These are not words!

Was discussing with a friend an old philosophy question of his: "Can you be sure that you are looking at a sheet of paper". We all recognise that the moment he starts to answer that question he has belied any attempt to throw doubt on it being a sheet of paper, and it being written upon in English and this being a philosophy exam &c. The answer, if it believes it is an answer, must recognise the normative assumption of question and answer papers &c.

Another take emerged. What if the question is answered Magritte style. "You can be certain that this is not a sheet of paper." This is in fact true because a sheet of paper is not in the English language, only "a sheet of paper" is in the English language. So when you are reading you are on a different level from "realit

y". Words become what they mean when you read, they are not the black marks on the page. Using Google translate I can create a sentence in Chinese "這些都是不言". To me these are just marks on a page. To Chinese readers they are just marks on a page, but they can also undergo the Necker Cube shift to those minds skilled in Chinese reading and become meanings in the mind.

Now show me a "word"? Let me take the words "a tree". What does this mean? It is not a trick question we all know who speak English. It means any, not being specific, tree which is usually a tall plant with woody stem and in summer has lots of leaves. So a tree is not a word: it is a tree! A word is the marks on the page, referred to as "a tree" with quotation marks. Ths btw is how do you refer to the quotation mark itself... with the name "quotation mark".

So if words are the marks on the page then exactly as with the sheet of paper, the sentence "these are not words" is actually true when it is read and has meaning. It is only false when it is just marks on a page, but then it has no semantics and so can't be true or false. They are not words these are in fact meanings. You are reading words is true. But "you are reading words" has no semantics, as we officially aren't bothered with the meaning of the words in quotes. In reality a reader will try the semantics of the quote to get to know what is said. But ")D£Z" is a valid part of an English sentence because quotes don't have to make sense; they simply draw attention to the marks on the page.

If "These are not words" is a true sentence when read for meaning then how can "this has four words" be true when read for meaning? If words make up a sentence then "this is a sentence" is also false when read for meaning.

So how can a sentence refer to itself? We allow the marks on the page to be a symbol or name for the meanings. My name "Alva" doesn't mean anything when used as a name with a capital letter. But in Spanish, where the name is from, "alba" means dawn. Obviously my name is not to say I am the light that comes before the sun rises (the exact nuance I was told by a Spanish speaker) it is just a blank symbol for me. So we can ask, for instance, what the meaning of "The swan swam down the Swale." is using the marks on the page to refer to an, as yet not got, meaning. And this sentence is perfectly meaningful: "The sentence you are reading" because, it correctly identifies that you are reading a sentence. But a sentence can't directly refer to itself because the marks on the page are different from the meaning. If the marks on the page were the meaning then we wouldn't need to read and sentences would just be true by themselves (this is the basis of SRH)! In which case what about the old problem "This sentence is false". Thankfully this is just marks on a page. It is only a problem when some unfortunate soul reads it and tries to make sense of it. Actually it could be revised for better accuracy in light of this blog to, "The meaning of the sentence you are reading is false." since the "sentence" is just syntactic marks on a page and it is the meaning that we are referring to and saying is false. But what is the negation of that sentence?

Let a function x:M(x) = {1,2,3} separate sentences into three sets those for which M(x) =1,2 or 3. We have a semantic function then on our set of possible sentences X whose members are named small x.

Let another function y:T(y) ->{true, false} separate sentences into true or false.

The standard liar paradox above applies the truth function directly to the sentences in X so that we can say that "this sentence is false" - as though the sentence was actually materially false independent of any external judge and jury to evaluate the sentence - that is the problem with the traditional interpretation and where the SRH has its challenge. But a bit of thought in this blog has shown that this is actually over simplified. What is actually happening is that the meaning of the sentence named by the marks on the page is false - rather than those marks on the page. So it is actually the M(x) function that is false. So the sentence is saying that M(x) is separating sentences into the wrong sets. Now we always take truth T(x) to be part of the meaning function M(x) so when we understand the meaning of the sentence "It is false to say 'dogs can fly'" we also get the truth of the quote. But what is being rejected in "The meaning of the sentence you are reading is false." is not the sentence "itself" (which SRH says is impossible) but the meaning function M(x). So the paradox doesn't create a loop any more, because once the meaning has been rejected we just take the sentence to be marks on a page and read on which is what we actually do with the liar paradox (who ever gets stuck for very long). "There is no meaning to this sentence" looks like our new version of the paradox but actually this sentence is just false, because there is meaning to the sentence which is how we start to get into paradox but then we just reject the sentence as making a false claim. Simple.

It seems this deeper look at words and meaning has dusted out the old paradoxes and while touching on the SRH it doesn't use it. It turns out that meaning can refer to itself but without the creation of paradoxes. I need to let this sink in and think about what is happening here in more depth.