Dear Cristi,
Thanks a lot for writing this very interesting essay -- I enjoyed it very much. I have some questions and comments. First the questions:
1) You say that all definitions in a dictionary are circular, and that physics is all about syntax. But there's a sense in which the liar paradox ('I am a liar') can be seen as the emergence of semantics from syntax, since by manipulating purely syntactical rules, the system ends up saying something about itself, namely that it has limitations. (This point is made by Hofstadter in "Gödel, Escher, Bach"; I also mention it in my essay). I think that this emergence of semantics is something rather weak compared to the point you are making (since it only talks about limitations and does not explore all possible meanings), but I was wondering what your thoughts on this point are.
2) You talk about "the collection of all true statements about the physical the world". But I worry about whether this is well-defined. If you define a set in the standard way (namely: for any property, there exists the set of elements that have that property), you can construct Rusell's paradox, which leads to inconsistencies. You mention this after Principle 2, as if it were a limitation of what we can know, but I think it is also a limitation of what can be properly defined mathematically.
3) You say that language is only about relations. I wonder what is your stand on the problem of universals in philosophy. (That is, how do we recognize an apple if all apples are particulars of the concept of an apple. The concept is the universal, which we never experience.) I am trying to understand whether your standpoint is equivalent to saying that there are no universals.
Now the comments:
1) I liked your idea that meaning is subjective and private (and I also mention this in my essay), but I don't find it scary, I guess I find it kind of beautiful... I see it as the power of words -- as what a poem can do to you.
2) You mention that the coarse graining of a deterministic system can be nondeterministic. In an essay for this year's contest, Flavio del Santo makes a similar point, in particular with regard to classical mechanics.
Thanks again for your very interesting input.
Sincerely,
Gemma