Exploring Kant's Critique of Pure Reason

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What is knowledge? How can humans know things about the world? Humans have pondered the answers to these philosophical questions since ancient times. Socrates and his student Plato laid the groundwork for epistemic discourse with their enquiries as to how one can come to know what virtue is. As the perplexities endure, unanswered, different schools of thought emerge, each proposing its own systems of belief with regards to epistemology. Descartes and other rationalists have asserted that we can know the world through reason alone; Empiricists have argued that we can only learn through experience.

With the 1748 (1) publication of his Enquiry concerning Human Understanding, David Hume explored rationalism and empiricism. In his discussion, he made the skeptical conclusion that correct knowledge about the world is ultimately impossible. Influenced by Hume, a German philosopher named Immanuel Kant awakened himself from what he called a “dogmatic slumber” (2) and began exploring the nature of human reason. In this essay, I will explore Kant’s epistemology and its implications for Hume’s skepticism.

In chapter four of the Enquiry, Hume drew a distinction between two different kinds of objects of thought (Hume 28, 29). In the one category, he placed what he called “relations of ideas.” These objects, such as math and geometry, are true a priori. They have no dependence on anything that actually exists within the universe. These thoughts are instead dependent on a certain framework; for example, statements such as “All bachelors are unmarried men” belong in this category because we can reason them to be true without actually asking every bachelor whether or not he is married.

Hume called second category of enquiry “matters of fact.” Matters of fact are proven empirically, or a posteriori – That is to say, they are dependent on actual experience with real things. Matters of fact tell us things about the world. That “All bachelors are happy” is an example of a matter of fact, since it makes a general statement about real objects rather than a connection between ideas. Hume asserts that “All reasoning concerning matter of fact seem to be founded on the relation of cause and effect,” (Hume 29) an idea that has dire consequences for empirical knowledge.

Cause and effect relationships are used to make statements about matters of fact, but such conclusions may not be logically sound. Hume says that cause and effect is inferred from past events (Hume 30). We see something happen, and we see the result. From this, we infer that if the same cause occurs again, then the same result will follow. Such a conclusion would assume that the past will necessarily resemble the future (Hume 35), a proposition for which there is no guarantee.

According to Hume, this division between the a priori and the a posteriori makes knowledge about the world impossible. Our a priori thoughts can only give us true statements about the ways in which ideas relate to one another. Our a posteriori thoughts can give us statements about the world itself, but due their groundings in inferences about the future, they cannot be anything more than speculation. Hence, the two classes of reason are mutually exclusive to one another, and neither can provide a certain statement about the world. It is this distinction, “Hume’s Fork,” that Kant will explore.

In the introduction of the Critique, Kant discusses judgments. For Kant, a judgment has a subject and a predicate. In “All bachelors are unmarried men,” “all bachelors” are the subject and “are unmarried men” is the predicate. He draws a line between two kinds of judgments: The synthetic and the analytic. This demarcation is made by way of the containment criterion. The containment criterion asks whether or not a proposition’s predicate is contained in the subject. For example, in the case of the analytic, Kant tells us that “the predicate B belongs to the subject A, as something which is (covertly) contained in this concept A,” (3) whereas in the case of the synthetic, the predicate statement is not contained in the subject. Combined with Hume’s ideas about the a priori versus the a posteriori, and their implications for matters of fact versus relations of ideas, this distinction between analytic and synthetic provides us with a schematic of reason as demonstrated in the following table, reproduced from Analytic and Synthetic Judgments before Kant (4):

	a priori	a posteriori
analytic	relations of ideas truths of reason	none
synthetic	none	matters of fact truths of fact

The crux of Kant’s argument is against the skeptical notion that the a priori and the synthetic are exclusive to one another. He hopes to illustrate that certain (ie. “true,” not “particular”) statements of fact can be made.

In order to find the synthetic a priori judgments that Kant proposes, we only need look as far as space and time. When Kant writes about space and time, he is referring to our perceptions of these things. While empiricism’s philosophy states that we learn about space and time through experience (that is, space and time are a posteriori), Kant asserts that our ideas of space and time are a priori structures that provide the lens through which we experience the outer and inner world, respectively (5); Space and time are not things that we have learned about, but innate processes through which our mind goes about its business.

Kant illustrates his perspective with thought experiments. With regards to space, he says that “We can never represent to ourselves the absence of space, though we can quite well think it as empty of objects. It must,” he continues, “therefore be regarded as the condition of the possibility of appearances, and not as a determination dependent upon them.” (CPR B-38, 39) Since we can’t conceive a universe without space, space is a constant. It is a priori. It is innately a part of our cognitive processes.

Kant also claims that space is one indivisible intuition – that there are no separate spaces, only parts of one space. Hence, we can’t empirically experience all of space (especially because it is infinite), and we can’t empirically experience numerous separate, smaller spaces. We also can’t experience small parts of space and expect our empirical findings to generalize to all of space. “The whole of space is prior to its parts; The former is presupposed for the union of the latter.” (6) After making these assertions, Kant applies the same arguments to time.

According to Kant, an a priori space should also lend us the idea of a synthetic, a priori knowledge of geometry. Kant discusses the synthetic nature of geometry in the Prolegomena. He uses the congruency of two figures to prove his point. When one tries to prove two triangles as being congruent, each triangle does not contain within it the concept of being identical to the other triangle. (Prolegomena 284) Thus, a conclusion about congruency cannot be derived analytically. It must be reached by synthesis, using innate (a priori) ideas about space.

Having made his arguments for geometry and space, Kant makes analogous arguments for math and time. When we say that math is synthetic, we must remember that an important part of the containment criterion is that “contained in” can, in a sense, mean “defined by.” “An idealized version of an analytic judgment would be one of the form ‘All AB are A,’ or ‘all C are A,’ where ‘C’ is defined as ‘A and B.’” (7) Thus, as Kant says, “The concept of 12 is by no means already thought in merely thinking this union of 7 and 5; and I may analyse my concept of such a possible sum as long as I please, still I shall never find the 12 in it.” (CPR B-53)

So where do we get this concept of twelve from? According to Kant, our understanding of time is crucial for our understanding of math, “For neither coexistence nor succession would ever come within our perception, if the representation of time were not presupposed as underlying them a priori.” (CPR B-46) Succession, in turn, is necessary for math. Kant is able to illustrate succession in the case of 7+5 by counting on his fingers: “I now add one by one to the number 7 the units which I previously took together to form the number 5, and with the aid of that figure [the hand] see the number 12 come into being.” (CPR B-53) Of importance, here, is the phrase “come into being,” which finalizes Kant’s point that the 12 is synthesized from this union, not found analytically.

With its exposition of the synthetic a priori, Kant’s Critique is successful as a refutation to Hume’s claims and provides us with a new way of thinking about the debate between rationalists and empiricists; For Kant has shown a way for us to cross Hume’s fork, and in doing so, gain true knowledge about the world. Although Kant’s work hasn’t solved all of philosophy’s problems – debates about his writing continue to this day – we can at least give it the honor of being a decent step forward.

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1. Hume, David. An Enquiry Concerning Human Understanding and Other Writings. Ed. Stephen Buckle. Cambridge: Cambridge University Press, 2007. Pg xxxiii.
2. Kant, Immanuel. Prolegomena to Any Future Metaphysics. Trans. Paul Carus. Berlin: Akademie, 1911. Pg 260.
3. Kant, Immanuel. Critique of Pure Reason. Trans. Norman Kemp Smith. London: Macmillan & Co LTD, 1963. Pg B-10.
4. Beck, Lewis White. Essays on Kant and Hume. New Haven: Yale University Press, 1978. Pg 81.
5. Kant on Pure Reason. Ed. Ralph C.S. Walker. New York: Oxford University Press, 1982. Pg 31.
6. Seung, T. K.. Kant: A Guide for the Perplexed. London: Continuum International Publishing Group, 2007. Pg 11.
7. Kant on Pure Reason. Ed. Ralph C.S. Walker. New York: Oxford University Press, 1982. Pg 20.