Immanuel Kant (1724-1804); Wiki Commons (Public Domain)
In his important book Critique of Pure Reason, Immanuel Kant (1724-1804) wrote about the sources of human knowledge. In the Critique of Pure Reason, Kant attempted to forge a compromise between the Rationalists and the Empiricists by showing that both reason and the senses contribute to human knowledge.
In so doing, Kant wants to be able to claim for human beings a kind of knowledge that is necessary (a statement is necessary if it is impossible to deny it), yet tells us about the world. The Rationalists, whose kind of knowledge is represented by mathematics and geometry, have knowledge that is necessary but that does not tell us about the world. For example, the Pythagorean Theorem is necessary, but it does not tell us about the world because there are no perfect triangles in the material universe.
On the other hand, the Empiricists, whose knowledge comes from the senses, have knowledge that tells us about the world but that is not necessary. For example, I may think that I am typing away at my computer right now, but the Rationalist Descartes would point out that I may be mistaken — I may actually be in bed dreaming that I am typing away at my computer. Another example: I may think that the world has turned different shades of yellow overnight, but although this is what my senses tell me, I may actually be suffering from jaundice, a disease in which the sufferer sees only different shades of yellow.
The Distinction Between A Priori and A Posteriori Knowledge
According to Kant, “There can be no doubt that all our knowledge begins with experience. … But though all our knowledge begins with experience, it does not follow that it all arises out of experience.”
That is Kant’s thesis statement. In giving evidence to support his analysis of knowledge, Kant used several terms that we will have to define. Among these are the terms a priori and a posteriori.
A priori knowledge is completely independent of sensory experience. Here are some examples of a priori statements:
- 2 + 3 = 5.
- The square of the hypotenuse is equal to the squares of the two sides (the Pythagorean Theorem).
- A thing is equivalent to itself; that is, A is equivalent to A.
- 2 + 3 = 3 + 2.
As you can see, mathematical and geometric knowledge is a priori knowledge. This is knowledge that is completely independent of sensory experience.
A posteriori knowledge is knowledge that is wholly empirical; that is, knowledge that we learn from our five senses. Here are some examples of a posteriori statements:
- There is a lightning storm outside.
- The grass is green.
- The basketball team from Ohio University in Athens, Ohio, wears green and white uniforms.
- There is a Wendy’s in my hometown.
As you can see, a posteriori knowledge is completely derived from the senses.
The Distinction Between Analytic and Synthetic Judgments
Kant also makes a distinction between analytic and synthetic judgments. By “judgments,” Kant means what we today call “propositions.” A proposition is a statement that affirms or denies something and that is true or false. Examples of propositions include “All bachelors are male” and “The grass is green.”
An analytic statement is one in which the predicate is contained in the subject. For example, the statement “All bachelors are male” is an analytic statement. Since “bachelor” means “unmarried male,” the predicate “are male” adds no new information to the subject “All bachelors.”
The strength of analytic statements is their necessity — meaning it is not possible to deny them. Since the predicate is contained in the subject, analytic statements are necessary. The weakness of analytic statements is that they don’t tell us anything new — the predicate merely conveys an idea that is already in the subject.
A synthetic statement is one in which the predicate is not contained in the subject. For example, “My computer is a Macintosh” is a synthetic statement. The predicate “is a Macintosh” adds information to the subject “My computer.”
The strength of synthetic statements is that they tell us something new because the predicate is not contained in the subject. The weakness of synthetic statements is that they are not necessary — it is possible that I have made a mistake. Perhaps I am so ill informed about computers that I can’t tell the difference between a Macintosh and an IBM computer that uses Microsoft Windows.
More Kinds of Sentences
We can combine the terms a priori, a posteriori, analytic, and synthetic in meaningful ways. For example:
- “All bachelors are male” is an analytic a priori statement. We know that this statement is true without having recourse to sensory knowledge, so therefore it is a priori. In addition, it is analytic because the predicate does not add information to the subject.
- “The grass is green” is a synthetic a posteriori statement. We know that this statement is true if we look outside and see that the grass is green (there has been no drought recently and snow does not cover the ground). Since we can check on the truth of this statement by using sensory information, it is a posteriori. In addition, it is synthetic because the predicate adds information not contained in the subject.
A kind of sentence that is impossible is an analytic a posteriori sentence. A posteriori statements are made after sense experience — that is, they are dependent on sense experience — but analytic statements are made independently of sense experience, so analytic a posteriori statements are impossible, being a contradiction in terms.
However, this leaves synthetic a priori statements. This kind of statement would be very useful to human beings, because this kind of statement would be certain, yet it would also contain new information. Kant believed that this kind of statement really exists.
According to Kant, the following sentence is an example of a synthetic a priori statement; that is, it is both necessary and informative:
- “7 + 5 = 12.”
The synthetic a priori statement “7 + 5 = 12” may surprise you, as you may think that it is an analytic a priori statement. However, according to Kant, you can analyze “7 + 5” all you like, but you will never find “12.” Since the predicate “= 12” is not contained in the subject “7 + 5,” the sentence “7 + 5 = 12” is synthetic.
To say the same thing in other words: If “7 + 5 = 12” were to be analytic, the predicate “= 12” would have to be contained in the subject “7 + 5.” But according to Kant, this is not the case, because all the subject “7 + 5” tells us is that the numbers 7 and 5 are being added together. The subject “7 + 5” does not tell us what the sum of these two numbers will be.
In addition, the statement “7 + 5 = 12” is also a priori. It is a necessary sentence that we know without having any sensory experience. After all, numbers don’t exist in the physical universe. You may have seen five apples, but you have never seen a “five.” The number “5” written on a chalkboard is only a symbol.
Furthermore, even if we take seven apples and five apples, put them together and count twelve apples, all that our sensory information would tell us is that these particular apples added together total twelve apples. It would not tell us that all groups containing seven apples and an additional five apples will total twelve apples.
Are you still unconvinced that the mathematical statement “12 + 5 = 12” is synthetic? Quick, analyze this subject — don’t use a calculator! — “the square root of 123.456789” and then fill in the predicate of this sentence:
“The square root of 123.456789 equals ….”
Are you still convinced that mathematical statements of this kind are analytic?
Causality and the Categories of the Understanding
According to Kant, the sentence “Everything which happens has its cause” is a synthetic a priori sentence. This is something that we know prior to sensory experience and the predicate adds something that is not contained in the subject.
Therefore, according to Kant, causality is a synthetic a priori concept. It is one of Kant’s twelve “categories of the understanding,” in terms of which we must think about the world. In other words, our minds are made in such a way that we must think about the world in terms of causality and 11 other synthetic a priori concepts. One of these other synthetic a priori concepts is the concept of substance.
In Kant’s analysis of human knowledge, both reason and the senses play a role. Knowledge begins with sensory experience; however, the mind contributes concepts in terms of which we must analyze that sensory experience. In other words, we must analyze our sensory experience of the world in terms of such concepts as cause and effect, and substance.
In doing so, we have no choice. Our minds are made in such a way that we have to experience the world in this way. It is possible that cause and effect, and substance, do not really exist. But if they don’t, we will never be able to tell because we are prisoners of our own minds.
To conclude this essay, let me tell you about Peter Ustinov, a noted actor, director, teller of stories, writer, wit, etc. Someone once asked him why he read so many books. He replied that he did so because since he is a prisoner of his own mind, he wants it to be well furnished.
Note: The quotations by Kant that appear in this essay are from his Critique of Pure Reason, translated by Norman Kemp Smith.
Copyright by Bruce D. Bruce; All Rights Reserved
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