Kant’s analysis of pure mathematics in Prolegomena to Any Future Metaphysics is perhaps the best and most intuitive example of the very counter-intuitive concept of a priori synthetic judgment. In the chapter “The Main Transcendental Question First Part,” Kant demonstrates how the science of mathematics is indeed both a priori and synthetic by arguing that our concept of mathematics is inevitably filtered through, or even wholly shaped by the lens of human experience of space and time—an experience which is inarguably a priori (Prolegomena, 36). In many ways it seems that this analysis is a direct response to empiricist ideas, particularly the problem of induction proposed by Hume. Taken as such, that is, a critique of empiricism, Kant is doubly successful as he proves that not only is knowledge intuited a priori, but that such knowledge is more valuable and valid than empirical knowledge.
It is easy to default to empiricism when one examines the nature of the natural sciences, and even the nature of pure mathematics. This tendency seems to come from our concern with causality in science, which leads to the assumption that the very nature of scientific discovery is caused by empirical observation (e.g. Newton saw the apple falling before he intuited gravity). Kant’s response to this tendency is to attack the very nature of empirical observation by arguing that perception of space and time underlies our observations, that we inevitably know,a priori, the nature of space. He critiques empirical observation based on the limitedness of our senses: “everything which our senses may be given…is only intuited to us as it appears to us, not as it is in itself,” and argues that it is in fact our deeper, innate understanding of the same senses that allows us to understand that, for example, “a line should be drawn to infinity” in mathematics (36). Mathematics, in this way, becomes the perfect example in which to explore not only Kant’s idea of synthetic a priori reasoning, but also to solve Hume’s problem of induction. Hume argues that since we can only know that which we observe, we can never really know anything, as at any time, we might observe something to the contrary (e.g we know the sun will rise each day, but one day it may not). Kant, however, in his examination of mathematics, demonstrates that not only can we know something and synthesize new knowledge about it, but we can also see it demonstrated empirically. Importantly, it is that we can know itfirst and with a certainty that empiricism cannot provide. Looking back at Kant’s example of 5+7=12 in the previous section, it becomes clear that the synthesis of 12 from 5 and 7 not only follows with necessity but with more certainty than say, the counting of stones, could empirically provide. If this process of a priori synthetic reasoning is actually more reliable than observation, perhaps even closer to the thing-in-itself, then Kant has truly discovered “sure path” that metaphysics can tread (139).
With Kant’s question: “Is Metaphysics Possible at all,” he is commenting that since we are asking the question then metaphysics is not solidly considered as science. While it has a long history it is not based on actuality. According to Kant, he is setting forth the beginning for further discussion and discoveries. Therefore to have the future determine its solidness.
ReplyDeleteCan you explain how does Kant prove that knowledge is intuited a priori? Having good sound and real intuition can be hard to prove (recall the Pro. Ashley Vaught stated he sees flying pink elephants), until time and experience comes to pass to prove to people of our intuition. I wonder if that’s what you meant by “perception of space and time underlies our observations.” Also, by this are you saying that the nature is caused by observing it and hence (I’m guessing) by our perception of nature?
Responding to Linna’s comment, I think the “intuition” of flying pink elephants might be more appropriately described as what Kant in “Main Transcendental Question, Second Part” calls daydreams that occur when the imagination “does not cautiously hold itself inside the limits of experience” (Prolegomena to Any Future Metaphysics, 68). He warns that the understanding must think and not get lost in daydreams when it sets out to organize the “elementary cognitions that dwell in it prior to all experience but must nonetheless always have their application in experience” (69). So the concepts of flying, of pink, and of elephants would be separate concepts perhaps gained individually from separate experiences and only fancifully placed together by an imagination that is stepping outside the lines.
ReplyDeleteAdditionally, I think our modern understanding of the word intuition has different connotations than the German word Anschauung, which it is translated from in Kant’s original text. We may think of ‘following our intuition,’ meaning ‘trusting our unexplained feelings,’ but Kant uses the word intuition to describe “a mental representation that is particular (not abstract), and that presents objects concretely (as an image does)” and contrasts it to concepts, so that intuition represents a single object rather than an abstract group of objects (xxiii-xxiv).
"Taken as such, that is, a critique of empiricism, Kant is doubly successful as he proves that not only is knowledge intuited a priori, but that such knowledge is more valuable and valid than empirical knowledge."
ReplyDeleteI’m confused by this line so maybe I have either misread you or Kant. My impression of Kant’s general idea is that our innate, a priori intuitions, such as space/time and causality, is that which structures our sensations into the world as we experience, which is then linked to concepts to make it into something concrete. In other words, empirical knowledge is a result of sensations shaped by our a priori intuition; that random whatever stuff out there in the world (and Kant believes there is something “out there” as he is not an idealist) is given coherence by the perceiving mind, which is a mental framework with time and space built in, and that which is conceived and given a concept is what we call empirical knowledge. With this understanding in mind, I'm confused by what you mean when you say that "not only is knowledge intuited apriori", and I have trouble understanding how empirical knowledge can be any more or less "valid" than the mental framework that gave rise to experience.
“It is easy to default to empiricism when one examines the nature of the natural sciences…” but is it? When Newton saw the apple drop, he didn’t say “oh that must be gravity.” Instead, he made a hypothesis that something was making that apple fall to the ground. He tested his hypothesis, and found out that it was indeed gravity. The object is gravity, not the apple falling. The concept is the apple falling. That concept of “what goes up must come down” shaped what we now know as gravity. It is the same with all other experiments in the natural science. For example, when you go to the doctor, they check your symptoms. From there, they make a hypothesis as to what disease you may have and call for a series of tests. These tests will either confirm or repute their hypothesis. Nature must confirm the hypothesis; in this case, the test results must confirm the diagnosis. The diagnosis cannot occur just by observation; it must be tested and confirmed. Kant agrees with this way of thinking and states “intuitions which are possible a priori can never relate to things other than objects of our senses” (34). This means we can hypothesize what something may feel like when we’ve never touched it. We can hypothesize what something my look like when we’ve never seen it. Disease, gravity, and all other components of the natural sciences do deal with our senses, and we can have intuitions a priori.
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