Problems of Logical Typing: The “One” and the “Unity”

Abstract

While we can count the oceans (or apples, elephants, money, etc.), we cannot do the same with the water (or sand, wind, temperature, etc.) in a meaningful way. However, we can instead measure the amount of water. It thus appears that we have to do with two, logically distinct types of information, one of which is discontinuous and subject to counting, whereas the other is continuous and subject to measuring. These accordingly correspond to the digital and analog information types, which respectively obey to the “on or off” and “more or less” logic. The distinction of logical types implies that these two types of information are in a relationship of perceptive exclusion, as evident in logical paradoxes. This problem of logical typing is ubiquitous, as it reflects our inherent incapacity to simultaneously perceive the discontinuity and continuity. The reality of this problem can be clearly traced back in the development of natural sciences. Most clearly however, the universality of the problem of logical typing revealed itself in the efforts to reduce the content of mathematical theories to formal logic.

Everything that is numbered depends on the one, and the one depends on nothing.

—Meister Eckhart