Math: Discovered or Invented?
What is Math? Was it discovered or invented? How do we Know?
Before we begin, we should define both “discovered” and “invented”.
“Discovering involves locating or gaining knowledge about something that was previously unknown or unseen. The word is especially associated with finding new places (as in discovering new lands) and scientific breakthroughs (as in discovering a cure).”
With that, “discovered” simply means that we gained knowledge of something that was already there.
Inventing means to produce (something, such as a useful device or process) for the first time through the use of the imagination or of ingenious thinking and experiment
Inventing means to create something. It wouldn’t have been there if not for the creator, it is dependent upon him/her.
With that, let’s begin:
What is Math?
The question today is an analytical question in philosophy (meaning that whatever answer we come upon would be true in virtue of its meaning or false in virtue of its meaning). It doesn’t need experimentation to answer, it simply needs concise definitions.
That is why the metaphysical question of “what is math?” naturally would come up. So then — what exactly is math?
Math is a way of putting the natural world into numerical terms or numbers. This begs the question though — what exactly is a number? A number would be anything that measures something and quantifies it in a particular way. For instance, if I posit the proposition, “all bachelors are unmarried” and it just so happens that there are 300 bachelors in existence, then I could’ve just said, “300 bachelors are unmarried” or “100% of all bachelors are unmarried”.
What’s the Solution?
Most mathematicians will tell you that you discover math and that it isn’t invented. Which is exactly what James Brown, a scientist, says,
“Working mathematicians overwhelmingly are Platonists. They don’t always call themselves Platonists, but if you ask them relevant questions, it’s always the Platonistic answer that they give you.”
A “platonist” simply means you believe in the theory of forms made by Plato. The theory of forms states that math is abstract and exists in a non-physical realm outside of time, space, and matter. Platonists believe math is discovered and not invented.
We also need to understand that mathematics is descriptive — not prescriptive. Largely known as “the map and the territory” fallacy, coined by Alfred Korzybski, it means that people are often too quick to confuse something that describes reality with reality itself.
Numbers do not exist outside of a mind, they come from the human mind — just as Logic does. Obviously something cannot exist and not exist at the same time and the same way (this is known in Logic as the law of non-contradiction). The problem however is that this is not the case because we say it’s the case, it’s a description of reality to say that that’s so, but reality is by no means contingent upon how we describe it.
This gives us two ways to look at this issue. Either a) math exists outside of the human mind in a non-physical realm — as Plato said or b) math is created by man to describe the natural world.
Personally, I believe mathematics was created by human minds to put the natural world into numerical terms, that doesn’t, however, means that we could perhaps change 2 + 2 to equal 5. So this also presents problems — it’s objectively true that mathematics exists and that 2 + 2 = 4, however it’s also true that mathematics was made by man to describe the natural world —just as a man would use a map to describe his territory, hence the name “map and the territory fallacy”.
The map could be wrong, that is to say it leads you in an improper direction from where you wanted to go. In contrast, the map could be as objectively true as mathematics is when it states 2 + 2 = 4. That doesn’t mean the map was discovered just because what it states about reality corresponds, it was still invented by man to describe. It by no means was discovered as some say it is.
