Mathematics: Numeric Logic

Not only does mathematics prove useful during each day of my existence for matters ranging from trivial to complex, but it is the only discipline other than logic that can grant one absolute certainty about something just by reflecting on and understanding the terms one is using.  However, math itself is nothing more than the numeric application of logic, but it is still considered a separate discipline--this is why "logician" and "mathematician" can be distinct occupational titles, despite the similarities of concepts that the two occupations share.

Three of the most basic types of mathematics taught to students are arithmetic (using the processes of addition, subtraction, division, and multiplication), geometry (calculating values corresponding to shapes and figures), and algebra (solving for unknown variables in equations).  To help demonstrate that math is nothing but an application of logic into the realm of numbers, I will explain what an equation is before assessing algebraic equations.  A number is a symbol assigned a certain value of quantity.  An equation is a series of numbers divided into two sides by an equal sign (=), with the total numeric value of one side being identical to the total numeric value on the other side.  Each side can initially have a differing quantity of numbers, but the collective numbers on each respective side must add up to the same value.  I will compare the first law of logic, otherwise called the law of identity, and a simple math equation:


A is A (something is what it is)

1 = 1


As you can see, an equation is just a mathematical restatement of the logical law of identity--a thing is what it is.  Just as an apple is an apple and an arm is an arm, a certain numeric value is what it is.  Different quantities and variations of numbers can be added to reach the same value:


5 + 4 = 3 + 3 + 3


Despite the difference in the number of values on each side, each side ultimately adds up to the same value of 9.  Algebraic equations involve unknown variables that one must identify by rearranging values.  As with questions about logic, there are legitimate, verifiable answers to equation problems.  Consider the following equation which has a variable that appears on both sides:


X - 36 + 17 = X - 19


If one uses numeric values consistently, X on one side will be identical to X on the other.  Just as the conclusion of a sound logical syllogism must by necessity follow from any preceding premises in the syllogism, the value of one side of a sound equation must, by absolute necessity, equal that of the other or the equation is incoherent.

Mathematics can scare people--but people who understand logic and recognize that math is just an application of logic into the realm of numbers may find it far less intimidating than before!  Use of numbers is not something that only concerns a group of elitist mathematicians, for everyone must utilize some knowledge of at least basic mathematics to even be aware of when they are looking at a certain quantity of something.  But math offers more than just everyday convenience; it provides absolute certainty about numeric values.  Because of its inherent logicality, one can know mathematical truths a priori, merely by reflecting on concepts, the concepts of which are true by necessity although the words used to refer to them are arbitrary.  For instance, what I mean by two plus two equals what I mean by four even though, were I never exposed to the mathematical terminology of any particular society, I could have used other words instead of "two" and "four".  Thus, people interested in studying necessary truths will find mathematics very useful in their pursuits.  For in understanding logic, one understands how to interpret sensory information (recognition of quantity), how to grasp immaterial truths that cannot be false, and how to have absolute certainty regarding assessment of numbers.