# Natural and Formal Languages

May 12, 2020 · 22:40 pm

When we communicate with other people, we usually use English or some other language that is mutually understood between both parties. These languages are known as natural languages, and they are very convenient. Natural languages allow people to communicate with each other.

However, in annoying cases, ambiguity arises. Syntactic ambiguity occurs because the English language resolves multiple meanings into similar or identical sentence structures. For example,

I tripped over the dog wearing dark sunglasses.

can either mean myself or the dog was wearing dark sunglasses. English isn’t verbose enough to have syntax that clarifies these kinds of ambiguities.

In other cases, semantic ambiguity can happen. The most famous examples are puns where the author takes advantage of a word’s double meaning. These miscommunications make natural languages difficult to use when explaining more formal concepts that require rigor such as science and math.

Formal languages are able to convey ideas without risking vagueness. For example, if someone writes $1 + 1 = 2$, there is absolutely no risk of misinterpretation that one plus one equals two, other than the possibility that the reader does not yet know arithmetic or the medium of writing is visually unclear.

So why do we learn English? To communicate with other people. Why do we learn Math? To convey exhaustive accurate ideas that would otherwise be at a risk of misunderstanding.

Streaming direct thought dumps from Yuto Nishida.
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