Critique of Pure Reason #1

What is the Critique of Pure Reason all about?

The Idea of Transcendental Philosophy

Experience is without doubt the first product that our understanding brings forth as it works on the raw material of sensible sensations.

Kant stated in the premise he wrote the Critique in order to solve a serious problem with metaphysics, one which this, his transcendental philosophy with solve. in typical fashion, he doesn't exactly tell us what he means by “typical fashion, he doesn't exactly tell us what he means by “transcendental philosophy.” While you may be unsure as to what the problem is, he does give us the means to solve it. Whatever its problems, metaphysics can be redeemed if we can only answer the question:

How are synthetic a priori judgments possible?

We can get a sense of what the problem is by untangling this question.

Cognition: The German word is “Erkenntnis,” which can be translated as knowledge, perception, discovery, insight, or realization (becoming aware or conscious of something). It is that mental process that enables us to acquire knowledge which one can only do through a process of forming judgments or propositions which one can only do by forming empirical concepts which in turn can only be done by receiving and processing sensations. In his notes (R2740), Kant wrote

Erscheinung (Anschauung)
Wahrnehmung (Empfindung mit Bewustseyn) 
Erfahrung (Warnehmung nach Regeln)

This can be translated as

Appearance (Intuition)
Perception (Sensation with consciousness)
Experience (Sensation according to rules)

To acquire experience is to think according to rules which is to learn and eventually to know. Kant refers to this experience process as cognition. There are different types of cognition, i.e., different ways of thinking, learning, and discovery, but in this work, he is primarily concerned with "theoretical” or “speculative” cognition, that is, the understanding of the real world around us. In another note, R2741, he writes

“Erfahrung ist die Übereinstimmung der Warnehmungen (empirischer Vorstellungen) zur Erkentnis eines objects.” Translated: Experience is the agreement of perception (empirical ideas) with knowledge of an object. In order for me to know that that animal that I see is a dog, I have to match my perception of it with what it is that I know of dogs. How then, we may ask, do I learn about an animal that I've never seen before

Concepts and Judgments: The most elementary concepts, e.g., the concept of quantity, is a general principle that in concept form. It tells us what form an object has to take in order to be understood, that it must be measurable. Quantity is not itself an object; it is a rule or form that objects must take. In conceptualizing the rule, however, we are able to make it an object pure thinking. Actual objects that are not merely objects of thought empirical, like the concept dog, tree, rain showers, etc..

A judgment is a strings objects together in a logical order, whether we are talking about pure concepts or determine an objects. When we think about objects, we attach predicates to it (try thinking of something without a predicate or quality). When I see a dog, I might say to myself, “There’s a dog.” Then I might attach other predicates, “That’s a big fluffy dog.” Knowledge then is this capacity to string concepts (dog, big, fluffy) into propositions or judgments. So when Kant asks, “How are synthetic judgments a priori possible?” we know he is asking about a type of proposition, a type of sentence that strings together concepts and enables us to acquire knowledge.

A priori vs A posteriori: Kant will distinguish between empirical and “pure” or non-empirical concepts or judgments. Pure concepts , that is a priori concepts, are not empirical. A nonempirical concept might be some pure concept that is not observable in nature. Kant believe logical relationships, e.g., quantity, quality, etc., are concepts that are separable from nature in thought (which is why pure mathematics is not empirical)., but they are not completely inseparable because Kant says that experience is needed to inform us that we have these concepts to begin with. Nature thus acts like a mirror in some sense, revealing to us our own inner, pure capacities (just as those capacities reveal to us the workings of Nature). More often than not, however, he is referring to judgments which contain empirical concepts BUT which can be adjudicated for truth or falsehood without reference to observation. Kant believes this is possible with mathematics, logic, and any abductive reasoning that includes empirical premises, but whose syllogistic conclusions are arrived at purely logically.

So if that is what is meant by a priori, then a posterior refers to that which is not pure, a judgment which can only be ratified by observation. The judgment, “I have a beard,” can only be ratified by checking me out to see if I actually have one. Other judgments, e.g., “the earth is round,” can be a priori or a posteriori depending on whether or not I’m deducing that judgment by observation of the earth (I take a rocket into outer space and look down at the earth) or abductively, that is a priori (I deduce from the observation of the Coriolis effect or time zones, which are empirical premises, that logically the earth must be curved). I suppose whether or not I have a beard could be deduced a priori. If you had seen me yesterday clean shaven (if you had this empirical premise), you could logically conclude that it’s impossible for me to have grown a beard since yesterday.

Analytic vs synthetic: So now we understand that a judgment is declarative proposition which is essential in knowledge acquisition and we know that a priori refers to math and logical deduction rather than a proposition that is verifiable solely through observation. An a priori judgment is a proposition or a sentence in which the predicate can be verified as being connected to the subject through purely logical or mathematical ratification. It will say that any such judgments are universally necessary, i.e., that logical judgments aren't open to subjective interpretation or dependent upon individual observations.

So what does Kant mean by “synthetic.” The concept that some predicates are contained in the subject (an analytic judgment) was understood by philosophers as far back as Plato, but we have Kant to thank (or blame) for the particular terms: analytic a priori, synthetic a posteriori, and synthetic a priori. An analytic judgment is one in which the predicate is necessarily connected to the subject. A synthetic judgment is one which is not necessarily connected. “The dog is big” is clearly a synthetic subject since not all dogs are big. I can think of small dogs without contradiction, but that bachelors are unmarried men I cannot think without contradiction.

In the judgment, “bachelors are unmarried men,” marriage and men are the characteristics of the concept, bachelor. And the judgment, “the dog is big,” size is a characteristic of the object, dog. Analytic judgments compare concepts to each other; synthetic judgments compare objects to concepts.

We now get to question — what is a synthetic a priori judgment? There certainly exists synthetic a posteriori judgments (that the dog is big can only be verified by observation) and analytic a priori judgments (bachelors are unmarried men are necessarily connected, even identical, concepts). Are there analytic a posteriori judgments? Judgments in which the predicate and subject are necessarily connected but still which require empirical confirmation? Obviously not, this is a contradiction in terms. (We might say that it is an analytic a priori judgment that analytic a posteriori judgments are impossible as this is all baked into the definitions of these terms.) There do exist, however, synthetic a priori judgments, judgments in which logic is all that is needed for confirmation BUT only for judgments that depend on spatiotemporal framing. Mathematics is one example and theoretical science, what Kant would have called “natural philosophy ” and what we did today call ““natural science,” is another.

To understand this better, we need to observe what happens when we string subjects and predicates together in judgments of fact. When we say that bachelors are unmarried men, we are effectively saying something like a = a. We are only connecting the subject to what is essentially itself. When we say the dog is big, we are connecting the concept of dog to something we observe in nature. Sensation allows us to make this connection. So if we are not relying on sensation to connect the subject and predicate and if the predicate is not merely reflecting the subject, how are we able to make mathematical and scientific connections? This is essentially what the big question boils down to.

In this case, the connective tissue is provided by intuition itself (remember what Kant calls “intuition” we call “perception”). Individual perceptions, are to be sure a posteriori, that flower looks green to me, it looks blue to you, but WHAT IS NOT INDIVIDUAL is that no matter what color you see, Kant guarantees that we will all see flowers in a spatiotemporal framework. And we will do this not just when we see the flower, but also when we close our eyes and imagine the flower. Green and blue might be an empirical or a posteriori intuition in perception (as well as concepts in thinking) but space and time are universally necessary forms of perception.

So what does this have to do with mathematics being synthetic a priori? Kant gives the example of the synthetic a priori judgment 7 + 5 = 12. The “=” sign would seem to indicate identity, something like a = a, but Kant says that in this case the “=” sign is not telling us what 12 is identical to. It is telling us how to construct 12 from 7 and 5 and demonstrates how when learning to count, children first need to use their fingers. They are not identifying 12 with 7 and 5, they are constructing 12 from 7 and 5, they are deducing 12 from 7 and 5.

Still not convinced that mathematical judgments add synthetic a priori? Maybe this example from §1 of Kant's Inquiry Concerning the Distinctness of the Principles of Natural Theology and Morality, published in 1763. He offers the following judgement: A trapezium is composed of four straight lines bounding a plane surface with no opposite parallel sides.

We know this is not an an analytic proposition for many people, before we tell them how to construct this trapezium, there is no pre-existing concept of one—not until after we've mathematically or axiomatically defined it, not until after we've constructed it.

Okay, hopefully I've convinced you that the proposition is not analytic, but why not synthetic a posteriori rather than synthetic a priori? If children are counting their fingers, aren't they doing arithmetic by observation?

No. Remember my example of the earths roundness, how it can be verified empirically but can also be deduced logically. Thankfully , because we know how addition works, we do not have to count our fingers or any objects for that matter to add sums like 1,085,342.685439 + 8,548,463.3335. The point is not that we don’t use empirical observation tools to arrive at mathematical answers. The point is that we know the truth of these answers and that our calculators and abaci work because of logic and the sensory conditions of space and time.

So then the question of how are synthetic a priori judgments possible is asking: How is it possible to apply logic to obtain new knowledge that isn’t merely a clarifying of concepts we already know?

Knowledge is both the subject and problem of transcendental philosophy, a problem in the sense of trying to ascertain how it is that we are able to acquire knowledge and rely on it. (Unreliable knowledge would be mere belief.) How is it that using logic and our intuition for perception, we are able to arrive at knowledge and produce sciences that develp and maintain this knowledge?

With this work, Kant divides the metaphysics of his time into two new branches that we recognize today. That branch of metaphysics that was referred to as natural philosophy becomes natural science, and what is left becomes cognitive science or logical positivism or philosophy of language or analytic philosophy, etc. Against this, a counter movement will form of Romanticism, Idealism, and what will later be termed Continental Philosophy (existentialism, phenomenology, postmodernism). You might even go so far as to say that Kant is the father of all these later movements.