Immanuel Kant on the limits of knowledge

In the preface to his Prolegomena, Kant asks the following provocative question:

If metaphysics is a science, why is it that it cannot, as other sciences, attain universal and lasting acclaim?

Metaphysics is the branch of philosophy that deals with fundamental questions about being: what it means for something to exist, what reality is as opposed to mere appearance, and so on.

Despite the fact that these are the ‘big questions’ of the human condition, philosophers still can’t agree about definite answers to any of them. Whereas a natural science like physics has been uncovering truths and building on them over time, metaphysics doesn’t have a historical heritage; or at least, one hasn’t materialized yet.

We might generalize this finding to philosophy as a whole. Its history spans thousands of years, but it isn’t so clear that ‘progress’ has been made in the same way it has for science. For example, alchemy progressed to the more rigorous study of chemistry; can we say that any single philosophy has developed in a similar way?

Kant says that this is a property of philosophy itself. Philosophy, specifically metaphysical inquiries, must reconcile with the noumenon: a realm that is completely unknowable to human understanding. By introducing the noumenon to philosophy, Kant sets a fundamental limit on knowledge and radically transforms what it means to seek truth as a finite being.

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Kant arrived at the noumenon by investigating 4 possible kinds of propositions.

First, there is a distinction between a priori and a posteriori propositions. a priori propositions are those which can be made absent of any world experience. For example, if I’m told that a soccer player was signed to a club for 3 million dollars, I know that he was signed for more than 1 million dollars. This is a true statement that I can make without ‘looking about’ in the world for it, because it relies on strictly logical relationships.

By contrast, a posteriori propositions are those which require some empirical investigation; some ‘going out there’ to look for it. For example, the statement that the Nile is the longest river in the world required us to go out and measure it: it isn’t an artifact of simple logic or mathematics.

Meditating on this distinction, we find the following rule:

a priori statements are always true; a posteriori statements are subject to disproof

So far, this gives us 2 categories of propositions. But Kant introduces a further distinction between analytic and synthetic propositions. Analytic propositions are those which can be made owing to strict definitional properties. They reason they are true is that we have assigned certain definitions to certain words.

examples of analytic propositions: ‘a triangle has three sides’, ‘dogs are mammals’

By contrast, synthetic propositions should be read exactly as the word suggests: they produce something new. ‘The Nile is the longest river on Earth’ is a synthetic proposition because nothing about the Nile per se includes the definition ‘is the longest river on Earth’. Therefore, this truth adds something new to our knowledge of the Nile, and of the world in general.

examples of synthetic propositions: ‘the Nile is the longest river’, ‘the beaches in the Caribbean are white’

Kant directs our attention to the possible overlaps between these 2 distinctions. First, it is clear that all analytic statements are a priori. When you say that dogs are mammals, you can always say this outside of world experience because this is simply a definitional property of our understanding of ‘dog’ and ‘mammal’.

Moreover, most synthetic statements are a posteriori. After all, if you added something new to our understanding of a concept, you probably needed to go out into the world and experience something. The statement that the Nile is the longest river is a synthetic a posteriori one: it is not a definitional relationship, and it required experience of the world.

But Kant directs our attention to an interesting chimera: the synthetic a priori proposition. This is a proposition which adds something new to our understanding, but could nonetheless be made absent of any world experience.

Consider the proposition, ‘a line is the shortest path between two points’. It is synthetic because you can’t arrive at it simply by consulting the definitions of ‘shortest path’ or ‘points’. But it is also a priori because you don’t need to experience the world to know it: all you need is your own mental intuition about the nature of space! Thus, Kant concludes that some synthetic propositions are a priori.

examples of synthetic, a priori propositions: ‘a shape needs at least 3 sides’, ‘every event has a cause’

How are synthetic a priori propositions possible?

For Kant, the paradox of synthetic a priori statements reveals the existence of the noumenon. The question is the following: how could it be that we can discover necessary truths about the world that don’t require experience of the world?

Consider a geometer who is working on proofs in his study. He can verify synthetic propositions while sitting comfortably at home, armed with only his intuitions about space. The reason why he’s able to do this, Kant says, is because he isn’t uncovering truths about geometric objects themselves. Rather, he’s uncovering truths about the formal conditions of our experience of objects.

In the case of geometry, this formal condition is space. The geometer can find lasting and necessary (a priori) truths about figures because he is uncovering certain properties about the form of space itself. When he says “a line is the shortest path between two points”, he is not saying something about lines or points, but rather, about the way in which we experience lines and points.

Suddenly, it isn’t so surprising that geometry can give us eternal truths without the need for empirical data. Since space is a formal condition of all our experience, understanding the necessary properties of space itself gives us geometric solutions that must generalize for everything presented to our experience.

Kant calls this procedure the transcendental deduction: coming to conclusions about the world by investigating the formal conditions of experience, not the contents of the experience.

For Kant, then, space and time are formal categories of our experience which automatically structure our interaction with the world. The resulting reality is the world of the phenomenon: things as they are presented to us. The question now becomes: if all our experience is filtered by space and time, what can we say about reality as it stands outside of these categories? To use Kant’s terminology, what can we say about things-in-themselves?

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The noumenon is the world of things-in-themselves: objects (if we can still call them that) which exist outside of human observation and experience.

If we want to deliberate on the nature of these objects, we must necessarily concede that they exist outside of space and time and are therefore not presentable to us in our phenomenal experience of the world. Kant stresses that our relationship with the noumenon is a strictly negative one: all we can say about it is that we know absolutely nothing about it.

For Kant, this explains why metaphysics hasn’t been able to establish itself as a proper field of study. Sciences like chemistry and physics deal with objects that are presented to us in space and time: the phenomenal realm. But the goal of metaphysics is to uncover truths about the most basic form of reality: what might exist outside of these fundamental categories. Therefore, it must tally with the noumenal realm, which is strictly inaccessible to humans.

By subjecting philosophers to the anthropomorphic conditions of space and time, Kant limits their knowledge to what exists inside these categories, thereby disposing of metaphysics altogether.

We are reminded of Ludwig Wittgenstein’s formula that “whereof one cannot speak, thereof one must be silent”. For Kant, the objects which metaphysics — and perhaps all of philosophy — endeavors to study is far beyond human comprehension. We therefore cannot say a thing about it.

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