Comment by vlovich123
2 years ago
Is mathematics just the study of all possible languages that are constructed from strict internally consistent rules?
2 years ago
Is mathematics just the study of all possible languages that are constructed from strict internally consistent rules?
Mathematics is the study of things you can convince people are true without physical evidence.
I like this one. Succinct and to the point.
However this would also include religion :\
Not if you added "...using only pure logic".
Religions do not convince with pure logic.
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Two different religionists can have a conversation and agree on what is true?
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No, because some possible languages are far more interesting than others.
I don't think that's a problem: if there are uninteresting languages, then you must study them, then work hard to prove that they are uninteresting first. That is, mathematics indeed does study uninteresting languages.
.. mathematics is the same for me as GP said: you have a set of symbols, a set of rules, now derive true statements. (Or at least this is a good view, but other views can be also good.)
Most mathematicians don't feel that way.
There are uninteresting languages that can be considered, but nobody considers them unless a reason arises to do so.
Attempting to prove that they are uninteresting is not itself an interesting problem, because it is easy to prove that such proofs do not generally exist. Indeed things become interesting not because they are inherently interesting in and of themselves. But because something else that is already interesting turns out to connect to the not yet interesting thing, and studying the not yet interesting therefore becomes relevant to the interesting one.
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So Japanese grammar is math?
English grammar can be. Buffalo is an animal, a city, and a verb meaning "to bewilder and confuse". As a result the following can be proven.
The word buffalo, repeated any number of times, can always be parsed into a valid English sentence. If the number of times it appears is prime, it can only be parsed into ONE possible English sentence.
This is clearly a statement of mathematics!
No, it is a mathematical statement about linguistics. It should not be surprising that mathematics can be used to describe things. Everything in the universe can be described by mathematics--even truly random, acausal events have probability distributions which are described by mathematics. But being described by mathematics does not make it mathematics. That's a type error.
I think so, but it wouldn’t be very interesting. The rules of Japanese grammar mathematically could only tell you if something is in the Japanese language or not. The other challenge is that human languages tend to be filled with exceptions and intentional violations of rules for creative effect. That kind of stuff doesn’t really fly in mathematical languages.