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Metaphysics  -  The field of philosophy that investigates the constitution, nature, and structure of reality. Metaphysics goes beyond physics to examine the reality behind the phenomenal world. It asks questions that cannot be verified in experience: "Does God exist?" "Is the soul immortal?" "What are the ultimate constituents of matter?" "How are mind and matter connected?" and so on. In the Prolegomena, Kant argues that this kind of "dogmatic" metaphysics can never arrive at satisfying answers because our faculty of reason cannot teach us anything about things in themselves. He tries to replace dogmatic metaphysics with his own critical metaphysics that sets about examining the constitution, nature, and structure of knowledge.
Analytic  -  A statement whose predicate concept is contained in its subject concept. An example is "all bachelors are unmarried." The concept of being unmarried is part of the concept of "bachelor," so the predicate does not say anything new. Instead, it offers an analysis of a part of the concept of the subject.
Synthetic  -  A statement whose predicate concept is different from its subject concept. Such a statement joins two different concepts together, and in doing so, produces new and interesting judgments. The Prolegomena makes much of synthetic judgments that can be known a priori, since they constitute mathematics, pure natural science, and metaphysics.
a priori  -  Knowledge that can be gained prior to any experience. Mathematics is a form of a priori knowledge, because we can sort out mathematical truths in our head. Kant also refers to a priori cognitions as necessary, since nothing in experience can possibly contradict them. Synthetic a priori judgments are thus important, since they are necessary and interesting truths that we can know prior to any experience.
a posteriori  -  In contrast with a priori cognitions, a posteriori cognitions consist of knowledge that we gain from experience. These generally have to do with facts about objects in the world, like "all swans are white."
Intuition  -  A translation of the German word Anschauung, this word means more exactly a perspective or a point of view. According to Kant, our faculty of sensibility is structured by intuitions. There are two kinds of intuition: pure and empirical intuitions. Our pure intuitions are our concepts of space and time that we apply to everything we perceive. Once we have applied our pure intuitions of space and time to sensations they become empirical intuitions, that is, sensations that exist in space and time. Kant argues that our pure intuitions of space and time can be exercised independent of experience, and serve as the basis for mathematics and geometry.
Concept of the understanding  -  These concepts, listed in Kant's table of categories, give a law-like structure to experience. While the empirical intuitions of our faculty of sensibility give us only subjective knowledge of experience, the faculty of understanding makes our empirical intuitions objective by applying to them universal concepts such as cause and substance. On their own, these concepts in their pure form serve as the basis for the general laws of pure natural science, such as "every effect has a cause."
Sensibility  -  The faculty that gives structure to the report of our senses. Our senses perceive things in themselves, and our faculty of sensibility applies our pure intuitions of space and time to give form to these sensations. Sensations combined with pure intuition makes empirical intuitions. The faculty of sensibility ensures that whatever we perceive we perceive in space and time.
Understanding  -  The faculty that gives an objective, law-like structure to our experience. Our faculty of sensibility gives us empirical intuitions, and our faculty of understanding applies to these intuitions the pure concepts of the understanding to give them objectivity. Empirical intuitions combined with pure concepts of the understanding make appearances. The faculty of understanding ensures that whatever we perceive, we perceive as following the laws of cause and effect and so on.
Reason  -  The faculty that deals exclusively with the human intellect. Though our reason aspires to answer metaphysical questions about the nature of things in themselves, it is incapable of doing so. However, reason is capable of surveying all possible knowledge, and as such can be applied in a self-critique. Kant recommends a new kind of metaphysics that uses reason to investigate the grounds and justification for human knowledge.
Thing in itself  -  Things in themselves (ding an sich in German) are the ultimate constituents of reality. However, we can never perceive things in themselves directly. We only perceive their appearances with our senses and mental faculties. Nonetheless, we can infer these appearances have a cause, and we can infer that things in themselves are this cause even though we can know nothing about them.
Appearance  -  What we think of as "nature" is essentially a set of appearances. Appearances are sensations that have been structured by our faculties of sensibility and understanding in such a way that they appear to us in space and time and seem to follow certain laws and regularities. These appearances are caused by things in themselves, but are given form by our faculties.
Sensations  -  Sensations are the raw material of sense data. These are the impression things in themselves make on our senses. They are subsequently structured by our faculties of sensibility and understanding, but they come to us in a chaotic, simple form.

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I find Kant more compelling, taken at face-value

by DannyBoyPoker, April 10, 2014

One gathers the impression from what is here, that Kant's not terribly compelling, or plausible, whatever his historical importance. I think this is debatable.

About the claim that is made here, that Frege was the first to point out that geometry is not synthetic a priori. Well, this implies that indeed, geometry is not synthetic a priori. However, Some believe that Frege was wrong. I'll note that I'm also reading, here, about how this position 'was given a boost by Einstein's relativity..' That is to say, that Einstein's relativity<... Read more


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