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Does Math Homework Even Exist?

numbers

Image taken from upload.wikimedia.org and modified under Creative Commons License.

Almost every culture on Earth has developed some form of number systemArabic numerals are one of the most popular today, but there are countless alternatives; the Romans used Roman numerals, the Egyptians had a special set of characters, and the Babylonians counted in base 60!

The concept of having a certain amount of things has sprung up all around the world in hundreds of independent peoples, from the Inuit of Northern Canada to the natives of Australia. It’s easy to see the usefulness of being able to communicate exactly how much food you have or how many wolves are chasing you, but it still raises an important question:

What is a number?

Like most things in philosophy, the dictionary definition doesn’t help us much. According to Merriam-Webster, a number is a “word or symbol that represents a specific amount or quantity.” Well, we knew that much already.

Perhaps a better question would be: Is a number a physical object?

Referring back to the dictionary definition of a number, a number represents a certain amount of something. It can represent anything from the quantity of atoms in a glass of water (something inherently material) to the amount of thoughts you have in a day (perhaps something not-so-material). The similarity between these examples is that they are both cases of a number representing something else.

Maybe we should refine our question even further: Can a number materially exist without representing something else?

To help answer that, I pose a question to the reader: What is five? Perhaps you think of the Arabic numeral 5, or the Roman numeral V, or something more material such as holding up five fingers. The problem with all of these answers is that they are all represented in some way by five. The numerals are simply symbols that mean five (they aren’t five itself), and the fingers are directly represented by five. This leads us to conclude that a number cannot physically exist without representing something else.

So, let’s modify our question once more: Is a number a thing?

This is a little more tricky. We know that a number alone is not a material thing, but that does not necessarily mean it is not a thing at all. The property of being a thing is not limited to physical objects – aren’t thoughts things? Isn’t consciousness a thing? Isn’t nothing a thing? A thing can be an idea – so it that what a number is? An idea?

pi

Pi is a mathematical constant and an irrational number. Is it really only an idea?

Now we can rewrite our question for a final time: Is a number an idea?

We’ve concluded that a number IS a thing, but is NOT a material thing. That only leaves us with one conclusion: if a number is a thing but is not a material thing, a number must be an immaterial thing. Concept or idea or whatever you want to call it, numbers exist inside our minds. We create them and use them to further our communication skills and our understanding of the world around us, and they are an vital part of our everyday lives. Every computer program is a collection of 0s and 1s, and mathematical formulae govern countless aspects of our daily routines. We take numbers and we apply them to the world around us, but numbers themselves are not material. Why would they be?

 

 

3 Responses to Does Math Homework Even Exist?

  1. Jess says:

    I really liked this!

    One thing that I noticed at the end of your point was that you mentioned binary code (one’s and zeros, that is), and it made me think of how numbers that are not one and zero can be represented by binary versions of themselves. This isn’t so much a question as an interesting concept that what we think of as basic numbers (i.e. 5) can still be broken down into strings of numbers that aren’t so simple.

    But anyway: I also wanted to ask if you thought it would be possible to form a working society that did not require numbers.

    ((Personally, I think that in theory it may work, if only because it isn’t on Maslow’s hierarchy. On the other hand, if every culture has come up with some form of numbers, surely that means that something is going right.))

     
  2. Pingback: Mathematical Platonism: Eat Some Delicious Pi | Talons Philosophy

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