"What relation must one fact (such as a sentence) have to another in order to be capable of being a symbol for that other?" (Bertrand Russell)
What is it about a sentence that allows it to represent a fact? Let's not take the answer for granted. And let's not assume the question is unanswerable. Let's begin with a sentence of a kind familiar to scholars:
Bertrand Russell said that "the essential business of language is to assert and deny facts".
Notice that this is not a sentence about either language or facts but about Bertrand Russell. It represents something he "said", i.e., wrote. It says that somewhere in Russell's writing the quoted sentence may be found. What is interesting is that it can say this without it being true. This is the most important clue to its capacity to represent. Many years ago, Karl Popper provided a much need counterpoint to the "verificationism" of the logical positivists by suggesting that the meaning of a proposition lies as much in what makes it false as what makes it true.
Consider the analogy of a map. We all know that the purpose of a map is to represent a territory. A good map will lead you to where you want to go. A bad map will mislead you. But it can only do this if you read the map as a representation of where you are and where you want to go. If all maps were made merely for the purpose of hanging decoratively on walls, i.e., if no one ever tried to get anywhere with their guidance, they would no longer represent their territories. But the map represents the territory even if I don't travel in order to verify it. The map tells me that Stockholm is to the north of Copenhagen. I don't have to go there in order to understand what this means.
But I do have to know how to read the map. Think about what that sentence about Bertrand Russell represents, what it means. First of all, the proper name has to refer to the famous philosopher, friend and mentor to Ludwig Wittgenstein, author of Principia Mathematica. Also, as I said, it must be taken not quite literally; Russell wrote it rather than said it. But I haven't yet said where; it is made true or false by the whole of Russell's work. (The whole of his life if we didn't narrow "said" to his professional writings, but let it refer to every utterance, spoken or written, by Russell.) Imagine a map that shows Stockholm to be to the north of Copenhagen but not how far. In fact, I can be much more precise:
In his introduction to Wittgenstein's Tractatus, Bertrand Russell said that "the essential business of language is to assert and deny facts".
And more precise still:
In his introduction to Wittgenstein's Tractatus, Bertrand Russell said that "the essential business of language is to assert and deny facts" (p. x).
Indeed, in order for that page reference to make sense I have to provide the 1961 Routledge edition as my source. Page x is actually the second page of the introduction. This is like putting lines of longitude and latitude on the map, and specifying a scale. To a properly trained reader, there is now a single page on which we may find or not find the quotation. And here's a twist I hadn't planned when writing this post: if you do go to check my quotation against its source you will find that Russell says "assert or deny" not "assert and deny" (as I discovered when I went to source to get the page number). That is, there is an inaccuracy in my representation of Russell's words, and those words, remember, are what my sentence is about. Someone who understands my words will get to the right place, and will confirm that it's the place I meant, but will find that it's not quite as I said it would be.
We'll continue this on Wednesday.