Lately, I’ve been exploring this book, which I will refer to as simply “The critique” from now on, by following the lectures by Robert Paul Wolff and decided to put my notes here in case someone finds them useful. This is a summary. The ideas expressed in it belong to Immanuel Kant. The phrase “Kant thinks” can accompany each sentence from it, but it is omitted for brevity and ease of reading. But at the same time, it is not objective - I am interpreting the ideas in the book the way I understand them, which may or may not be the way your philosophy professor interprets them. Also, the text is not in any way a substitute of reading the book itself - rather my aim was for it to help people who read the book by providing an additional viewpoint into what is happening in it.

I put my original research in a separate article about Kant’s categories.

Why I am reading this book (not related to the book itself, you can skip it)

One year ago, while wandering in an antique bookshop, I found a very well preserved and pretty-looking little book, which also looked quite interesting. Being fond of manually-printed books I got it partly as a collectible and partly because it was short and looked interesting. The book was called “Critique of practical reason” and, as it later turned out, it was the second of Kant’s critiques the first one being the much larger “Critique of pure reason”. Realizing that I bought part two without having part one felt unpleasant, but I did not want to drop the whole thing, and the respect I feel to people who dedicate their time to writing books prevented me from going straight to part 2. So I decided to go with it. I purchased the first book which turned out to be several times longer than the second one and started studying it.

Before we begin

Philosophy is a strange beast - its position as kind of a middle ground between science and, literature (or religion, as per Bertrand Russell) makes it, in some respects, harder than both of these disciplines - unlike novels and scientific paradigms, no philosophical work can be viewed by itself. So the only way to go forward is to go deeper into the rabbit hole. Here are some things that you definitely have to know about in order to read this book.

Historical context

The Critique is an epistemological work, which means it is about knowledge. For a long time, epistemology has introduced a distinction between the two main ways in which we obtain knowledge, according to which each thing is known either a priori or a posteriori. A statement is said to be known a priori if it is not derived in any way from experience. Imagine a mind which exists independently from a body, with no possibility to communicate with the outside world. Everything that this mind can know about the world is a priory knowledge. Everything else, all the knowledge that we gain through experience as individuals is a posteriori.

The idea of a priori statements is as old as philosophy itself with many philosophers believing that we should not trust our senses and that observation is not a valid way of obtaining knowledge. At the time when the Critique was published, this view was held by people such as Rene Descartes and Gottfried Leibniz who were collectively known as rationalists and held some very extravagant (and some ridiculous) theories. Here is a piece by Rene Descartes which characterizes this view (a variation of the famous “Cogito ergo sum”):

But I have convinced myself that there is nothing in the world, no sky, no earth, no minds, no bodies. Does it now follow that I too do not exist? No: if I convinced myself of something, then I certainly existed. But there is a deceiver of supreme power and cunning who is deliberately and constantly deceiving me. In that case, I too undoubtedly exist, if he is deceiving me; and let him deceive me as much as he can, he will never bring it about that I am nothing so long as I think that I am something. So after considering everything very thoroughly, I must finally conclude that this proposition, I am, I exist, is necessarily true whenever it is put forward by me or conceived in my mind. [From Meditations on First Philosophy]

An opposing view - that we can claim that we know something only if we know it from experience (a posteriori) were held by another school of philosophy - the empiricists, represented by Locke, Berkeley and Hume. It is the attack on the principle of causality made by the latter which inspired Immanuel Kant to write the Critique:

It appears that, in single instances of the operation of bodies, we never can, by our utmost scrutiny, discover any thing but one event following another, without being able to comprehend any force or power by which the cause operates or any connexion between it and its supposed effect. The same difficulty occurs in contemplating the operations of mind on body- where we observe the motion of the latter to follow upon the volition of the former, but are not able to observe or conceive the tie which binds together the motion and volition, or the energy by which the mind produces this effect. The authority of the will over its own faculties and ideas is not a whit more comprehensible: So that, upon the whole, there appears not, throughout all nature, any one instance of connexion which is conceivable by us. All events seem entirely loose and separate. One event follows another; but we never can observe any tie between them. They seemed conjoined, but never connected. And as we can have no idea of anything which never appeared to our outward sense or inward sentiment, the necessary conclusion seems to be that we have no idea of connexion or force at all, and that these words are absolutely without meaning, when employed either in philosophical reasonings or common life. (David Hume, 1737)

Roughly speaking where rationalists placed religion and faith, the empiricists placed science and observation.

Emanuel Kant’s idea was to create a system which unites these opposing views in a cohesive whole, where each of them has its rightful place. To do that, he rejected the rationalistic notion that we can know something about the real world just by thinking, but he also argued that experience is not the only source of knowledge. To prove this last point, he ventures to find out how the human mind actually works - what is it that we actually know a priori (in other words, what we are programmed to know since our birth) and how valid it is.

What is this book about

I already started talking about what is the Critique about, but before we fully answer that question we need to introduce another distinction between logical statements. This is the distinction between analytic statements (or tautologies as they are also called) and synthetic statements (as you will learn, Kant likes to divide stuff in two). Analytic statements are ones which are derived from other statements via logical rules. The most famous example of such statements is Aristotelian-style syllogisms, for example, if we know that “Athenians are mortal and Socrates is an Athenian” we can conclude that “Socrates is mortal.” Such statements are called tautologies because the conclusion consists of nothing more than a repetition of what is already known. Analytic statements are, therefore, not very interesting. It is the synthetic statements (i.e. everything else) that are the subject of the book.

It is obvious that analytic statements can be deduces a priori i.e. I don’t need to have any experience with Socrates or Athenians to conclude that if Athenians are mortal and Socrates is an Athenian, then Socrates is mortal. It is equally obvious that the main way to gain synthetic knowledge is a posteriori - through experience. But do we have synthetic a priori knowledge (or transcendental knowledge, as Kant also calls it)? According to Kant, we do.

The word “Critique” means “a detailed analysis and assessment of something.” When we say “pure reason”, we mean pure from experience (a priori). Kant begins writing with the firm conviction that such knowledge exists (i.e. real knowledge about the world which is not perceived through the senses) and then ventures in an inquiry to prove that that is really so and what are the boundaries and the objective validity of such knowledge.

Last one before we actually begin, I promise (you can skip that one as well)

Heraclitus was a prominent Greek philosopher from the pre-Socratic era. Most of his works are now lost save for interpretations from other philosophers and short slogans the most famous of which is “everything flows”. Still, we know that, in his philosophy, Heraclitus painted a picture of a world which was (as this phrase suggests) characterized by constant change and in which nothing remains the same from moment to moment. “In the same river we both step and do not step”, he said “, we are and we are not.” A tragic view, due to which he was known as “the Weeping Philosopher” as opposed to his “colleague” Democritus who, having theories which were more akin to contemporary scientific thought, aiming to help us explain and make sense of the world, was known as “the Laughing Philosopher”.

It is not that Heraclitus’s thoughts don’t make sense. But theories which make sense by themselves are not the same as theories which help us to make sense of the world. A theory which does both of these things is a true science, provided it only operates in its own (usually very limited) scope (Darwin’s theory of evolution is scientific only when we talk about animal species, not human societies, for example). A theory which allows us to make sense of the world without itself making sense can be a religion or another kind culture-shaping doctrine.

And what about such sceptic theories which make sense by themselves without actually telling us anything useful like that of Heraclitus, or like David Hume’s attack on the causality principle, which inspired Kant to write the critique? They habituate a weird limbo. While they do provide interesting insight, they are not something that most people would choose to study, or even want to know much about. Which is understandable - there is no takeaway in such theories. They tell us nothing about how we should live our life, or what we should do when we feel that we’ve lost direction. All they do is to confuse us and make us more unsure of us, so in a way, they are the opposite of useful. Throughout history, they have been sometimes banned, and, more often, ignored by the general public because rarely fit into an overall picture which is promoted as something we should follow. Some people like to study them as mental exercises. Even more extraordinarily, there are ones who are ready and willing to incorporate them into their worldview. Such people are willing to dedicate themselves to searching the ultimate truth, while at the same time preserve a healthy (and even unhealthy) dose of scepticism and the knowledge that such thing does not really exist. They are motivated to dwell into philosophy a little (or a lot) deeper and really try to make sense of even the most sceptic theory in a way that also, tells them how to live their life, or at least gives them a hint. And although the result of their efforts seems a bit artificial at times (as Kant’s critics always like to point out for his philosophy) it is interesting, if only due to the fact that it reaches the limits of the knowable.

Why do they do it? Sure, mainstream philosophical doctrines have their internal inconsistencies, but that does not stop people from making use of them and, is not such a big deal, realistically speaking if you want to get down to it - all ideas are bogus at some level, so the only objective way to compare them is by their utility where the simpler and more rewarding ones will easily win by the “Ignorance is bliss” principle. Is it for the fame (probably not) or due to some quasi-religious dedication? Surely, this is an interesting question, but currently, I want to know this:

If everything changes all the time, how can we step into the same river twice?

Transcendental doctrine of elements: Transcendental Aestetics

We said that the transcendental knowledge is knowledge of “synthetic a priori statements about the world”. But what do we mean when we say the world and can we really know something about it? To answer this question, we must make another distinction: the distinction between objective reality, consisting of “things in themselves”, and the image with which this reality manifests itself to us as “phenomena” or “sensation” that we experience. We saw that rationalists are interested with objects as themselves and not so much in how do we perceive them, while empiricists think that we cannot know anything unless we perceive it and are often focused on how the human mind works. Those are really different paradigms, so we cannot really choose one or another. It is possible, however, to incorporate the interest of both parties by studying both the world of things the way we perceive them and the outer, objective world. Introducing this distinction and talking about the two worlds separately makes things much more precise. It allows us to postulate that everything that we ever perceive as true is true, at least when it relates to the world as perceived by us. What about the objective reality? If we follow this line of logic then things in themselves have to be, by definition, unknown.

And because the only way for us humans to know something is to perceive it, we must begin our quest for transcendental knowledge with the science of transcendental perception or as it is also called transcendental aesthetics.

We claim that the idea of space, along with the idea of time is the only notion that allows us to construct a priori synthetic statements about the world as perceived by us.

On Space

Here are some arguments about why space is an a priori concept, that is one that is inherent in the human mind:

• The sense of “uniqueness” of space - the human mind cannot perceive more than one space, more than one universe.
• Many statements about geometry, are considered undisputedly true, without having a proof (for example how do we know that space has three dimensions, or that the sum of two sides of a triangle is greater than the third side). We cannot deduce this from anywhere, and yet they are too universal for us to say that we obtained them from experience.

Space is an a priori concept about the world as perceived by us. But it is even more than that - it is the medium that enables perception itself: you can imagine an object void of any of its qualities, but not void of space. For example, each object has a color but you can imagine an object without its color, or imagine it without its scent. You can even imagine an object without the concept of time, as you do when doing geometry, but you cannot imagine an object without first positioning it in the space. Because of this, we may say that space is not only a property of the world as perceived by us, but is also somehow a property of the objective world. In effect, space binds these two worlds together.

On Time

Many, if not most, of the of the things that we said about space, can also be said about time. Like space, it is universal and unique - we can only perceive one timeline, that is, for every two events we can always say that one comes before the other. Space and time are the two components that shape our reality - space allows objects to co-exist, and time enables their states to form a succession and thus enables change.

Unlike space, though, time is not in any way connected to the objective world, and the notion of the existence of one unique timeline is also not objectively true (kudos for Kant for finding that out exactly 124 years before Einstein’s theory of special relativity). Time is a human-made concept that does not exist in the objective world. It is, however, a very important component of our inner, subjective world and it closely related to the idea of self-perception - without the notion of time, the concept of the self won’t exist either, because what is the “I” if not the collection of all perceptions experienced throughout my lifetime.

The notion of time allows us to represent ourselves as actors in the world, and the notion of space allows us to perceive that world as observers. If we take space and time, as known a priori (and we should as they are the only two things that can exist without the presupposition of some other object existing) we have a stable framework for perceiving the world around us.

Transcendental doctrine of elements: Transcendental Logic - Transcendental analytics

Perception is a necessary condition for obtaining knowledge, however, perception does not constitute knowledge by itself - we obtain knowledge by thinking. But thoughts by themselves also don’t constitute knowledge either. Think about scientific theories, for example, say a scientist speculated about the experience of objects called “black holes”. Can we say that the scientist they knew something about the object before the object was observed? No, because no matter how sophisticated the theory is, it was still just a theory, and the theoretical object “black hole”, is a different object that actual black holes that exist, no matter how similar they are.

Now imagine a person who does not know about black holes theory but who, through his telescope, sees a black hole (or rather the way in which a black hole messes up the orbits of some other bodies). He/she is on the other side - he/she is perceiving the thing, but he/she does not have any idea what it is. His/her observation is useless without a theory that explains it, and a theory is useless if it does not have an application. To put that in simpler terms:

knowledge = perception + thought.

The science that deals with the way we think is, of course, called logic. Logic can be general and can be specific to some domain like accounting, biology etc. And the general logic, we can divide to pure and applied where the applied part is everything that is related to the human mind as such (the psychological part, so to say). Taking away all else, pure logic contains just a few fundamentals that we know a priori and are essential to the way we think. Pure logic is, therefore, synonymous with “first order” logic - a fact which is proven (as much as it can be) by Kurt Godel in his completeness theorem. Therefore, these a priori concepts are the concept of a negation, the AND and OR operators and, of course, the forall… there exists structure which allows us to define functions.

Is pure logic also transcendental, in the sense of the word that we used when we talked about transcendental aesthetics - a prerequisite for a priori knowledge? Not quite, since, as we said earlier, logic does not constitute knowledge. That is, logically-correct statements are not necessarily true. Transcendental logic is, then, is pure logic but only insofar it is related to objects of sensibility i.e. it is the science of understanding.

But if it is true, as we said earlier, that perceptions are essential for acquiring knowledge, can we talk about transcendental logic independent of perceptions? In other words, can we make logical assertions about an object in the real world, without using our sensibility i.e. without first perceiving the object? The answer to that question is that we can, by applying the same tactic that a scientist uses to formulate their theories. By saying “Suppose that such and such object exists” or “Let X be such object that”. In other words, we can not know anything about a given object until we see it, but we can delay the moment when we perceive it, and think about it in advance. The technical name of these judgments is “functions” - they produce knowledge, but only when given knowledge in advance.

So, for example, I can be walking a wood and thinking something like:

Suppose that I had a body which ran on a liquid substance that was distributed to its limbs by a series of tubes, called blood. Suppose further that there were other beings (which I will call “bears”) possessing, as part of their bodies, sharp objects that are capable of tearing these tubes out, thus spilling the substance.

If that were so, then I would try to avoid being in a close proximity with those beings.

Jokes aside, even the most abstract hypothesis must rely on some logical concepts, such as the concept of a cause and effect. These concepts are the pure concepts of understanding and are as time and space, part of our a priori arsenal for acquiring knowledge

Transcendental Analytic: Analytic of concepts

Transcendental logic is analytical by nature. All logic that is not analytical consist of fallacies, which are discussed in the second section called - transcendental dialectic. The main subject of the transcendental logic are the pure concepts of the understanding, which we discussed earlier and this chapter is an attempt to discover and systematise them.

By the way, I am not following the systematic structure of the book closely, simply because the structure is way too complicated for me to do that in such a short resume. If you want to know more about various structures in this book check out this resource.

Of the transcendental guide for the discovery of all pure concepts for the understanding

If we use functions to abstract away all objects of experience in our thought, we will discover that each judgment (or each statement if we are using the language of logic) that we make has four main characteristics - quality, quantity, relation and modality (modality is not a characteristic of the judgment per se) - with three different ways to classify each statement under each of those characteristics:

Quantity - What are the objects that the statement is valid for?

• Universal: for all
• Particular: there exists A
• Singular: there exist unique A

Quality - What do we want to say about the object or objects?

• Affirmative: A is B
• Negative: A is not B
• Infinite: A is non-B

Relation - If our statement is a composite statement, what are the parts of which it is composed of and how do they stand against one another (concerns combining several statements into one)?

• Categorical: P (no relation)
• Hypothetical: if A then P
• Disjunctive: either P or Q

Modality - is the statement actually true (unlike other distinctions, this one has to do not with the content of the statement but with its connection to the environment).

• Problematic: possibly P (we do not claim that P is true).
• Assertoric: P (we claim that P is true).
• Apodictic: necessarily P (P is necessarily (axiomatically) true).

Each statement can be categorized by all three of these characteristics, for example, the statement:

There necessarily exist a unique A such that A is Boris Marinov.

is a categorical, apodictic, singular, affirmative statement.

If we take the judgments from this list in the respect with which they relate to reality, we arrive at a table that defines preconceptions for all possible characteristics and attributes that can be said about a thing or things. We call those “pure concepts of understanding”, or categories as they are known historically (as per Aristotle).

Quantity

• Unity (measure) - recognition of a thing as one
• Plurality (plurality) - recognition of there being several things
• Totality (whole) - unification of all things (of a given group) as one.

(Note that for this category the order is not the same as the table of judgments - the category of unity corresponds to singular judgments, the category of plurality - to particular judgments and the category of totality - to universal judgments (the argument is made by Frede and Kruder, I read about it here)

Quality

• Reality - recognition of presence
• Negation - recognition of absence
• Limitation - recognition of a thing as both present and absent (e.g. in different time periods).

Relation

• Inherence and subsistence - representation of a thing as being inherent, everpresent
• Causality and dependence - representation of causal effects (things being dependent upon other things)
• Community - representation of a relation where one thing causes the other and the other way around (causality of a substance as reciprocally determining another substance)

Modality

• Possibility - Impossibility - speculation for the possibility/impossibility of a given thing
• Existence - Non-existence - perception of a thing as existing/non-existing
• Necessity - Contingency - acceptance of a thing as inherently true (existence given through possibility itself)

Of the deduction of pure concepts for the understanding

We already discussed how our sensibility allows us to perceive all kinds of objects, using the a priori concepts of space and time. We discussed the mind’s thinking apparatus which allows us to build all kinds of theories about our world, both simple and very complex. But how do these things come together? That is to say, how do we take an astrological object that we see in the sky, and a scientific theory and say “this actual object is an instance of this theoretical object”.

The key to understanding this is to realize that theories rarely talk about one particular object. Rather, a theory encompasses a whole set of objects, or (even before arriving to a definition of what “object” means) a set of intuitions. Scientific theories are a type of concepts, a concept being a general rule which enables synthesis of a manyness (or manifold as Kant calls it) of perceptions into a unified whole. These concepts are, then, a prerequisite of knowledge

When we look at the sensibility we can almost feel what we know a priori, however, with reason, things are not that intuitive. That is why it isn’t enough just to state the categories - we must prove that they are indeed valid. In order to do that, we must examine more closely the process we called synthesis

Synthesis

This unification of many objects, under one concept, is what actually unites our sensibility with our mind’s logical facilities, enabling knowledge. The process is called synthesis and we can see that it is not objective - it is an act of the imagination (one person with might argue that no object in the universe fits the description of a black hole completely, while another might find the description matching all kinds of objects which were never intended to be described by the theory). The process consists of three stages:

1. Apprehension - a representation of an object (phenomenon) is perceived by the senses.
2. Reproduction - the image of the object (a picture, if you will) appears in the mind.
3. Recognition - a preexisting concept which matches (the image of) the object is found and connected to it.

Note that the process of synthesis is only possible due to our conception of time. Time allows us to unite different representations that we perceive, which resemble one another in some respect and classify them as instances of something which we already know.

By viewing time in the way that we defined it (as the form of our inner sensibility) we solve the paradox related to the person who passes the same river twice:

Problem: If we are strict enough (as we should be, if we are interested in philosophy) we cannot justify and make sense of the identity of an external object. That is if yesterday I cross at a river which is on my way, and then on the next day go to the same place and cross a river again, I cannot really say that I crossed the same river as before - neither is the river the same as it were yesterday, nor am I.

Solution: The connection between the river I crossed yesterday and the one I crossed today is actually pretty simple - both were crossed by me, and I decided to perceive them as one and the same river, based on my perceptions and logic. Furthermore, I too am the same person as I was yesterday, just because I remember yesterday. It is my memories - the placing of my perceptions on the temporal scale that make up my personality and my world.

The solution might appear quite anticlimactic at first, but it is quite exciting once you realize that accepting it means that all rules for making sense of the world are subjective. In the same way, as God is said to breathe life into a dust figure and thus making it a living thing, we, human beings, breath into our image of the world around us, the laws of nature. Does that mean that our knowledge subjective? It does. Does that make it an illusion? Not entirely, for it is based on the reality that we experience, therefore it has something to do with it. For example say you have a goal to study all great works of philosophy which were ever published. Here are many ways to approach this task:

• Prepare a list of those works and start reading them one by one.
• Start with reading the writings of the ancient philosophers, and then the ones that came after them and repeat till you go to the present days.
• Pick the work that you consider the greatest and study it first, then study the works which it references, and those which are referenced by it and so on.

All those approaches are based on subjective choices and each of them encompasses a slightly different concept of which the great works of philosophy are. However all of them “work” i.e. the end result is that you will be an expert in philosophy.

Note also that there is no other way to approach this task, that is not to say that there are no other approaches, but that you cannot study the great works of philosophy without following an approach. But since all of them are subjective, you cannot have knowledge that does not have a subjective element in it.

This difference between the subjective and the objective aspects of knowledge and perception is also captured in the Heraclitus’s fragment which I used in the introduction - this is made evident if we consider it in its entirety:

In the same river we both step and do not step, we are and we are not.

One way to interpret this is that we are only insofar we consider that we step into the same river and we are not when we don’t make that assertion, and that perception is basically the same thing as self-awareness - that each thing we “know” about our environment is somehow equivalent to something we assert about ourselves. Accepting that two rivers which we saw during different times are actually one and the same river is a choice that we make (e.g. because it seems practical) and it is this choice which defines us as individuals, while at the same time enabling our perceptions - if we are able to see things as they are in themselves, they won’t make any sense for us (simply because nothing makes sense by itself), but when we perceive them as part of a bigger picture, build around our earlier perceptions and choices (e.g. around ourselves), we are able to “know” something about them. We perceive rivers as things that we can cross, things from which can drink etc. All other objects and people, we perceive based on the ways in which we relate to them and it is these relations (and the subsequent actions based on them) that make us individuals.

Transcendental Analytic: Analytic of principles

Now let’s examine in detail how are the above transcendental concepts are applied to the sensible world, enabling us to reason about it i.e. how do we judge if a given appearance falls under a certain concept.

Introduction. Of the Transcendental Power of Judgment in General

If concepts are rules, then judgment is the ability to say if a given object or event follows a given rule. An ability which must require something more than good knowledge of the rules and the of instances themselves, as it is not possible to, as we said earlier, to base our judgments solely on logic - with logic we can only make sure that a given system of statements is consistent within itself.

In order to understand how judgments happen, we have to look at the faculty of sensibility and to see how do the pure concepts of understanding are related to it.

Of the Schematism of the Pure Concepts of the Understanding

Perceptions and concepts are, by themselves, not bound with one another, they are merely the product of two different faculties of the mind. So in order for them to be united, a third component must be involved, acting as a mediator between the two. This components is the concept’s schema.

When we talk about “normal” concepts, we can say that their schemas are just procedures for generating images that fall under the concept, e.g. using the schema of a dog the brain can produce an image showing, for example, how does a dog look when viewed from a certain angle and then, compare this image to the images produced by the faculty of sensibility and determine if the animal it is seeing is a dog. The pure concepts of the understanding do not have images, but still they must have schemata, in order to be used. A concept’s schemata describes how can a concept be used to recognize objects in the world of sensibility, which, as we discussed, is the only world to which we have access to. In effect, it is limiting the concept, in order to make it useful.

As we said, perception is inherently subjective and is the result of the inner sense of the individual. That is why the pure concepts’ schemata are bound to the form of the inner sense, that is to time.

Here are the schemas of each of the categories:

Quantity - the producing of time.

• The category of quantity corresponds to intuition. The schema of all categories of quantity is the concept of the number i.e. of successive addition of one object to another.

Quality - the filling of time

• The schema of all categories of quality is the increasing or decreasing quanta of sensation which the transition between (perception of) existence and non-existence of objects in time.

Relation - connecting perceptions according to a rule in time-determination.

• Inherence and subsistence - permanence in time
• Causality and dependence - succession of events insofar as it is subject to a rule (events causing other events in time).
• Community - co-existence according to a universal rule.

Modality - time itself

• Possibility - Impossibility - determination of a thing at some time or other.
• Existence - Non-existence - existence in some determinate time.
• Necessity - Contingency - existence of object at all times.

System of All Principles of the Pure understanding

Let’s now outline the principles according to which judgments are undergone.

System of All Principles of the Pure understanding: The Supreme Principle of All Analytic Judgments

The supreme principle of all analytic judgments is simply the principle of non-contradiction which states that something cannot both be and not be e.g. “an unlearned man cannot be learned”.

System of All Principles of the Pure understanding: The Supreme Principle of All Synthetic Judgments

The principle of analytic judgments is valid for synthetic judgments as well, however it is not sufficient to justify their existence, as it can only falsify one concept by comparing it with another and, while the truth of a synthetic judgments can be determined merely by looking at judgments themselves, analytic judgments are inherently bound to objects in the real world.

So what, then, would the principle of such judgments be? The only reason we can know about objects in the real world in the first place is because we experience these objects. This principle holds even for objects that we have not yet seen - the key word here is “yet” - even if we haven’t experienced a given object, it should be possible for us to experience it if it is real, and it is this possibility of experience which makes the object real and gives the concept of it validity. Even concepts as space and time would lack objective validity if it weren’t necessary for experience.

And, as we said earlier, experience is the result of synthesis, so the supreme principle of all synthetic judgments is that every object is subjected to the necessary conditions of synthetic unity of the manifold of intuition in a possible experience.

System of All Principles of the Pure understanding: Systematic representation of All of the Synthetic Principles of the Pure Understanding

Besides being the source of rules (concepts) according to which intuitions are judged, understanding also contains the principles for applying these rules, which we call “principles of the pure understanding”. We can derive those principles using the table of categories. Here they are:

• Quantity - Axioms of intuition
• Quality - Anticipations of perception
• Relation - Analogies of experience
• Modality - Postulates of empirical thought in general.

We may divide these categories in relation to their use in experience into mathematical (quantity and quality) and dynamic (relation and modality) where the former defines our objective reality as such and the latter describes the laws which it follows - if we view the humans’ ability to perceive as a formal system, then the mathematical categories contain the definition of the system and the dynamical ones supply the general laws for using it in an empirical setting in terms of its scope of validity, the category of relation being the more interesting of the two, because it is this category which postulates the world itself is lawful i.e. that it is possible to understand and predict its behavior through the employment of logic. Let’s review those principles.

Quantity - Axioms of intuition

The principle for using the category of quantity is: “All intuitions are extensive magnitudes.”

Here “extensive magnitude” means magnitude that is a result of a continuous aggregation of different amounts of stuff over time.

Unity

Plurality

Totality

To understand what this means, let’s go back to the process of synthesis. Recall that intuitions constitute the “raw material” from which representations are produced. But in order for these representations to be deduced, we have to experience change. And the only way to do that is for these intuitions from one moment to the next to be compared to one another in some way. For example, to perceive an objects as moving, we must compare its current position with its position from some time ago. It is only through expressing the position of an object in mathematical therms that we can perceive it, only by saying “the current distance between me and this object is equal to the distance from a moment ago plus or minus some other amount, we can say that the distance has changed. This formula can tell us how fast is the object moving but we also need it to perceive that it is moving at all or even that it exists. Else we would be seeing just see a stream of different images which as far as we know would have nothing to do with one another.

Therefore, we can view all intuitions as amounts of different stuff or, in other words as different kinds of extensive magnitudes, the most important of which being the object’s magnitudes in space, or in other words its size and dimensions, and an object’s magnitude in time, or its duration.

People have wondered why is mathematics so unreasonable effective for analyzing the physical world? This theory of perception provides an answer to that question - perhaps it is simply because we perceive by means of numbers.

Quality - Anticipations of perception

The principle for using the category of quantity is: “In all appearances the real, which is an object of sensation, has intensive magnitude, that is, a degree.”

Reality

Negation

Limitation

In the chapter on quantity, we said that to perceive an objects as moving, we must compare its current position with its position from some time ago. But in order to do that, to perceive change and time, we must first perceive that the object exists in the first place. So beside the extensive magnitude or the successive states of the object, there is one more magnitude at play here - the degree of the realness of the object. In our everyday thinking, we often refer to things as either real or unreal (just like in logic we split statements to true and false), but actually the “realness” of an object is not a binary value. For in order for us to recognize an object as real, we have to connect the appearance (or impression) that we perceived of the object with a concept that we have. And that connection is always a matter of degree - it is not just the matter of whether you had or had not seen something which resembles it, but a matter of how much does the concept resembles the impression.

The degree of realness of an object (its intensive magnitude) is a prerequisite of perceiving the it’s position and other extensive magnitudes. Note how inherently paradoxical the connection between the two is: on one hand , the notion of existence of objects is needed to realize that objects change and in this sense the notion of the real must come before the notion of time and succession. But on the other, the notion of time and succession is needed to realize that time and space exists at all, and that realization is surely needed for postulating the existence of objects.

Relation - Analogies of experience

Their principle is “Experience is possible only through the representation of a necessary connection of perceptions.”

Inherence

Causality

Community

So far we reviewed the principles of quantity and quality which we dubbed the mathematical principles, because they explain how an experience can be reasoned about mathematically: using the principles related to quantity we unite (aggregate) what we see and hear from one moment to the next into a cohesive whole, therefore producing time. Using the principles related to quality, we are able to perceive in this list, all kinds of different events and objects. And together, these principles allow us to form a picture of reality as we know it.

But being mathematical these principles are only useful to think about how things are in principle i.e. they are based on axioms. Namely, they take the existence of experience for granted i.e. in order to analyze the connections between our perceptions, we must assume that such connections must exist, that our perceptions are indeed connected in time. You might say that the existence of this connection (between the world from one moment to the next) is obvious from experience, don’t forget that this connection must come before experience, as it is what makes experience possible in the first place.

When we see a phenomenon that is at the same time unexplained and very real (it affects our senses very much), we often say that there must be some explanation for it. The analogies of experience provide this firm belief in the fact that there always must be an explanation.

We saw that experience is strongly linked with the concept of time. For that reason, the three analogies of experience that are related to the categories of relation correspond to the three modi of time: permanence, succession and simultaneity.

First Analogy: Principle of Permanence of Substance

“In all changes of appearances, substance is permanent; it’s quantum nature is neither increased nor diminished.”

As the principle of relativity teaches us, all motion is relative i.e. it can only be observed given an appropriate reference point. The same principle is valid for all change - in order to perceive change in a given system, we must first postulate the existence of something which never changes to which we can compare everything else. Let’s call this thing “substance”.

Substance is not a relation, but it is a prerequisite for postulating any kind of relation, so naturally it occurs in many scientific theories. In the law of conservation of energy, stating that energy can neither be created nor destroyed and can only be transformed or transferred from one form to another, energy is basically viewed as a form of substance.

Moreover, the existence of time itself is based on the concept of a substance - for the defining characteristic of time is the unity - there is only one time. And this unity presupposes the underlying unity of matter i.e. substance.

Second Analogy: Principle of Sucession of Time According to the Law of Causality

“All alterations take place according to the law of the connection of cause and effect”

We saw how the principle of permanence allows us to perceive changes in appearances, but not all changes in appearances are changes in the objects themselves.

For example, when perceiving a house, we can first observe its roof and then its basement, but that does not mean that the roof causes the basement to exist. Or for example, we can perceive smoke and then perceive fire, but that wouldn’t mean that the smoke caused the fire, as opposed to the other way around.

More generally, sensing any type of change does not mean that it (the change) is happening objectively - in order an objective change to be perceived, the changes in appearances that we see should be classified under a specific relation with one another. And this relation cannot be anything else but the relation of cause and effect. The whole existence of objects is only possible if these relations exist.

But wait, aren’t these cause and effect relations the result of experience, rather than a prerequisite of it? No, because without them, without the causal law there wouldn’t be any experience to begin with.

Third analogy: Principle of Simultaneity According to the Law of Interaction or Community

“All substances, as far as they can be perceived as simultaneous in space, are in thoroughgoing interaction.”

Although the category of causality gets all the attention when it comes to this triad, it is not the whole picture (what a wordplay, eh?).

In the previous analogy we established how to perceive succession and here we are talking about how to perceive simultaneity.

Same argument as in the previous analogy applies - seeing several appearances at the same time is not enough to establish that these appearances correspond to simultaneously existing objects. In order to postulate that, we should observe some relation between the objects, indicating that they coexist. This relation is called community (interaction).

Community is actually nothing more than a reciprocal cause and effect - that two substances exist simultaneously is indicated by the fact that each of them “contains within itself the causality of certain determinations in the other substance and, at the same time, the effects of the causality of that other substance.” For example, when we are looking at stars and planets, the light that is emitted by them and that enters our retina provides community that indicates their simultaneity.

(This example is one of the many times when Kant seems to anticipate Einstein’s theory of special relativity (Einstein had studied Kant a lot, by the way.))

Modality - Postulates of empirical thought in general.

1. That which agrees with the formal conditions of experience (in intuition and in concept) is possible.
2. That which is connected with the material conditions of experience (with sensation), is actual.
3. That the connection of which with the actual is determined according to universal conditions of experience is (exists as) necessary.

possibility/impossibility

existence/non-existence

necessity/contingency

Unlike all other categories, the categories of modality are not concerned with the observed phenomena (objects, appearances etc.) but with the observer. This is why Kant says that they are not objectively synthetic (as all other categories), but it’s subjectively synthetic.

A concept is possible only when it doesn’t contradict our intuition (e.g. the laws of math, logic, science etc.) But possibility itself does not guarantee that the concept exists (the only concepts that exist just because of their possibility are the pure concepts of understanding). In order to confirm that it exist i.e. that it is actual, we must seek an instance of it. And the only place where we can do that is in experience, because there is no other way for us to perceive anything. Finally, there are thing that must be true, as a precondition of what we actually see, these things must be true necessarily.

More simply put, these postulates frame the basis that we people use to think about stuff.

1. We have ideas about how things are and deem them possible.
2. We check if our ideas are actually true.
3. We find deeper principles that go beyond what we actually see, and we accept them as necessary.

There is a paper about the role of necessity.

I also wrote an article that explores the third category of each triad.

Transcendental doctrine of elements: Transcendental Logic - Transcendental dialectics

Introduction: Of Transcendental Illusion

In the chapter “Transcendental analytics” we presented the pure concepts of the understanding and then we argued that their usage was valid, but only when it is related to objects of (possible) experience. However, people often don’t realize that and so they start believing that these concepts can be used to characterize and reason about things that we cannot experience too. This leads to all kinds of illusions, due to which Transcendental logic has been called the logic of illusions. Illusions which are particularly hard to pinpoint, because they are the result of applying otherwise correct thinking habits, which have just gone outside of their domain (which is, again, experience). This chapter would examine such illusions with the purpose of helping us identify them.

Introduction: Of Pure Reason as the Seat of Transcendental Illusion

The end result of applying the categories to our perception is the understanding, which is kind of a unification of one and the other. Although subjective, as there is more than one way to analyze a given set of perceptions, understanding as such cannot be wrong, as it merely represents the world as it appears to us, producing according to which this world can be understood.

But once we try to structure the rules themselves and to search for the principles from which those rules originate, we go outside the realm of possible experience and into the realm of reason. Just as understanding unifies appearances into rules, reason unifies rules into principles.

To understand what reason is better, let’s look at the structure of the syllogism.

“Athenians are mortal” “Socrates is an Athenian” Therefore “Socrates is mortal.”

Notice that the second line “Socrates is an Athenian” is a simple observation, while the first one “Athenians are mortal” is something much more - there is no way for us to know from experience that athenians are mortal. This claim is unconditioned, not constrained in either time nor space (we don’t merely say “All athenians who lived between 500 and 300 BC were mortal” or even “All athenians who are alive today are mortal”). In other words, we are not identifying a specific set of objects that we are talking about, but instead make general claims about all objects this is what characterizes reason.

And as time and space are the only sources of intuition and as intuition is the only way for us to gain information, it is easy to see that all principles that are deduced by means of reason are different from anything that can be deduced by experience - they are abstract, and as such subjective.

Book I: Of the Concepts of Pure Reason

Continuing to compare reason and understanding, we might as ourselves what are the “building blocks” of reason, as we already know that understanding does have its building blocks or it’s “pure concepts” as we call them - the categories. The pure concepts of reason we would call “transcendental ideas”, as used by Plato.

Of the Concepts of Pure Reason: Of Ideas in General

What are ideas? According to Plato they are concepts, ones which are much bigger than anything that we can experience. An example of idea is the idea of justice that is discussed in the Republic (and the republic is itself a good example of an idea-driven approach).

According to Plato, ideas are divine and they come before all existence e.g. the idea of humanity predecedes the first human. Even if we don’t agree with him about the nature of ideas, we still cannot neglect the importance of ideas in our thinking e.g. the idea of justice is needed in order to organize our society properly. So we need to investigate them further.

Of the Concepts of Pure Reason: Of Transcendental Ideas

Of the Concepts of Pure Reason: System of Transcendental Ideas

Book II: Of the Dialectical Inferences of Pure Reason

TODO

Transcendental doctrine of method

TODO

Glossary

A priori - a piece of knowledge which you are born with e.g. it is imprinted in your brain. Serves as a starting point for all other knowledge.

A posteriori - a piece of knowledge which is derived from experience.

Analytic - a piece of knowledge which is acquired through analysis of another piece of knowledge i.e. knowledge which is valid in all possible worlds

Synthetic - a piece of knowledge which is acquired through synthesis of sensory or other data i.e. knowledge which is valid in this world only.

Sensibility - the mind’s faculty for receiving representations from the world i.e. an umbrella therm for our senses (touch, sight, smell etc.)

Intuitions - The data which is obtained by sensibility, in its most unprocessed format. Not to be confused for, or mixed with, concepts e.g. “bird” is a concept. The intuition for a bird may be, for example, the sound of flapping wings.

Manifold of intuition - The sum total of intuitions that are being perceived by an individual. The term highlights the fact that intuitions are not unified with one another, e.g. the sound of a bird flapping its wings and the sight of that same bird are two completely different intuitions which, in so far as they are viewed as just intuitions and not in their relation to concepts, have nothing to do with each other.

Understanding - the mind’s faculty of producing knowledge by mapping concepts to intuitions.