Philosophy of matematics and language Essay

This essay has a total of 2423 words and 10 pages.

Philosophy of matematics 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 “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. It’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 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 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 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
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 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
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