The Philosophy Discussion Forum

Our Grammar Matrix is produced, by taking the two intelligible concepts of Language, given perceptible names such as limit and material within limits, or relative and its correlatives, noun and verb, multiplied by the two physical requirements of perceptible Grammar systems, Symbol sets and the methods of recursively using them, produce Common Grammar, Arithmetic, Algebra and Geometry. Common grammar gives us a relatively unordered method of naming, from speech to indexing systems using letters. Arithmetic gives us the order to enumerate sequentially, Algebra takes both Common Grammar and arithmetic, but still the motion of the hand is relative. All of these are applied to both the perceptible and intelligible.

However, geometry pairs the motion of the hand to the two elements of a thing, producing a completely metaphorical, or intelligible system of Grammar. It allows you to provide, as Plato and the Bible intimates, perceptible paradigms for every possible concepts. But just like every grammar, it requires intelligence. You can never understand what is indicated by any grammar of system, beyond your own level of intelligence.

Common grammar is easy, in so far as it provides names which any fool can parrot. Geometry is the most difficult because it is completely intelligible, and thus requires the greatest intelligence to use.

Even Aristotle wrote that you can display all of arithmetic using common grammar.

Your post astutely observes the correlation between diverse grammatical structures and the representation of perception, intellect, and abstract thought. Furthermore, it posits a necessary correlation between increasingly abstract language and the requisite intellectual capacity, culminating in geometry as the most intellectually demanding field. Can you elaborate more on how the concept of "limits" and "material within limits" relates to the structure of grammar and its application in other disciplines like mathematics? Also, do you think there is anything in your post which my finite intellectual capacity failed to perceive?