Theory of Mathematics and Spoken Language

Several languages exist in the field of mathematics such as arithmetic, algebra, geometry, trigonometry, calculus, differential equations, topology, and statistics. Everyone of the languages of mathematics just listed comprise the study of specific expressions of language used to talk about what is found to be different types of things. Thus trigonometry is a developed language to talk about triangles whereas statistics is a developed language to talk about patterns in the frequency of occurrences, but often the languages of mathematics get applied in ways that extend past the immediate things that they had been designed to talk about. Overall, when the rules are studied for making a language of mathematics, what is found is that all languages of mathematics can be explained to operate according to a certain set of rather abstract forms, and those abstract forms are the subject of the study known as mathematical logic.

Ideally all of the abstract forms in logic can be used as templates, and when those templates are combined with the axioms (assumptions) about the world and such, then what emerges from those templates is a language. Mathematical logic thus for mathematics is very much like the field of linguistics for natural language. Overall, in natural language (otherwise known as spoken language) the description of the language that defines the language is called its grammar, but in mathematics the grammar of each language of mathematics is usually identified with definitions of basic language concepts.

Grammars thus are in a since both found in mathematics and in natural language text books, and Grammars are not necessarily logic and they are often not necessarily language in its final form. A grammar will combine the ideal forms of logic and also combine the most basic assumptions that a language makes in order to produce a set of rules for working within and constructing everything in that language. Overall, thus logic is the farthest removed study with language being the most immediate to practical application, and grammars become like the middle man between logic and language.

Despite best efforts even if the purest form of logic would be applied to produce the best possible grammar in order to produce the most accurate and exact language (either mathematical or natural) the actual expression of language could never arrive at all thoughts possibly expressed through language because inconsistency would always emerge from reality not being fully numerically identical to the language that expresses the reality. Kurt Godel understood the idea that all languages could only produce incomplete and inconsistent results as he developed what is known as the completeness and incompleteness theorems, and this development showed logic to be both complete and consistent in contrast to language that is neither. Overall, basically the idea is that logic itself is both complete and consistent, but once depiction's of reality enter into the pure forms that logic has to offer, then what results is something that can never be complete and consistent because the model of reality can never be exactly the same as reality itself.

I would argue however that with the world having evil, thus models of reality could never truly match reality because of evil. My case also is that logic as a master template for all expression is like a archetype that all of reality is manifested through. Reality gets generated through these templates, and than some of that reality gets directed at evil (the nothingness of non existence). The point thus is that although we might know these archetypes (or templates) in part, they nevertheless exist in perfection regardless of our ability to fully ascertain them.

The value thus of the school of Plato to teach archetypal creationism for about a thousand years, and for Aristotle to develop the subject known as logic along with the first university is that all things would flow from logic in a archetypal way. Although such a concept may not have been fully realized at the time, it nevertheless is behind linguistics and mathematics today even if people do not recognize it. Overall, spoken language and mathematics thus ideally are derived from the same archetype as two distinct things that show evidence of the general nature of the archetype that they came from.