Philosophy On The Mesa

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1. Omid - August 8, 2009

Consider the following statement: “All triangles have three angles.” According to Kantian philosophy, this statement is “analytic” and “a priori”. It is analytic because the concept of the predicate (i.e., “three angles”) is already contained within the concept of the subject (i.e., “triangles”). Moreover, the statement is a priori because its truth is necessitated before empirically verifying it. Suppose that I have never seen a physical representation of a triangle, and hence, of a point, line, and angle. Further suppose that someone orally instructs me as follow:

1. A “point” is a unit having a definite position. Further, a “point” is the beginning of dimension, but not itself a dimension, and likewise the beginning of a line, but not itself a line.
2. A “line” is a juxtaposition or extension of points extended in space.
3. An “angle” is the distance or space between two intersecting lines.
4. Every triangle is composed of three straight lines whereby each line intersects other two lines, causing formation of three angles (one at each intersection), and that the sum of the three angles amounts to 360 degrees.

Assuming, again, that I have never experienced a physical representation of a triangle, do you suppose that, upon receiving the instructions enumerated above, I immediately mentally apprehend that the statement “all triangles have three angles” is a priori analytic statement? To understand the statement, won’t I need to have at least some empirical experience of—either in representational form or else—a point, position, extension, straightness, line, space, dimension, intersection, distance, and measure? My point is that some, if not all, a priori analytic judgments seem impossible to be purely mentally grasped prior to and without aid of any sensory experience. The truth of the statement seems contingent upon how the subject (i.e., “triangle”) is defined, and whether the definition corresponds to the concept of the predicate (i.e., “three angles”). However, to understand the definition itself, it seems to me that one needs the aid of some sensory experience. Consequently, this indicates, at least in this particular case, that while the statement “all triangles have three angles” is analytic, it is not a priori—that is, its truth can not be verified without the aid of some sensory experience. I think it was Nietzsche who said that if we deduct the nervous system, then we simply miscalculate. What do you think?

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