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Meaning is not something that is particularly an end goal. That is why there is specific differenciation between the syntax (structure) and its semantics. Once

by Wiskerz 11y ago

Meaning is not something that is particularly an end goal. That is why there is specific differenciation between the syntax (structure) and its semantics. Once you isolate them, one could think of the structure itself and manipulate its related symbols, without worrying about their meanings. Sometimes surprisingly, some of these results map back to the meaning of the structure, but that is purely a byproduct.

Retra 11y ago
The manipulation of symbols it itself meaningful, because the symbols are real things that exist in nature. You may be working at a different layer of indirection, but it makes no difference to the usefulness of your work, because nature itself does no indirection (as far as we can tell); your results are always applicable to something real. Even if many mathematicians are so poor at explaining it that they'll just pretend it isn't true; that mathematics doesn't need a purpose. It does -- it just always has one.
- Wiskerz 11y ago
  As far as my limited knowledge permits, it may be that meaning does motivate the creation of the said symbols. A problem therefore can motivate the creation of a full set of symbols: Seven Bridges of Königsberg and Graph Theory; Calculus finds its root meaning in the necessity to formalize change. I also agree that the manipulation operates at an indirection but has meaning, I think the greatest example to that is problem reduction, that operates at a higher level of indirection but eventually maps back to a completely different meaning. But it is often times that the manipulation of the symbols is simply inspired by meaning, in fact, you can define abitrary operations on any system (by doing S -> S in a relation) without any useful semantic relevence to anything. Maybe we are cherrypicking the meaningful ones? But maybe the fact that you can do so implies a different meaning. Well I guess we will never know. If we define symbols to be part of nature then surely "The opposite of nature is impossible." Mathematics is effectively the study of things, therefore it has purpose, it can even study itself!
conceit 11y ago
> Meaning is not something that is particularly an end goal. No, of course it isn't. The goal is where meaning gets you to.
- Wiskerz 11y ago
  Unless you are studying the meaning of meaning, in which case the goal is the (second) meaning. (i.e https://en.wikipedia.org/wiki/Proof-theoretic_semantics https://en.wikipedia.org/wiki/Proof-theoretic_semantics ) I may be wrong though.

by Wiskerz 11y ago

Retra 11y ago

The manipulation of symbols it itself meaningful, because the symbols are real things that exist in nature. You may be working at a different layer of indirection, but it makes no difference to the usefulness of your work, because nature itself does no indirection (as far as we can tell); your results are always applicable to something real. Even if many mathematicians are so poor at explaining it that they'll just pretend it isn't true; that mathematics doesn't need a purpose. It does -- it just always has one.

Wiskerz 11y ago
As far as my limited knowledge permits, it may be that meaning does motivate the creation of the said symbols. A problem therefore can motivate the creation of a full set of symbols: Seven Bridges of Königsberg and Graph Theory; Calculus finds its root meaning in the necessity to formalize change. I also agree that the manipulation operates at an indirection but has meaning, I think the greatest example to that is problem reduction, that operates at a higher level of indirection but eventually maps back to a completely different meaning. But it is often times that the manipulation of the symbols is simply inspired by meaning, in fact, you can define abitrary operations on any system (by doing S -> S in a relation) without any useful semantic relevence to anything. Maybe we are cherrypicking the meaningful ones? But maybe the fact that you can do so implies a different meaning. Well I guess we will never know. If we define symbols to be part of nature then surely "The opposite of nature is impossible." Mathematics is effectively the study of things, therefore it has purpose, it can even study itself!

conceit 11y ago

> Meaning is not something that is particularly an end goal. No, of course it isn't. The goal is where meaning gets you to.

Wiskerz 11y ago
Unless you are studying the meaning of meaning, in which case the goal is the (second) meaning. (i.e https://en.wikipedia.org/wiki/Proof-theoretic_semantics https://en.wikipedia.org/wiki/Proof-theoretic_semantics ) I may be wrong though.