Philosophy of Mathematics and Language

Throughout its history mankind has wondered about his place in the universe. In fact, second only to the existence of God, this subject is the most frequent topic of philo-sophical analysis. However, these two questions are very similar, to the point that in some philosophical analyses the questions are synonymous. In these particular philoso-phies, God takes the form of the universe itself or, more accurately, the structure and function of the universe. In any case, rather than conjecturing that God is some omnipo-tent being, supporters of this philosophy expound upon another attribute habitually asso-ciated with the Man Upstairs: His omniscience. That particular word, omniscience, is broken down to semantic components and taken literally: science is the pursuit of knowl-edge, and God is the possession of all knowledge. This interpretation seems very rigor-ous but has some unfortunate side effects, one of them being that any pursuit of knowl-edge is in fact a pursuit to become as God or be a god (lower case Ð'ÐŽÐ'§gÐ'ÐŽÐ'Ё). To avoid this drawback, philosophers frequently say that God is more accurately described as the knowledge itself, rather than the custody of it. According to this model, knowledge is the language of the nature, the Ð'ÐŽÐ'§pure languageÐ'ÐŽÐ'Ё that defines the structure and function of the universe.

There are many benefits to this approach. Most superficially, classifying the structure and function of the universe as a language allows us to apply lingual analysis to the philosophy of God. The benefits, however, go beyond the superficial. This subtle modification makes the pursuit of knowledge a function of its usage rather than its pos-session, implying that one who has knowledge sees the universe in its naked truth. Knowledge becomes a form of enlightenment, and the search for it becomes more admi-rable than narcissistic. Another fortunate by-product of this interpretation is its universal applicability: all forms of knowledge short of totality are on the way to becoming spiritu-ally fit. This model of the spiritual universe is in frequent use today because it not only gives legitimacy to science, but it exalts it to the most high. The pedantic becomes the cream of the societal crop and scientists become holy men. ItÐ'ÐŽÐ'¦s completely consistent with the belief that mans ability to attain knowledge promotes him over every other spe-cies on Earth, and it sanctions the stratification of a society based on scholarship, a mold that has been in use for some time.

Now that weÐ'ÐŽÐ'¦ve defined the structure and function of the universe as knowledge, we must now further analyze our definition by analyzing knowledge itself. If the society is stratified by knowledge, there must be some competent way of measuring the quantity of knowledge an individual possesses, which means one must have a very articulate and rigorous notion of knowledge. At first glance, one would think that knowledge was sim-ply the understanding of the universe through the possession of facts about it. This un-derstanding creates problems, however, because it now becomes necessary to stratify knowledge, to say that this bit of information is inherently Ð'ÐŽÐ'§betterÐ'ÐŽÐ'Ё than that one. This question was first answered using utility as a metric, but it became obsolete because util-ity is too relative. A new, more practical answer was eventually found: rather than meas-uring knowledge, we should measure intellect, the ability to attain knowledge. Even though this has the same problem of stratification, itÐ'ÐŽÐ'¦s overlooked because philosophers believe that they know the best way to pursue knowledge. To them, the language of complete understanding is logical inference. If one can state a set of facts in the simplis-tic linear progression of statements using logical connectors, the information is in its most readily understandable form. The philosophers used this convention to rigorize mathe-matics, the rigorization process became associated with it, and logic suddenly became mathematical logic. The name stuck, as people refer to the process by that name to this day.

The previous analytic development is the essence of the modern understanding of the natural universe. It starts from the fundamental belief in a deity and transforms it into this mathematical logic, a system of communication that according to our summation minimizes the number of justifiable interpretations, therefore standardizing the universe. There are some limitations to this approach, however. The rationale is, by its very nature, a logical development: it constructs a functional model of the pure language that is con-sistent (i.e., free of contradiction). Therefore, the pure language inherits any limitations of logic by definitionÐ'ÐŽXin other words, it assumes that the pure language is (a subset of) logic. Secondly, even though itÐ'ÐŽÐ'¦s very rigorous in its approach, it presents pure language as an inherent truth viewed through the lens of mathematical logic, as opposed to pure language being synonymous with mathematical logic. This is an important but distinc-tion, but its subtle temperaments cause it to be frequently overlooked.

There are many ways to demonstrate the distinction between pure language and mathematical logic, most of which rely on the exhaustive nature of the pure language (as opposed to the restricted nature of mathematical logic). One particularly interesting way is to exploit their language status, and demonstrate a difference by contrasting their dif-ferent responses to a property of all languages: their evolution. The pure language is by definition the structure and function of the universe, i.e., therefore, change is taken into account in the definition (i.e., the Ð'ÐŽÐ'§functionÐ'ÐŽÐ'Ё of the universe). Therefore all kinds of lin-gual evolution are subsets of the pure language, and so the pure language is invariant relative to lingual evolution. (For example, assume that the pure language was changed from its original form to a variation of itself by a form of lingual evolution. What is the new variation? Well, since the lingual evolution is under the category of the pure lan-guage, the variation must be under it as well. Therefore no change really took place.) Contrast this with mathematical logic, a body of knowledge that evolves through use just as a spoken language. However, any changes in mathematical logic that develop through use arenÐ'ÐŽÐ'¦t referred to as such: we call such modifications mathematical discoveries. A mathematical discovery is considered to be Ð'ÐŽÐ'§fitterÐ'ÐŽÐ'Ё than is evolutionary prerequisite, and the former is usually discarded to a text on the history