[or] + [and] -- discrete vs. continuous
The dichotomy between discrete and continuous is pervasive in logic and mathematics. Discrete phenomena can be “chunked”, while continuous phenomena “blend together”.
This problem is analogous to the linguistic distinction between “count” nouns and “mass” nouns. Count nouns, as the name suggests, can be counted. They are things like cats, chickens, and tomatoes. Mass nouns cannot be counted. They are things like soil, water, and air. Trying to number them sounds bizarre.
*I bought two soils.
*I drank three waters.
The infelicity occurs because numbering is a discrete, disjunctive operation. Mass nouns, in contrast, are conceptualized as continuous and conjunctive. Dividing a cat, chicken, or tomato destroys the object, while soil, water, and air can be split ad infinitum without altering the essence of the noun.
Count and mass nouns show that the discrete / continuous problem is merely an application of the basic logical operators “or” and “and”. Mathematicians like Archimedes and Newton observed that the continuous emerges from the discrete as the “chunks” get smaller and smaller. The same reasoning applies to these logical operators. In the language of calculus, “and” is the limit of “or”.