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Are Mathematics, Logic and Music Languages?

[i:d77e2e7298]IB Theory of Knowledge (TOK) Paper[/i:d77e2e7298]
Are Mathematics, Logic and Music Languages?

Mathematics, logic and music all play rather important roles in the lives of most people and are used quite frequently to communicate certain things. However, does the mere use of these forms of admittedly limited communication qualify them as languages? I shall attempt to show that two, music and mathematics, act as languages by themselves, as well as become incorporated in the larger scheme of spo ken language, for which they serve integral roles. Logic is not a language by itself, but rather aids in the language process and provides a type of playing field for all types of language.
Mathematics is perhaps the more straightforward of the two to understand as a language by itself. It has a set of symbols which are used to convey certain messages and has rules which it follows in which one can convey these messages. These messages, whether they are as simple as “1+1=2,” or more complex like “º 3x2 + 2x + 3 dx = x3 + x2 + 3x + C,” can be understood by anyone in the world who has a basic working knowledge of mathematics. Needless to say, a more advanced knowledge of math is required for the more complex aspects, but the point remains the same: math fulfills the requirements of being a language. It works with a set of symbols to convey a message which can be understood by anyone who knows how to interpret the symbols.
Most may not think of math as a language, since it doesn’t work in the same manner that spoken languages work. While it is true that math cannot convey things such as emotion, it is quite useful in explaining most everything else. Superficially viewed, one might think of numbers as only being useful for describing quantity. However, when reminded of the role that physics plays in the natural world (which math in an integral part of), it goes much deeper. Math can describe motion, color and sound, among other things, in a purely mathematical form, which again, can be understood by anyone who is fluent in the language of math. Math reflects the aspects of human existence which are pure reason.
Music is perhaps a little less concrete in its existence as a language. To best discuss music, I will divide it up into two parts: musical notation and actual sound produced. Musical...

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