetic reasoning. It can't be Synthetic a posteriori because this is the core of Hume scepticsm is that he found out there is no justification for causality in experienece. So it must be Synthetic a priori. However, this posed a new problem — how is it possible to have synthetic knowledge that is not based on empirical observation — that is, how are synthetic a priori truths possible?

Kant uses the classical example of 7 + 5 = 12. No amount of analysis will find 12 in either 7 or 5. The concept "12" is not contained within the concept "5," or the concept "7," or the concept "+." And the concept "straight line" is not contained within the concept "the shortest distance between two points". (So it is a synthetic) but once we have grasped the concepts of addition, subtraction or the functions of basic arithmetic which govern the relation, the same principle applies to other numerals (for example 4+6 = 10) and it tells us something new about the world without having experience with 4, 6 or 10. It is self-evident, and undeniably a priori, but at the same time it is synthetic. And so Kant proves a proposition can be synthetic and known a priori. But not all synthetic propositions are a priori, for example "All bachelors are happy" has no concepts of rules to govern the relation so it always requires experience.

Kant concluded that the mind operates through a priori categories present independently from experience. However, for him, these categories are not  innate ideas but they are merely the way the human mind necessarily processes information (for example, the concepts of substance, causality, etc.). First they would remain entirely empty unless filled with experience gathered from the senses. They give no information whatsoever to what reality really is (the things-in-themselves), but merely indicate how one understands it with a limited, human understanding. (Condition for understanding).
Thus causality when thought as a synthetic priori, it is a concept governing the events happening in sequence which we can apply at other sequences of events to tell something new about the world each time, yet they are a priori whose justification does not rely upon experience. thus Causality doesn't require experience.

Kant created a revolutionary synthesis between rationalism and empiricism that shed an entirely new light on the question of innate ideas.

1. From rationalism, he draws the idea that pure reason is capable of significant knowledge but argues that pure reason is flawed when it goes beyond its limits and claims to know those things that are necessarily beyond the realm of all possible experience: the existence of God, free will, and the immortality of the human soul. Kant referred to these objects as "The Thing in Itself" and goes on to argue that their status as objects beyond all possible experience by definition means we cannot know them and in the Critique of Pure Reason famously showed how all arguments for the existence of God are flawed, that the received views about the simplicity and immortality of the soul were problematic, and that our freedom could never be cognized. Yet, all is not lost, for Kant believed that the existence of God, the immortality of the soul, and the freedom of the will must be considered as postulates of morality and not objects of knowledge. It follows that problems which according to Kant are beyond experience cannot even be raised by pure reason.
2. Kant noted the peculiarity of Locke's suggesting that, after deriving all concepts from experience and reflection on experience, he could demonstrate the existence of God and the immortality of the soul, matters lying well beyond all experience. So to the empiricist he argued that while it is correct that experience is fundamentally necessary for human knowledge, reason is necessary for processing that experience into coherent thought. He therefore concludes that both reason and experience are necessary for human knowledge. In the same way, Kant also argued that it was wrong to regard thought as mere analysis. In Kant's views, a priori concepts do exist, but if they are to lead to the amplification of knowledge, they must be brought into relation with empirical data, without the concepts, intuitions are nondescript; without the intuitions, concepts are meaningless."

Kant achieves what he calls a Copernican revolution in philosophy by turning the focus of philosophy from metaphysical speculation about the nature of reality to a critical examination of the nature of the thinking and perceiving mind. In effect, Kant tells us that reality is a joint creation of external reality and the human mind and that it is only regarding the latter that we can acquire any certain knowledge. Kant challenges the assumption that the mind is a blank slate or a neutral receptor of stimuli from the surrounding world. The mind does not simply receive information, according to Kant; it also gives that information shape. Knowledge, then, is not something that exists in the outside world and is then poured into an open mind like milk into a cup. Rather, knowledge is something created by the mind by filtering sensations through our various mental faculties. Because these faculties determine the shape that all knowledge takes, we can only grasp what knowledge, and hence truth, is in its most general form if we grasp how these faculties inform our experience.

Essentially he is the philosopher who first came up with the idea that our mind constructs our experience. Just because humans think or feel about things does not make what they think or feel reality. No matter how hard we think or feel, we cannot overcome the constraints of our own minds. Kant legitimized the idea of perspective meaning everything, which opened the door to all kinds of other movements.
The external world, he writes, provides those objects - noumena, of "things in themselves", the supra-sensible reality beyond the categories of human reason - that we sense as a sensory input (experience) and it is our mind, though, that processes this information about the world by applying the categories of  understanding allowing us to comprehend it as a phenomena. These categories are a priori features of our mind that permit our sensible apprehension and ordering of representations of objects.
Quantity - Unity, Plurality, Totality.
Quality - Reality, Negation, Limitation.
Relation - Inherence and Subsistence, Causality and Dependence, Community.
Modality - Possibility or Impossibility, Existence or Non-Existence, Necessity or Contingence.
Also besides categories there are sensibilities which form the representation of objects which are space and time.

For example, say a subject says, "The sun shines on the stone; the stone grows warm," which is all he perceives in perception. His judgment is contingent and holds no necessity. But if he says, "The sunshine causes the stone to warm," he subsumes the perception under the category of causality, which is not found in the perception, and necessarily synthesizes the concept sunshine with the concept heat, producing a necessarily universally true judgment.

Kant's rejection of the more specialized branches of metaphysics is in part grounded in this earlier claim, that any attempt to apply the concepts and principles of the understanding independently of the conditions of sensibility (i.e., any transcendental use of the understanding) is illicit. Thus, one of Kant's main complaints is that metaphysicians seek to deduce a priori synthetic knowledge simply from the unschematized (pure) concepts of the understanding. The effort to acquire metaphysical knowledge through concepts alone, however, is doomed to fail, according to Kant, because (in its simplest formulation) “concepts without intuitions are empty”

Kant's Antinomies

They are contradictions which he believed follow necessarily from our attempts to conceive the nature of transcendent reality. He used them to describe the equally rational-but-contradictory results of applying reason to the universe of sensible perception or experience (phenomena). Empirical reason cannot here play the role of establishing rational truths because it goes beyond possible experience and is applied to the sphere of that which transcends it. The Reason has its limits.

The First Antinomy (of Space and Time)

    Thesis:
        The world has a beginning in time, and is also limited as regards space.
    Anti-thesis:
        The world has no beginning, and no limits in space; it is infinite as regards both time and space.

His argument for the thesis was that if the universe did not have a beginning, there would be an infinite period of time before any event, which he considered absurd. The argument for the antithesis was that if the universe had a beginning, there would be an infinite period of time before it, so why should the universe begin at any one particular time?

The Second Antinomy (of Atomism)

    Thesis:
        Every composite substance in the world is made up of simple parts, and nothing anywhere exists save the simple or what is composed of the simple.
    Anti-thesis:
        No composite thing in the world is made up of simple parts, and there nowhere exists in the world anything simple.

The Third Antinomy (of Freedom)

    Thesis:
        Causality in accordance with laws of nature is not the only causality from which the appearances of the world can one and all be derived. To explain these appearances it is necessary to assume that there is also another causality, that of freedom.
    Anti-thesis:
        There is no freedom; everything in the world takes place solely in accordance with laws of nature.

The Fourth Antinomy (of God)

    Thesis:
        There belongs to the world, either as its part or as its cause, a being that is absolutely necessary.
    Anti-thesis:
        An absolutely necessary being nowhere exists in the world, nor does it exist outside the world as its cause.

Practical Reasoning

Practical reason, on the other hand, is the power of the mind engaged in deciding what to do. It is also referred to as moral reason, because it involves action, decision, and particulars. Speculative reason, which is the use of reason to decide what to believe.Kant was the first to speak of the Practical reasoning limits and being critical of it.

"If one cannot prove that a thing is, he may try to prove that it is not. And if he succeeds in doing neither (as often occurs), he may still ask whether it is in his interest to accept one or the other of the alternatives hypothetically, from the theoretical or the practical point of view." The presupposition of God, soul, and freedom was then a practical concern, for "Morality, by itself, constitutes a system, but happiness does not, unless it is distributed in exact proportion to morality. This, however, is possible in an intelligible world only under a wise author and ruler. Reason compels us to admit such a ruler, together with life in such a world, which we must consider as future life, or else all moral laws are to be considered as idle dreams.

Proofing something requires experience of it and a capacity of the mind of the subject to structure it using the categories in the subject's mind, God and other metaphysical concepts can't be proved.

Morality

Kant is known for his theory that there is a single moral obligation, which he called the "Categorical Imperative", and is derived from the concept of duty.

"Act only according to that maxim whereby you can at the same time will that it should become a universal law without contradiction."

The categorical imperative is an attempt to identify a purely formal and necessarily universally binding rule on all rational agents. The Golden Rule, on the other hand, is neither purely formal nor necessarily universally binding. It is "empirical" in the sense that applying it depends on providing content, like "If you don't want others to hit you, then don't hit them." Also, it is a hypothetical imperative in the sense that it can be formulated, "If you want X done to you, then do X to others." Kant feared that the hypothetical clause, "if you want X done to you," remains open to dispute. He wanted an imperative that was categorical: "Do X to others." And this he thinks he discovered and formulated. Kant thought, therefore, that the Golden Rule (insofar as it is accurate) is derived from the categorical imperative

Kant divides the duties imposed by this formulation into two subsets:

1. we first have a perfect duty not to act by maxims that result in logical contradictions when we attempt to universalize them. The moral proposition A: "It is permissible to steal" would result in a contradiction upon universalisation. The notion of stealing presupposes the existence of property, but were A universalized, then there could be no property, and so the proposition has logically negated itself.
2. Imperfect duty: you do not attract blame should you not complete an imperfect duty but you shall receive praise for it should you complete it, as you have gone beyond the basic duties and taken duty upon yourself.