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I asked similar question on the "Theoretical Computer Science" board and theoretical computer scientists advised me ask it here, in "Philosophy". So...

Is there any formal language such that any problem in the Universe can be described unambiguously using this language?

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    You are asking the exact same question as the logical positivists did one century ago, so you might want to research those. – Ben Jul 10 '13 at 21:30
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Is there any formal language such that any problem in the Universe can be described unambiguously using this language?

Depending on what you mean with language, one may say that the Universe itself is the language in which every possible problems are "formulated". You may then report your problem to commensurability between "the Universe", and "human representation abilities".

Maybe you'll be interested to reduce your problem to something like "Is there any formal language able to describe unambiguously any problem that human may face, lead to know if the problem have a helpful solution, and if yes, what move to do to perform it?".

If you consider "resolving a problem" can be reduce to "computing a solution", then you may want to look at the computability theory, and especialy to the halting problem and the decision problem.

The fact that there are undecidable problems will interest you, because it provide a negative answer to the question "is there an algorithm which is able to tell me if a given language is such that any problem in the Universe can be described unambiguously using this language?". At best you can have an algorithm that will never meet such a case and you may only conclude that you don't know, but potentially will if the answer is no.

  • Yes, it's it. Just wanted some generalization. – vortexxx192 Jul 12 '13 at 20:39
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You might try Carnap's famous (but often neglected) Der logische Aufbau der Welt (The Logical Structure of the World). Here is a link to a survey article (unfortunately, behind a paywall). As part of his project he devised a language which he thought could be used to do pretty much what you ask. The project is largely considered a failure, but very interesting nonetheless.

Lojban is a language which is syntactically unambiguous, so the grammar of the language is unambiguous. But, the semantic component of any language will (plausibly) rely upon the intentions of speakers which introduces a large chance for ambiguity. At this point it would seem to be a question of the cognitive power of the language's speakers, given the demands you place of being able to describe "any problem in the Universe", it seems highly unlikely that any person could devise such a language.

As to the question of whether there is some actual language that does what you describe, I'm pretty confident the answer is "no". The more interesting question is whether such a language is even possible.

Now, could an omniscient being with limitless computational power devise such a language? There it seems that there is more room for optimism. Ted Sider in his Writing the Book of the World speaks about a fundamental language that can (in theory) be used to resolve ambiguity that leads to merely verbal disputes over substantive problems. But even Sider stops short of making the strong claim you're asking about.

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    Here is an earlier (March 25 2009) draft of Pincock's paper that eventually (November 25 2009) ended up in Philosophy Compass. – Hunan Rostomyan Sep 7 '13 at 4:16
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One fixed static universal language would probably run into issues illustrated by Berry paradox and similar paradoxes. Nik Weaver has written some (too easily) accessible short pieces around these themes, see for example the introduction of "Constructive truth and circularity". If I understood the response to a question about these short pieces on the FOM mailing list correctly, these writings are not considered as "wrong", but just as "too trivial".

That said, the above objections just apply to fixed static universal languages. There could by dynamic evolving languages which are able to describe unambiguously any problem in the Universe, in the sense that from any concrete language and any concrete problem, another concrete language able to express the problem would be accessible from the given concrete language.

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I don't see how. If a formal language can do as you suggest, describe anything and everything, then it must be able to describe natural languages.

But in natural languages new words are being minted all the time to describe new ideas. For example, Software. This word can be read by someone in Shakespeares time, but would he be able to make any sense of the word? No, because the concept that is the referent of this word was not invented until the early 20C.

Further the words in a Natural Language also have a nimbus of meanings that vary in both time & place - American English is different from British English, and from Chaucers English. The English spoken by a music-obsessed teen is different from that of an finance-obsessed adult.

Also, any formal language must be interpreted by a mind - otherwise it remains merely a string of symbols without any meaning. This then gives scope for ambiguous or alternative readings. (A comparison here is with the non-standard interpretations of a formal theory/language, for example there is a non-standrad model of Peano Arithemetic).

Finally, mathematics makes a study of formal languages, and under reasonable assumptions, given any formal language L there is a truth that cannot be proven by that formal language. This is the content of Gödels theorem. Of course this doesn't answer your question, which is - is there a formal language that can describe any problem. But, consider this problem: Describe the proof of this truth. If this is acceptable as a problem, then the formal language L cannot answer this problem.

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Yes there is. It is the language on which you wrote your question. All other languages including math are subset of your current one. If you look at the history of thought you will see that many thinkers at the end of their life realized the almost infinite power of our language. See Witgenstein for example. People often fly in the clouds of imagination forgetting that these clouds are created by our own good old human language.

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Isn't mathematics exactly this language you're longing for?

There are complexity classes and every problem can be assigned to a class. Problems can even be mapped to other problem instances.


Maybe you should take a look at the concepts behind a turing machine.

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    Mathematics isn't a language. It's a collection of theories that form a discipline, with many of these theories using distinct mathematical languages. – Dennis Jul 12 '13 at 0:55

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