# Terrouge Firebird

Many months ago, I began an article about knowledge, math, and literature. As I progressed, it became clear that the article was really a combination of two articles. Consequently, this article will focus only on the philosophical aspects with a light touch of literature. Next month, the article will dive deeper into prose.

To have knowledge, a person has to do something because there's no such thing as a free piece of knowledge. After all, even the most basic types of knowledge require a certain amount of observation. For example, for you to know your computer is not exploding into shards of molten plastic and metal, you must be smelling the air, feeling the heat (or fortunate lack thereof), looking at the computer, or a combination of the above. For the sake of the writer's sanity, the article will only look at two approaches to mathematical knowledge.

Let's consider the basic premise for knowing mathematical facts. One common view claims that math is the study of things that exist whether we know it or not. All things exist independent of mathematicians, space, and time. Since that would make math completely abstract, the truths from these eternal things will also last forever. In short, the product of a sine and cosine will continue to haunt trigonometry students for centuries. In the rest of the article, I will call it by its academic name, Platonism.

For illustration, we can look at page 18 of Mossflower where Gonff comments, "'What's a bit of warm food and drink between mateys?'" Underlying the question's literary purpose is the philosophical foundation. Gonff's assistance to the hedgehogs exists before someone reads about it. It exists even though the viewer may have no idea that such a novel even exists, much less the particular incident with the Stickle hedgehog family. Fortunately, the incident continues to exist even after being observed by the reader in his mind's eye.

If one considers the more mathematical "a bit," it also becomes evident that the specific mathematical trait exists regardless of the audience's existence. Just like Gonff's relationship with the hedgehogs, the singularity of the "bit" is preserved. In short, no matter how many times you close and open the book, the ink never changes to read "some bits," "scattered bits," or even "one hundred bits."

Alternatively, one could also say math is a discussion about things that only exist in the mind's eye. According to anti-Platonist realism, mathematical conversations are nonsensical babblings about things that only exist to the people talking about the objects. Consequently, proofs are true because a mathematician declared long ago that in his mental picture of the world, the proof is true. Undoubtedly, students struggling in math classes would subscribe to the view that math only exists in the heads of their teachers with no obvious relevance to reality.

A more concrete example of anti-Platonism in Mossflower occurs when Gonff, Martin, and Young Dinny encounter a crab in pages 241 to 243. At first, the crab seems to be "a fencer without a sword" and a fatal showstopper. However, once the crab seizes Martin's staff, Gonff realizes that the crab is too foolish to let go. Consequently, the crab becomes part of Gonff's comedic dance on the beach. Though one might say the crab is the same, the three woodlanders would surely beg to differ. The fearsome crab is reduced to a foolish dancing object with a piece of wood trapped in its claws. The first is fatal. The second is comedic and harmless. Both are abstractions of reality that only exist in the threesome's minds.

Such models are regularly used in math, and mathematicians readily concede the differences between models and reality. For example, one would be hard pressed to find a mathematician who insists that the Earth is a perfect sphere. Similarly, a crab is not actually a fencer, and the crustacean is certainly not a comedic dancer, at least, not intentionally. Despite the differences, the abstract models still manage to be useful. One can make fairly sound physical claims about the Earth as a sphere, and the three woodlanders are amused by the second abstraction of the crab.

Both Platonism and anti-Platonist realism provide useful views of literature. It is up to each person to decide which view he wants to take. I suggest using both and wish you the best as you read books from the two opposite points of view.

Going Deeper:

Routledge Encyclopedia of Philosophy Articles:

Please note that the Routledge Encyclopedia of Philosophy requires a subscription. You may be able to access it through your school, library, or business.

Mossflower:

Page number references refer to the U.S. paperback version with a 10-digit International Standard Book Number (ISBN) of 0-380-70828-0 and a 13-digit ISBN of 978-0-380-70828-4.