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Is mathematics just the study of all possible languages that are constructed from strict internally consistent rules?

by vlovich123 3y ago

saalweachter 3y ago
Mathematics is the study of things you can convince people are true without physical evidence.
- adastra22 3y ago
  I like this one. Succinct and to the point. However this would also include religion :\
  - saalweachter 3y ago
    Two different religionists can have a conversation and agree on what is true?
    - vlovich123 3y ago
      Within the lens of the other religion probably. Except from hardcore zealots, religious people often agree on true things that they find in common between religions (eg idol worship being a sin, murder, adultery, etc etc).
  - btilly 3y ago
    Not if you added "...using only pure logic". Religions do not convince with pure logic.
    - munch117 3y ago
      The problem is that now you need to define what "pure logic" is. Here's my definition: Math is the study of intersubjective knowledge.
btilly 3y ago
No, because some possible languages are far more interesting than others.
- bmacho 3y ago
  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.)
  - btilly 3y ago
    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.
    - vlovich123 3y ago
      The uninteresting languages are still part of mathematics though. It’s just that we choose not to explore them because we don’t think there’s any value. If you limit it just to the languages that we find interesting, then “what is mathematics” is a fluid definition depending on what we choose to focus on today whereas my definition is a bit more durable. Also, on the topic of “uninteresting”, if I recall correctly number theory (or discrete math) was explored by a mathematician claiming it’ll never have any application and that’s why he was doing it, only for cryptography to come by within a century after that. At least if I recall the apocryphal story told to me in class correctly. Erdos seems like he’d line up time wise and focus wise but I can’t find any quotes from him to that effect so maybe I’m misrembering?
adastra22 3y ago
So Japanese grammar is math?
- vlovich123 3y ago
  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.
- btilly 3y ago
  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!
  - adastra22 3y ago
    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.

Is mathematics just the study of all possible languages that are constructed from strict internally consistent rules?

saalweachter 3y ago

Mathematics is the study of things you can convince people are true without physical evidence.

adastra22 3y ago
I like this one. Succinct and to the point. However this would also include religion :\
- saalweachter 3y ago
  Two different religionists can have a conversation and agree on what is true?
  - vlovich123 3y ago
    Within the lens of the other religion probably. Except from hardcore zealots, religious people often agree on true things that they find in common between religions (eg idol worship being a sin, murder, adultery, etc etc).
- btilly 3y ago
  Not if you added "...using only pure logic". Religions do not convince with pure logic.
  - munch117 3y ago
    The problem is that now you need to define what "pure logic" is. Here's my definition: Math is the study of intersubjective knowledge.

btilly 3y ago

No, because some possible languages are far more interesting than others.

bmacho 3y ago
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.)
- btilly 3y ago
  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.
  - vlovich123 3y ago
    The uninteresting languages are still part of mathematics though. It’s just that we choose not to explore them because we don’t think there’s any value. If you limit it just to the languages that we find interesting, then “what is mathematics” is a fluid definition depending on what we choose to focus on today whereas my definition is a bit more durable. Also, on the topic of “uninteresting”, if I recall correctly number theory (or discrete math) was explored by a mathematician claiming it’ll never have any application and that’s why he was doing it, only for cryptography to come by within a century after that. At least if I recall the apocryphal story told to me in class correctly. Erdos seems like he’d line up time wise and focus wise but I can’t find any quotes from him to that effect so maybe I’m misrembering?

adastra22 3y ago

So Japanese grammar is math?

vlovich123 3y ago
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.
btilly 3y ago
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!
- adastra22 3y ago
  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.