I bought Critique of Pure Reason a little too early; for a few years, Kant’s breakthrough masterpiece just sat on my bookshelf collecting dust. I picked up on hints of Kantian philosophy in high school — references to a priori judgements and the categorical imperative in particular — but I was never formally introduced to the German philosopher’s work during that time. Finally, as my college-year readings increasingly cited ‘post-Kantian’ thinkers, I decided I had to tackle the work of this monumental figure whose importance was enough to split the philosophical timeline. Still, the book itself was too daunting for me. I used a few general sources that guided me through his logic; On Kant, which is part of the Wadsworth Philosophers Series, was especially helpful.
Then, I happened to find Kant’s Prolegomena to Any Future Metaphysics. As the word prolegomena suggests (pro-legein meaning to ‘say beforehand’ in Greek), Kant intended this book to be a preliminary address to all philosophers who wanted to investigate metaphysics, even going so far as to say “he who undertakes to judge or, still more to construct a system of metaphysics must satisfy the demands here made, either by adopting my solution or thoroughly refuting it and substituting another.” This actually reflects one of the driving motivations behind the Critique of Pure Reason, which was to define and set the limits of metaphysics. Therefore, the Prolegomena actually works as a nice summary of Kant’s positions in the Critique. Considering that it’s about 1/10th as long, I encourage anyone who wants to encounter the ideas of this article in their original source to try reading the Prolegomena if the Critique is too daunting.
Metaphysics: an investigation of truest reality
So, what is metaphysics? Again, attention to Greek roots will help us: meta- meaning beyond, and physics, which refers here to the study of the natural world. Whereas physics tells us about the natural world, metaphysics probes whatever territory may potentially lie beyond that, invoking questions such as ‘what is real?’ and ‘why does something exist rather than nothing?’. In this way, metaphysics is concerned with the essence of things as they exist in the truest reality.
For a long time, the lines of philosophy were drawn according to the concepts of appearance and reality: we can speak of how things appear to us, and we can speak of how things are in actuality. Because of our limitation as finite beings, these two categories don’t always line up, and by learning about the world we can come to a more perfect understanding of reality. This idea is captured by the Allegory of a Cave, an image evoked by Plato in order to describe the process of education and the position of the philosopher in society. Plato envisions the unlearned person as being imprisoned in a cave, free only to look at shadows cast by a fire which lies behind him. This person would live his whole life thinking that the shadows themselves are the truest reality, as opposed to mere appearances cast by the fire’s light. The philosopher, by contrast, is one who has freed himself from his chains and come to understand that the true form of reality consists of the fire’s light and the objects whose illumination creates the shadows. Using this metaphor, Plato depicts the difference between what the senses may initially portray as reality and the philosophical method which delivers us from illusion and guides us towards an understanding of true reality.
Kant’s contribution to metaphysics involved an elaboration of the appearance vs reality dichotomy which reconstructed it along the following lines: the phenomenal versus the noumenal. Whereas the phenomenal describes the appearances of objects as they are presented to our experience (what Kant calls our sensibility), the noumenal realm is the domain of the the thing-in-itself, which describes how the object exists ‘in true reality’, outside of our sensory access to it. In this way, Kant buries metaphysics by regulating it to the study of the noumenal: the noumenal which we can say nothing about.
The concept of the noumenal can be seen as one of Kant’s biggest contributions to philosophy. But in order to understand how he came to posit such a concept, we must follow his logic from the beginning of his Critique of Pure Reason.
The 4 categories of judgements
First, Kant introduces the distinction between analytic and synthetic propositions. Analytic propositions are those which can be made owing to the definitional properties of whatever is being investigated. ‘Gold is a yellow metal’, for example, is an analytic statement because yellowness is a definitional property of gold as a metal. We can think of analytic propositions as those which can confidently be made so long as you’re armed with an accurate enough dictionary. More examples include ‘a triangle has three sides’ and ‘humans are animals’. Nothing ‘new’ is being produced by analytic propositions: their truth comes from definitions that we’ve already assigned things.
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.
Let’s stick with the Nile example in order to introduce another concept that Kant utilizes: the a posteriori judgement. The best way to think of these propositions is that they require experience of the world. For us to have arrived at the truth ‘The Nile is the longest river’ an empirical measurement had to be made. Because the Nile does not have the quality ‘longest river in the world’ as an essential part of its definition, some exploration out-there was necessary to come to the truth of that proposition. One important aspect of a posteriori judgements is that, owing to their basis in empiricism, they are always open to being refuted. For example, some further exploration of the Earth may reveal that another river is in fact longer than the Nile, in which case the truth of the judgement ‘The Nile is the longest river’ would be negated.
By contrast, Kant defines a priori judgements as those which can be made absent of any world experience. Returning to our gold example, we find that arriving at the truth of ‘gold is yellow’ requires nothing besides the definitional property of both concepts. What first brought us to define ‘gold’ as a type of substance was its yellow hue, so yellowness was not so much something we discovered a posteriori about gold (in the same way we discovered that the Nile is the longest river), but rather something we came to apply as its definition. Because, then, there is no experience-of-the-world necessary to come to the truth of this judgement, it is defined as a priori. Being necessary, these judgements are stronger than a posteriori judgements; because they are not founded in experience, they cannot be refuted by experience either. No amount of searching on Earth could negate the truth of ‘gold is yellow’, or ‘a triangle as three sides’, or ‘a dog is a mammal’, because these are definitional statements.
These 4 descriptors — analytic, synthetic, a posteriori, and a priori — give us a way of categorizing all truth statements, and can be summarized in the following chart:
We can immediately see that Kant has made the following declaration: all analytic truths are a priori; none can be a posteriori. This makes sense, because returning to our description of analytic truths, we find that they rely only on the definitions of things as we know them already. In other words, you can discover analytic truths from the comfort of your sofa. The sofa-ness of analytic truths is what makes them necessarily a priori: you don’t need worldly experience to arrive at them.
However, synthetic truths are more nuanced. Intuitively, we want to say that all synthetic truths are a posteriori, meaning that all synthetic truths require experience. After all, synthetic truths ‘contribute something new’ about our understanding of the world, and this newness requires going out and finding something. You can’t sit on your couch and do that. And that’s correct: many synthetic truths are a posteriori. Our ‘snow is white’ and Nile examples were both synthetic, a posteriori truths: they’re not just true by virtue of definitions, and they rely on experience of the world to be arrived at.
But Kant brings our attention to an interesting chimera: the synthetic a priori truth. In other words, a statement which ‘contributes something new’ to our understanding of the world, but does not rely on experience in order to be arrived at! If this seems implausible, you can be assured by a few examples of what Kant considered to be the ultimate source synthetic a priori truths: geometry. Consider the proposition, ‘a line is the shortest path between two points’. Now, this statement is synthetic because you can’t arrive at it simply by consulting the definitions of ‘shortest path’ or ‘(two) points’. But at the same time, it’s 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! Other examples from geometry are ‘you need at least three lines to make a shape’ and ‘seven plus five equals twelve’. In addition, Kant views the statement ‘all events have a cause’ similarly. All of these, Kant argues, fall into the mystical category of the synthetic a priori .
How are synthetic a priori judgements possible?
This question is the guiding force behind Kant’s Critique of Pure Reason. Let’s rehearse their bizarreness. On one hand, they’re synthetic: they produce something new and enrich our understanding of the world. But on the other hand, they’re a priori: they require absolutely no experience of the world itself! I think a good way of capturing the paradox of synthetic a priori truths is to consider them necessary truths about the world that you can discover without experience of the world.
Kant’s entire philosophy, transcendental idealism, begins with an explanation for the existence of these peculiar kinds of truth. Here is his solution. Consider a geometrician, who is discovering synthetic truths about objects from the comfort of his sofa. The reason why he’s able to do this is because he is actually uncovering necessary truths not about objects themselves, but about the formal conditions of our experience of objects. If space is the fabric of our sensory experience, then understanding this fabric will tell us how all objects are necessarily presented to us because all objects are given to us via this medium. Space — as well as time — are two of such conditions of our sensibilities.
Thus, the reason why the sofa-bound geometrician can uncover new, non-definitional truths (synthetic) about the world of objects, without ever needed experience of the world (a priori), is because he’s not learning about the objects themselves, but about necessary relations of space, which is a condition of how objects appear to us. So by understanding this necessary condition of objects (space), he can then generalize and be sure that all other objects must conform to the solutions he found. Kant calls this procedure, which defines the engagement of the geometrician, the transcendental deduction of the concepts of space and time. From this perspective, it’s actually no surprise at all that the geometer can uncover necessary truths from the comfort of his couch. And this comprises the solution to the Prolegomena‘s first question: How is pure mathematics possible?
Kant says that space and time are necessary conditions of our experience of the world (“formal conditions of our sensibility”). Therefore, we only ever gain access to the appearance of objects. This might be read as a kind of idealism, which purports that the existence of objects relies on the thinking subject (us) and objective reality doesn’t exist outside of ourselves. But Kant is quick to reject such categorizations of his philosophy. Kant is not denying the existence of objects, but rather, affirming that our immediate understanding of these objects as existing in time and space are nothing more than conditions of our sensibilities. Unlike the Newtonian conception of space and time, which views them as absolute things out there in the world, Kant considers space and time as formal categories of our experience: the way human minds organize sensory information.
Introducing the noumenal
This brings us back to Kant’s idea of the noumenal. If we do want to deliberate on what the nature of an object-in-itself might be, divorced of our immediate formal sensibilities of space and time, we must necessarily concede that this object, what Kant calls the thing-in-itself (ding an sich), is outside of space and time and is therefore not presentable to us in our phenomenal experience of the world. The noumenal is a positive realm which Kant posits in his philosophy, but it is nonetheless wholly negative: we can know absolutely nothing about it. It is the domain of the noumenal that is the true territory of metaphysics: anything else is simply a study of phenomena, or reality as it is presented to us. And again, because the noumena is fundamentally inaccessible to humans, who carve out instead the anthropomorphic conditions of space and time, Kant is essentially disposing of the field of metaphysics altogether.
This is why Kant’s project in his Critique of Pure Reason can be understood as a challenge to metaphysicians: those philosophers who want to probe reality and its truest level. We appear to be confined by the formal conditions of our experience — space and time — which make extra-mental reality fundamentally inaccessible to us. Rather than operating on the Socratic distinction between appearance and reality, which can be uncovered by the philosopher, Kant introduces the distinction between the phenomenal and the noumenal. By tracing the existence and explanation of synthetic a priori truths, he deduces the impossibility of grasping the noumenal and says that metaphysics can say nothing of it.
Prophemy 