Philosophy Of Language Essay, Research Paper

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 philosophical analysis. However, these two questions are very similar,

to the point that in some philosophical analyses the questions are synonymous.

In these particular philosophies, 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 omnipotent being, supporters of this

philosophy expound upon another attribute habitually associated with the Man

Upstairs: His omniscience. That particular word, omniscience, is broken down to

semantic components and taken literally: science is the pursuit of knowledge,

and God is the possession of all knowledge. This interpretation seems very

rigorous but has some unfortunate side effects, one of them being that any

pursuit of knowledge is in fact a pursuit to become as God 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 admirable 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 spiritually 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.

It?s completely consistent with the belief that mans ability to attain

knowledge promotes him over every other species 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 we?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 simply the understanding of the

universe through the possession of facts about it. This understanding 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 utility is too relative. A new, more practical answer was eventually

found: rather than measuring knowledge, we should measure intellect, the ability

to attain knowledge. Even though this has the same problem of stratification,

it?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 simplistic 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

it?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 ?function? 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 aren?t referred to as such: we call such modifications mathematical

discoveries. A mathematical discovery is considered to be ?fitter? than is

evolutionary prerequisite, and the former is usually discarded to a text on the

history of the subject. Hence, we see mathematical logic as a static body of

knowledge that we change from time to time to fit our needs (which happens to be

in this case, the need to be more correct)?synonymous with any spoken

language. An example of the evolution of mathematical logic is found in the

varied ap-proaches for the approximations of the number . The number

 is a commercial icon in the pure language whose decimal expansion

(approximately 3.1415926535?) goes on forever, never repeating, never

terminating. The first approximations of this number come from ancient

manuscripts, like the Christian Bible. In I Kings 7:23, the authors used a sheer

estimation of the circumference of a circular lake, divided by its diameter, to

get a crude approximation of :   = 3. The ancient

Egyptian manuscript called the Rhind papyrus gives another approximation:

  = 3.1604938?. Such approximations represented the standard

in mathematical logic of the time period. To the respective members of the

cultures,  was a number not unlike the every numbers they dealt with;

the difference was they didn?t know it?s exact value. The above

ap-proximations of  were the closest that they could get to capturing

the ever-elusive num-ber; therefore, after many years of use in the society, the

approximation and the number itself became virtually indistinguishable. The line

was blurred between the pure language and the mathematical logic that

approximated it and, practically speaking, the number became . This was

the case until just after the turn of the age, about 150 BC, when the sec-ond

phase of approximation began. Fellows like Archimedes and Ptolemy used

geomet-ric means to approximate . They took geometric shapes with equal

sides, and calculated the ratio of their perimeter to their diameter to get an

estimation of the constant. Then, they doubled the number of sides, and

re-calculated the ratio to get a better approxima-tion of . This process

was very tedious (one mathematician did his calculations on a polygon with

262?roughly 4,610, 000,000,000,000,000 sides?to find the value of 

cor-rect to 35 decimal places), but it provided a new way of conceptualizing the

number . Rather than thinking of it as a simple number like the rest of

the numbers they knew, people now thought of this member of the pure language as

the holy grail of a geometric quest that had no end. One could continue to

increase the number of sides of various regular polygons to get closer and

closer to it, but in the end this geometric limit was un-attainable (because we

simply can?t draw a perfect circle). Then the fifteenth century rolls around,

and the famous mathematicians Newton and Leibniz discovered the calculus. When

applied to this old problem, they found that if we continually added and

subtracted the following fractions, we got closer and closer to the elusive

constant:  = 1 ? + ? + ? + ? + ? ?Suddenly, the matter of

approximating  [and therefore this part of the pure language] turned

from the geometric problem it had been with Archimedes? regular polygons to a

simple arithmetic problem of and adding and subtracting numerical terms. This

was a major change in perspective.? (Dunham, p.108) This shift in perspective

was a result of the discovery of calculus, and would the new trend in

mathematics. Just as in oral lan-guage, use (i.e., the use of logic to produce

mathematical discovery) intrinsically changed the conception of what exactly

 was. The above discussion uses the quest for the number  to

reveal two forms of evolution apparent in mathematical logic. The first is an

?unofficial? evolution, i.e., practical evolution that results from years of

use, while the second is an ?official? evolu-tion, i.e., evolution that is a

result of logical deduction. Since the pure language of the universe doesn?t

exhibit such change, these demonstrate that mathematical logic is inher-ently

different from the structure and function of the universe. There is, however, a

re-buttal to the above argument, another modification to the logical

construction that seem-ingly makes this difference disappear. If we assume that

the pure language is consistent (i.e., contains no contradictions), we can

define mathematical logic to be a translation of the pure language, and define

our discovery of the language (e.g., our approximations of ) to be the

lens we view it through. That way, logic is still the Supreme Being, and the

pursuit of it is again legitimized. All our problems are solved. The problem

with such a modification to our definitions is that it isn?t 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

aren?t 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), it?s 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 is inconsistent with what we know from other

mathematical excursions to be true: It may seem strange to define 0 

 = 0. [According to the pure language, the value of this ex-pression can

equal zero as well as any other finite number.] However, one verifies without

diffi-culty that with this definition the commutative, associative, and

distributive laws hold on [all of the numbers from zero to infinity] 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, it?s 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 arouse 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 don?t have to scrap the whole idea of logic all together; we must,

however, understand that logic isn?t neces-sarily the truth, and always is

neither the whole truth and nothing but the truth.