Henry Imler June 1st, 2005

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In the wake of Hume�s works, Metaphysics, as an objective philosophical discipline, was left in chaos. When applied correctly, Hume striped causality of its power and prestige. Metaphysics, the study of the underlying nature of the world, heavily relies on the idea of causation being intelligible. Hume argued that all meaningful ideas came from the senses and because we could not actually sense the causation of an event, our idea of causality in each specific occasion is unfounded. It was this difficulty that spurred Kant to rethink Metaphysics in general.

Kant tries to establish a set of founding principals on which to rest the foundations of Metaphysics. In doing so, he establishes four types of propositions: a priori, a posteriori, analytic, and synthetic. The first two deal with the origin of the proposition. A priori propositions are known from pure reason, whereas a posteriori propositions are known from experience. The last two types describe the relation of the predicate and the subject of the sentence. Analytic propositions contain in the predicate, knowledge that is known in the subject. Synthetic propositions on the other hand add the idea in the predicate to the subject. There are four possible combinations of the four types of propositions: a priori analytic, a posteriori analytic, a priori synthetic, and a posteriori synthetic. A priori analytic statements and a posteriori synthetic exist; their very definition allows them to necessarily exist.

A posteriori analytic propositions are impossible, for each of the terms exclude the other. Kant believes that Math, Science and Metaphysics lie in the last type, a priori synthetic propositions. It is questionable that this class of propositions exists. If it is not possible, then Metaphysics, as a science, cannot exist. If Kant can demonstrate that the class of a priori synthetic propositions does exist, by letting Math in, then he can use the same principles to allow Metaphysics to exist through a priori synthetic propositions. Kant uses a priori intuitions for a priori synthetic propositions in his first remark in the first part of the Prolegomena. His argument for the validity of a priori synthetic propositions of space and time are as follows.

1. A priori intuitions are known outside of experience.
2. Pure Geometry is an a priori intuition of space.
3. Pure math is an a priori intuition of time.
4. (C1). Pure Geometry and Pure Mathematics are known outside of experience.

5. Pure Geometry and Pure Mathematics are known outside of experience.
6. Pure Geometry and Pure Mathematics are the form of our ability to experience space and time.
7. Objects of sense are bundles of our experiences of space and time.
8. (C2). Pure Mathematics and Pure Geometry refers merely to objects of sense.

9. Pure Mathematics and Pure Geometry can only have objective reality on the condition that it refers merely to objects of sense.
10. Pure Mathematics and Pure Geometry refers merely to objects of sense.
11. (C3). Pure Mathematics and Pure Geometry have objective reality.

12. Pure Mathematics and Pure Geometry have objective reality.
13. Pure Geometry is an a priori intuition of space.
14. Pure math is an a priori intuition of time.
15. (C4). Pure Geometry and Pure Mathematics are necessarily valid of space and time.

Is the conclusion, Pure Geometry and Pure Mathematics are necessarily valid of space and time, true? In Kant�s view, three-dimensional geometry, or Euclidean geometry, is only possible form of space. However, with the onset of Einstein�s Relativity, we have learned that our previous intuitions about space and time were wrong; space is really four-dimensional and does not follow rules of Euclidean Geometry. This demonstrates the conclusion of Kant�s argument to be false.
Where in the chain of reasoning is the error? It is located in the original intuitions. The a priori intuitions that give rise to Pure Geometry, otherwise known as Euclidean Geometry, are incorrect. Our reasonings of the structure of space and of time were incorrect. If the reasonings before experience about time and space are wrong, what prevents the reasonings, or a priori synthetic propositions, before experience about the nature of experience to be incorrect also? If the reasonings about the nature of experience are also incorrect, then one is unable to correctly interpret experience. Once the interpretation of experience is rendered baseless, the foundation on which to build the science of Metaphysics disappears.

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