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.