This chapter gives a valuable account of the work of German philosopher Immanuel Kant (1724–1804). Kant developed a critical philosophy, which assumed that knowledge exists and sought to understand the character of that knowledge and how it is possible at all. The answers he found developed into a vast and detailed metaphysics. Russell gives him the principal credit of having conceived a priori knowledge that was not "purely analytic" and for elevating the essential discipline of epistemology to a 'first philosophy.'
The traditional concept of the a priori was necessarily analytic, which meant that the predicate was always implicit in the subject. An example is the statement: "A bald man is a man." The idea of a man is clearly implied by the phrase "bald man," producing an obvious and almost trivial assertion. Before Kant, the law of contradiction, that "nothing can both be and not be," was sufficient to prove the truth of all a priori statements; a bald man cannot be bald and not bald without contradiction.
The work of English philosopher David Hume (1711–76) was an important precursor to Kant's work. Hume revealed that many cases of analytic knowledge, the most conspicuous case being that of cause and effect, were in fact synthetic. Hume argued against the traditional rationalist belief that effect could be logically deduced from cause, and he concluded that nothing could be a priori known about the relation between cause and effect. In answer to Hume's skeptical thought, Kant (whose thought derived from rationalist origins) alleged that there were many other propositions besides cause and effect that failed as analytic truths. He held that arithmetic and geometric propositions were also synthetic in that "no analysis of the subject will reveal the predicate." His notable illustration was the statement "7 + five = 12." In themselves, neither seven nor five contain the idea of twelve, and they must be put together first. Such observations allowed him to make a distinction between the a priori and analytic. His description took the form: "All pure mathematics, though a priori, is synthetic." Kant then investigated how such knowledge, a priori and synthetic, was possible.
Other schools of philosophy have attempted to answer this question. The empiricists depended on experience to arrive at pure mathematical knowledge, through the repetition of instances. We already admitted that this answer is flawed because it is possible to grasp the proposition that "two and two make four," through reflection on one instance. Kant's solution poses a sophisticated metaphysical picture, which Russell sketches before responding.
Russell's account of the Kantian system of reason first separates our experience into two elements: the element owing to the physical object and the element owing to our own nature. The next structural feature of Kant's philosophy is the distribution of these elements. Russell writes: "(Kant) considers that the crude material given in sensation—the colour, hardness, etc.—is due to the object, and that what we supply is the arrangement in space and time, and all the relations between sense-data which result from comparison or from considering one as the cause of the other." Kant supports this view because he believes that we have a priori knowledge of "space and time and causality and comparison," but not of "the actual crude material of sensation."
For Kant, the physical object, the thing in itself, is unknowable. What we can know is the "phenomenon," the object in our experience. The phenomenon is a product of the thing in itself and us. Thus, as it comes into our experience, the phenomenon will acquire characteristics which "conform to our a priori knowledge." Further thus, this knowledge cannot be valid outside of our experience. Despite having knowledge that it is a priori in quality, we cannot extend it outside our experience to a thing in itself. Russell reads Kant's conclusion as an attempt to reconcile the rationalist picture with the empiricist one.
The major flaw which Russell finds in Kant's argument theory of a priori knowledge is the importance that Kant places on the nature of the observer. If we are to have "certainty that the facts must always conform to logic and arithmetic," then allowing human nature any influence on the a priori is a mistake. There is no reason, since our nature is a fact in the world, to suppose that we would not change tomorrow in such a way that "two and two are five." Russell thinks that this objection "utterly destroys the certainty and universality which Kant is anxious to vindicate for arithmetical propositions." Russell continues that his objection to Kant is clearly valid if we reflect but a moment on what we seek for the truth of our "arithmetical beliefs." We believe that two objects that we do not experience still make four objects, theoretically. Thus, our theory must account for a notion of the a priori unlimited by experience or the nature of the observer, independent of our thought about it.
Similar to Kant's perception of the a priori, other philosophers have frequently supposed it to have more to do with something mental, the way in which we think about the world rather than any fact about it. Russell formulates an analogy with the "law of contradiction" that makes this tendency apparent. From the law "Nothing can both be and not be," we can extrapolate the meaning that nothing can both have and not have a certain quality. We are convinced of this principle, not through outward observation, but through thought. Take the statement: "If a tree is a beech it cannot also be not a beech." On this hypothesis, we see a tree that we ascertain to be a beech, and we do not need to look again to ascertain that it is not a beech. It is natural to believe that the positive instance of the quality excludes the negative in the same instance. We do this by thought. Yet, the importance of this illustration is to grasp that the law of contradiction is "a law about things, not only about thoughts." The principle applied above is about ascertaining the existence of something. The law does not enforce itself on our thoughts in any way; if we think something is a beech it is not the case that we cannot think that it is also not a beech. The law "is not a law of thought."
A priori judgments are analogously understood. Our proposition "two and two are four" is not true owing to our nature, as Kant believes, because of the way our minds are constituted, and no fact about how are minds are constituted could make it true (if it were false). The proposition involves "all actual or possible couples" and is "applicable to whatever the world may contain, both what is mental and non-mental."
Russell finishes his inquiry into the a priori by remarking that our knowledge about it concerns things that do not seem to "exist, either in the mental or in the physical world." The quality of the existence that they do have is the quality assignable to qualities and relations. In the sentence: "I am in my room," "I" exist and "my room" exists, but does "in," exist? In the next chapter, Russell places relations, like "in," in a world apart from the mental or physical, a world important to the understanding of a priori knowledge.
It should be noted that in some considerable respects Russell's metaphysics resemble Kant's. Both thinkers divide the objects of our knowledge into an external world of physical objects and one essentially more internal, subjective. In Russell's case, this subjective element takes the name of sense- data, and matter, according to him, comprises the rest of the physical world. Their groundwork agrees. With respect to apportioning the a priori, Kant's system is in diametric opposition to Russell's. Kant thinks that the phenomena that Russell calls sense-data owe to the object because we do not have a priori knowledge of sense-data. Again in this chapter, we witness Russell's book in its capacity as an introduction to philosophy. Russell analyzes the arguments behind Kant's critique of reality. A priori knowledge comes into view as a synthesis of rationalist and empiricist ideas. Russell's attention to Kant in the edifice of his epistemic discussion is appropriate. Kant's influence on all later philosophy cannot be overestimated. He changed the landscape of philosophical thought, which led to the structure and fertile development of analytic and Continental philosophies as we know them today.