How do we translate natural language in to logic?

Here is a story. I wrote it for you all!:

“Once upon a time, there were four happy kids playing. They believed in magic., and wanted to go down to the woods to search for a witch. This was because they had been told that a witch existed, by their great aunt. She was the cruelest witch their aunt had ever known! They knew that they shouldn’t go, but they were curious. “Why shouldn’t we go?”, asked one child to another, and thus the journey started…”

Now - I hope none of you had any trouble understanding that? Good!

But logicians - we have a problem. As you may have noticed - I have deliberatly constructed a story that is infinitely complicated to formalise. Relax - I’m not going to ask you to try and formalise it for me (of course - I think that would be expecting a little too much from any of us. But if you could manage it - do it and make yourself famous!).

I have just a simple question - do you think that it would be possible to formalise it? Systems of logic have advanced greatly over the last 20 years - I believe that satisfactory defintions of superlatives have now been given, for example. But how far can the project go? Do you think that there are elements in the story above, or anywhere else in language that just aren’t ever going to be translateable in to formal systems?

Donald Davidson famously reduced all language to Tarskian semantics - and claimed that all meaning was simply a case of truth-conditons. And so (as was necessary for his theory), he stated that it was possible for all language to be re-written in logical formula. Evidently - his entire program fails if it isn’t - so he was bound to be prtty optimistic. Actually I agree with Davidson - but only superficially. I think that we will one day be able to successfully translate the whole of natural language in to logic. This is actually two assumptions - the first that language is compositional, the second that all meaningful sentences have truth conditions.

But am I granting logic too much power? Is the entire project to reduce meaning to truth conditions doomed? And if language isn’t truth apt - does this ruin philosophy as we know it? Wouldn’t it then be possible to formulate sound natural language arguments with no formal eqivilents?

Ironic that you should just now post fiction.

Logicians can only deal with statements. You needn’t have gone to such lengths.

“Are you well today?” cannot be formalised.

Many sentences have no truth value, because they are not statements. This includes many declarative sentences as well.

This is no hinderance to logicians, for they only seek analytic truths - which can be derived only from statements.

Statements are fictional.

This may be your view- but it certainly isn’t davidsons (nor any of his followers - probably the majority of philosophers of language and logic today) -. An underlying belief of much of what logicians do is that logic may one day be able to translate everything.

Davidson tried to reduce all meaning to semantics - and that means that everything meaningful must be truth apt. The project to show that everything meaningful is truth apt is on-going. Whether Davidson’s reductionism was correct or not - I believe that if all of natural language could be translated into formal logic - this would be a humongous achievement and reveal much about the complexities of language.

You say " “Are you well today?” cannot be formalised." I think this is interesting - questions are for sure a difficult project for logic (indexical questions not much more difficult - but still an added question) - but there are whole books devoted to showing how questions can be put into logic.

I can’t find any links to any of the books I want to reccomend - I just don’t think googlebooks has scanned them yet! but how about this (books.google.co.uk/books?hl=en&l … lc#PPR5,M1). The general percieved problems for logicians are questions, indexicals, belief/desire statements, attributive adjectives, statements abour existence (and many more - my story tried to illustrate most of them [and was deliberately ficticious to complicate things]), but very many argue that all, eventually, can be reduced to logic.

Of course logicians ultimately want to reduce everything to truth statements. But generally it is argued that non-statements like questions, imperitives etc are reducible to statements of some kind. Consider the amount of literature concerning the logic of commands (a brief look at Quinn’s Divine Command Theory, for example) . Logicians are certainly interested in formalising far more than statements - they are hungry to formalise everything.

My question was - is it possible?

I am familiar with Davidson’s work.

Let me know how he makes out.

I think you don’t speak for all logicians.

I didn’t claim too. I fully realise there is a split - that some philosophers of logic are interested in formalising everything while others aren’t bothered (I probably shouldn’t have wildly claimed it was a majority - my mistake). All I was asking was - is the project possible? I gauge that you think it isn’t!

I don’t see how it is possible, as many sentences are not intended to contain truth, yet do contain meaning. You can’t invent a truth value where one doesn’t exist. I also see no reason to try. Davidson is using a definition of meaning that no one else does. I think his attempts reveals the complexity of language because it failed.

Davidson’s project failed.

The problem lies in the need for an infinite regression of metalanguages to flesh out the truth conditions for even the most straight forward statement in a natural language.
Consider sentence 1.

S1 - “Snow is white” is true iff snow is white.

This sentence defines the conditions for “Snow is white” being true, but only if we already know the meaning of “snow is white”. S1 is not much help. S2 is required.

S2 - “Snow is white” is true in English iff la neige est blanche.

S2 tells us what it means for snow to be white, but only if we know the meaning of “la neige est blanche”. To define the meaning of “la neige est blanche” in terms of truth conditions, we require another sentence, something like S3.

S3 “La neige est blanche” is true in French, iff 雪是白的.

It should be pretty obvious to see where this approach is going. ](*,)

In S1 we use the same language on both side of the biconditional, and the result is vacuous. Using metalanguages on the disquotational side of the biconditional avoids the vacuity of S1, but only at the expense of generating an infinite regress of metalanguages, each language defining the truth conditions of the one that precedes it, but each requiring another metalanguage to define its truth conditions. One might try a trick like S4:

S4 - “雪是白的” is true in Chinese iff snow is white.

The conjunction of S1, S2, S3, and S4 trades an infinite regress for a vicious circle.

Davidson’s project seemed silly to me the first time I read it, and it seemed down right ridiculous when I studied it in depth for a class. If I recall, Davidson himself admitted the project did not achieve its goals. Moreover, Tarski himself cautioned against applying his system to natural language, saying the project was doomed to failure.To Davidson’s credit, his theory of triangulation can give the meaning of natural language utterances, but only in the Wittgensteinian sense of functional pieces within a language game.

Some people take great pleasure in looking at everything through a black and white lense of bivalence, but this is a physochological disposition, not an insight into some deeper metaphysical structure. Reality does not always present itself in in terms of true and false, and this richness of meaning is reflected in our natural languages.

It is possible.

However there is required much development.

Intuitively, when it is possible.