David Konietzko: Apart from its perhaps being the case that outlawing self-referentiality is merely ad hoc, and thus unsatisfactory, it also has the effect, as you correctly note, of outlawing perfectly respectable sentences such as “This sentence is in the present tense”.
JohnD: You write “The thought of ALL THOSE DIFFERENT LOGICS is quite disturbing. I thought since logic is the science of necessary inference (proper thinking) that we could rely on it to yield certain truths. But with so many logics to choose from, where does that leave us???”
I can appreciate your concern. When you consider all the possibilities that I mentioned in my previous post, it can induce a kind of intellectual vertigo. Perhaps an analogy will help. The basic theory of modern physics seems to be in trouble. Just how many basic particles do we have? Is string theory the answer to our questions? However, whatever may be the case with theoretical physics, we have no difficult getting on with our daily lives, weighing things, measuring them, comparing them, and so on. The inferential core of logic is like our everyday practices of weighing and measuring; the fact that theoreticians may be at odds and special extreme cases may cause us headaches, doesn’t in any way affect, say, the invalidity of the fallacy of the undistributed middle or the validity of the conversion of E-type propositions. This analogy may (or may not!) help: all analogies limp. The disquiet expressed in your post was one reason why I was suggesting that while these topics which we are discussing are interesting and exciting, it can be confusing and distracting to focus on them at the same time as one is trying to come to grips with a basic formal logic system.
David Konietzko: You write:”A sentence has a certain meaning precisely because people interpret it to have that meaning. Therefore, if it is in principle impossible to understand the meaning of a sentence, then it simply doesn’t have a meaning.”
The syntactically-in-order sentence “The kronxite instrumentality befummels reflexiveness cromulently” doesn’t mean anything because some of its key words don’t mean anything in English. Failure to understand it is not a fault in anyone’s understanding; no one can possibly understand it. This is to agree with the second sentence in your post.
The first sentence in your post is possibly ambiguous depending on whether ‘people’ means, assuming we’re using English, some particular special group of people who are competent in English or competent English speakers in general. A sentence could be well-formed in English and understandable to all competent English speakers; or it could be well-formed and understandable only to a proper subset of competent English speakers. In all cases, it would have meaning.