Philosophy Of Matematics And Language Essay Example For Students

Philosophy Of Matematics And Language Essay 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 Go d or be a god (lower case ?g?). 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 ?pure language? 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. Its completely consistent with the belief that mans ability to a ttain 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 weve 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 ?better? 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 stratific ation, its 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 definition?in other words, it assumes that the pure language is (a subset of) logic. Secondly, even though its 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 temp eraments cause it to be frequently overlooked. Beowulf Vs. Grendal EssayThe problem with such a modification to our definitions is that it isnt consistent with our practice. Because mathematical logic (or our conception of it at least) is a lan-guage, it has evolved considerably from its definition. Now, math excursions arent per-formed through discovery, but through construction: mathematicians state axioms (as-sumptions) and definitions, and logically derive all of mathematical from them. Mathe-maticians believe this process to be more rigorous than any other method of proof in that, aside from the ubiquitous set of axioms (axioms are a necessary part of every construc-tion), its logically impeccable. The quest for the truth has become a secondary concern, and the quest for the logically consistent has ran to the top of our list of priorities. For example, in the widely-accepted construction of the field of analysis (one of three ex-haustive subcategories of math), arithmetic involving infinity is defined in such a way that i s inconsistent with what we know from other mathematical excursions to be true:It may seem strange to define 0 ? ? = 0. However, one verifies without diffi-culty that with this definition the commutative, associative, and distributive laws hold on without any restriction. (Rudin, p.18)This reveals a subtle but intrinsic difference between the pure language of the universe (i.e., the truth) and mathematical logic in practice today. Another aspect of the logical construction that distinguishes it from the pure lan-guage is the linear progression. By its very nature, every logical argument is linear in its development: A implies B, implies C, implies D, etc. But, every line has a beginning, i.e., every logical construction has a beginning, a group of definitions and axioms from which all other results derive. (This seemingly obvious fact was stated earlier and even-tually logically proven.) Therefore, its necessary to first define, for example, what ? is exactly, and derive all other mathematical relationships involving ? from that. However, since the development states exact the nature of ?, all other results are not much more than mathematical coincidences; they become part of what is ? only in another construc-tion, where these facts are taken into account in the definition. This is not true of the pure language: as has become more and more apparent in science since the 1950s (and the new mathematics that arou se from it), nature is very non-linear. This means that there is no beginning or end to the truth: the number ? can be (intrinsically) many things at once, because there is no definition that nails down one interpretation of ?. Even though mathematical logic can be used to see the truth, the truth becomes unavoidably biased by it. There are many shortcomings of logic that keep it from being the pure language, the absolute truth, the Man Upstairs. Yet and still we have embraced this theology whole-heartedly (if not consciously, through societal conditioning). Our desire to com-pletely understand the universe (along with our belief that we can completely understand the universe) has blinded us into accepting falsehoods as facts. We dont have to scrap the whole idea of logic all together; we must, however, understand that logic isnt neces-sarily the truth, and always is neither the whole truth and nothing but the truth. Mathematics