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?