Prolegomena to Any Future Metaphysics, decoded

Immanuel Kant: Prolegomena to Any Future Metaphysics, edited

The sources of metaphysics

The ideas of metaphysics cannot be empirical; they cannot come from experience. The whole point of studying metaphysics is to learn things that are beyond experience. Therefore, neither the senses (which are the foundation of physics) nor internal experiences (which are the foundation of psychology) can be the foundation of metaphysics. Metaphysics must come from a priori knowledge: knowledge from pure understanding and pure reason.

Mathematics is the same; its foundation is pure understanding and reason.

What metaphysical thinking is. The difference between analytic and synthetic judgments

There are two kinds of a priori judgments. Some are ‘analytic’ and are explanatory. Some are ‘synthetic’ and add new information to the things we are thinking about.

Analytic judgments are definitions or clarifications. Someone could ask me, “What do you mean when you say ‘physical things have extension?’”. I would reply, “Physical things take up space”. I am defining and explaining “extension” but I am adding nothing to the idea. This is ‘analytic’.

On the other hand, if I declare “some physical things do not have mass”, I am adding information. If I analyze the idea ‘physical things’, I don’t think ‘massless’.  Masslessness is a new idea, not a definition, and it does not come from analysis of physicality. It is ‘synthetic’.

All analytic propositions are a priori, even if are about empirical things. “Gold is a metal” is an empirical a priori idea (it is not about an innate idea) and it is analytic (when I dissect my idea of gold, one of the things I know is that it is a metal. In fact, I do not know what gold is if I do not know that it is a metal).

Synthetic judgments are different

Judgments about experience are always synthetic.  That an object must take up space is completely certain and a priori, and that certainty cannot come from experience. If I know what an object is, I know it takes up space. I do not need to check several objects around me to verify this.

Mathematical propositions are always a priori, never empirical, because they are certain and necessary, not probable, and a priori ideas are certain.

You might think that 7+5=12 is analytic. But there is nothing in the ideas of 7 or 5 that contains the number 12. (Does the idea of 5 contain the number 3103, which is 5 less than 3108?) 7+5, then, is synthetic. Statements of arithmetic are always synthetic.

The general question of the prolegomena. Is metaphysics possible at all?

It would be great if there were a textbook of metaphysics. There isn’t. Nobody has ever accomplished anything in metaphysics, so there is nothing to put in the book.

Good metaphysics, textbook worthy metaphysics, should construct a priori propositions.

But is that even possible? Yes, because mathematics and physics construct them now.

The transcendental main question: How is pure mathematics possible?

How can reason make a whole branch of knowledge from only the a priori?

Math is very odd. Mathematical concepts are both abstract and concrete. For instance, I can prove things about all circles by proving things about one circle. The whole idea is there, in the intuition, ready to be built on.

But this just makes things harder. How do we know anything a priori?

There is only one way. We know about some things a priori before we know anything a posteriori at all. There are ‘forms of sensibility’ or ‘sense structures’. I cannot really imagine four dimensions, uncaused phenomena, or the end of space. These ideas simply cannot make sense because my mind is structured to ‘hold’ things (for instance) in three dimensions, with time running forward, and in a finite world. People simply conceive of things in certain, unchanging ways. These frameworks are the source of a priori knowledge

Space and time are foundational mental structures, and they lead straight to mathematics. Space gives geometry, and time gives numbers through the addition of units of time. We can even get to physics—time and space give us motion and extension, from which we can deduce the movements of bodies. Time and space, however, remain the foundation of the sciences.

Therefore, we have shown how mathematics is possible. It defines the structures of sensation and the necessary appearance of objects. I will never see an object in two dimensions, nor one in four; I cannot imagine the same object in two places at the same time; 7+5 must always equal 12; and all straight lines can be divided. By analyzing these a priori structures of my mind, I get to mathematics.

Obviously, the structure of my mind tells me nothing about what I will conceive; it only describes how I will conceive it. I may never see the northern lights, but if I ever do, I know that I will see them as colours in my field of vision. All objects of sense are like this; they all must conform to the rules of geometry and time.

The second part of the main transcendental problem: How is pure natural science possible?

Natural science, a priori and certain, binds nature. There are universal principles, too, such as the proposition that substance is permanent, or that everything has a cause. These are perfectly good laws of physics. How do we know them?

I am not concerned with things in themselves (I’ll get to those in a minute). I am thinking instead about the things we experience, or, to put it another way, the objects of possible experience. Our experiences follow regular laws, too; how do we know them?

We should start at the beginning. There are two types of experience: judgments of perception and judgments of experience.

That the room is warm, that orange juice is sweet and tonic is bitter: these are ‘subjectively valid judgments of perception’. Someday, I—or someone else—might experience things differently. After brushing my teeth, orange juice could taste bad. I could come in from a warm summer day and find this room cold. When I express subjectively valid thoughts, I am expressing something more than my opinion, but it is not much more than “I feel this now”.

With judgments of experience, it is totally different. I am asserting that I—and everyone else—will know these facts always. Air is elastic, space has three dimensions, light follows a straight line: these are things that are universally valid.

There are twelve possible aspects of experiences that are presented to the mind. I’ll give an example.

Imagine I see puppies in a canoe floating towards a waterfall. I can see that the water is putting the puppies in real danger, but that there are no people in the canoe. Right away, I can see that if I do not save the puppies, no person will be harmed.

The river flowing over the waterfall is the source of danger, but I do not know what caused the puppies to get into the canoe. I know, though, that they are not making this situation better by barking and being afraid of the water. They need to swim to shore, and they need to do that now.

If I jump in, I might save them. If I do not, I know that they will die. There is only one way to tell whether they can be saved—I’ll have to try.

This example illustrates the twelve categories of judgment:

  • According to quantity
    • Unity
      • I can count the things in the scene. There are individual puppies and one canoe.
    • Plurality
      • Puppies
    • Totality
      • All of the puppies are in danger
  • According to quality
    • Reality
      • The danger is real
    • Negation
      • But there are no people in the boat
    • Limitation
      • And no people will be harmed
  • According to relation
    • Substance
      • The water makes up the waterfall
    • Cause
      • The waterfall endangers the puppies
    • Reciprocity
      • They are also putting themselves in danger
  • According to modality
    • Necessity
      • The puppies will die if I don’t act
    • Possibility
      • And might if I do
    • Actuality
      • Only by trying will I find out if I could save them


This may seem complicated, but at root it is simple: I am not trying to explain the origin of experience, but what lies behind it and makes it possible.

The senses sense, and the mind unites these experiences into a consciousness, either subjective (relative to oneself) or objective (for all people everywhere), and either analytically or synthetically. New experiences, because they are combined with old ones, are always synthetic, and they are always in terms of the ideas of metaphysics.

Metaphysics gives us the shapes of thought, and it governs all possible experiences. I cannot imagine the time before the big bang, nor can I visualize five dimensions. Metaphysics says that all of my thoughts and experiences will have a certain shape, and it gives us the most a priori of a priori ideas. There is nowhere deeper for us to go.

These axioms of possible experience are the universal laws of nature, and we can discover them a priori. Thus, we answer the question “How is pure natural science possible?”.

There is a hierarchy of systems. Logic is the most basic. The rules of logic (such as “if a statement is not-not true, then it is true”) underpin everything. The axioms of metaphysics (like “There are no uncaused events”) rest on top of logic. The laws of nature rest, in turn, on top of metaphysics.

But this is important: we do not know much about nature. Take, for instance, a daisy. To us, it looks white. To a bee (which can see in ultraviolet) it looks different, much like a bullseye. So what colour is a daisy, actually? In fact, the question is a bit absurd. All metaphysics can say is that a flower, like every other visible thing, has a colour. Which colour? We cannot say. We cannot go directly from logic to the world.

Let’s return now to Hume’s problem with causes. He said that we have never actually observed one thing causing another. When two billiard balls collide, we do not see the first imparting its momentum onto the second. We only see one move, then the other move. Also, because Hume was an empiricist, he said, therefore, that we have no real idea of causality. And without causality, we have no science.

Logic gives me the outline of the idea of cause, though. I get from it the idea of the antecedent and the consequent: if A, then B. If a stone is left out in the sun, then it will become warm. I make this a general statement of experience: Sunlight makes objects warm. This is not quite a law of physics, but it is a law of possible experience. Any time, anyone leaves anything in the sun, we expect it to become warmer.

I do not have within me any idea of what causality is in-itself, unobserved, in the wild. I can only make sense of causality as a necessary connection between two experiences. I see the world in terms of causes; antecedents cause consequents, and they do so in my experience. I can only observe what I can observe, and I can only see it in the way that I do.

In fact, I do not have any idea of anything that is not experienced. There is a ‘noumenal’ world and a ‘phenomenal’ one. If the real world (ie the noumenal world) were 5 dimensional, or without causality, or lacked time, I could not know it. I only know experiences (phenomena) and their necessary connections and presentation (metaphysics).

Hence, when we try to talk about ‘substance’, ‘infinity’, the ‘Big Bang’, or the end of space, we are truly talking nonsense: We are trying to talk about things that we could not sense, we could not experience.

This has confused philosophers from the very beginning, back to Plato, who proposed that there was a special world of noumenal Forms. He thought that reality was the intelligible essence. Because he came from an earlier epoch, he should be excused.

From the earliest ages of philosophy, investigators of the pure reason have postulated, beyond the sensible essences (phenomena) which constitute the world of sense, special essences of the understanding (noumena) which are supposed to constitute a world of understanding; and since they held appearance and illusion for the same thing, which in an undeveloped epoch is to be excused, ascribed reality to the intelligible essence alone.

This does not mean I do not believe in an external world. Quite the contrary. When I say that there is an object of sense and a noumenal object, I am conceding that there is an external world, apart from us, existing in-itself. I just don’t think we know anything about what it actually is; we only know how it is presented to us.


Appendix: What will make metaphysics a science?

It took a while, but I was able to distinguish and separate space and time, the elementary conditions for sensibility, from the rest of the categories of understanding.

The categories make experience objective and systematic. They also put a limit on our discussions and should prevent us from going astray: there can be, for instance, no more uncaused causer or time before time.

Science is easy in comparison; scientific hypotheses are borne out or disproved by experience. In metaphysics, by contrast, there is no experience that would confirm or deny a conjecture, because metaphysicians deal with only the possibility of experience.

Is the soul a substance? Does god have a plan? Was there a beginning to the universe? What is at the edge of space? These are questions that do not make sense. They are pseudo-metaphysical questions that seem to be about the shape of the world. When we see, however, that metaphysics is about possible experience, we see that these questions are unanswerable; they are not framed in terms we can discuss.

Conclusion: On the determination of the boundary of the pure reason.

Space, time, the conceptions of the understanding, and the world of sensation do not add up to much. They determine no object and have no significance anywhere. We have no insight into things in themselves. Natural science will never discover the inner nature of things, that which is not phenomenon–and nor should it. Science should be about the phenomenal world.

Solution of the general problem of the prolegomena: How is metaphysics possible as science?

This much is certain: once you’ve tried my metaphysics, you will never go back to the dogmatic trash of souls and infinities. My criticism is to old metaphysics as astronomy is to astrology, or chemistry is to alchemy. The new metaphysics is finite and durable, and is capable of being completed.

Metaphysics must be a science, from bottom to top. Speculation and probability have their places, but not in metaphysics. It must be certain, universal, and true.

This what I demand of metaphysics.