I’m reading “The Universe and the Teacup” and am reconsidering thoughts I previously had in mathematics. One example is the popular idea that there’s something contradictory about the following statement. This sentence is false. When I was young, I simply accepted this logic of this, without thinking more deeply about it. Now I see the absurdity of thinking that there’s something contradictory in this kind of simple logic. Parsing English to understand logic is foolish. What does “this sentence” mean? It doesn’t refer to the sentence. The subject of the sentence is an element of the sentence, not the entire sentence. To refer to an entire sentence, one must use another sentence. That is the proper meta level of reference.
The next sentence is false. The previous sentence is true.
There is no iterative process to this. They are static statements. You cannot say, well the second sentence says that the first one should be, “the next sentence is true”, and then follow on with more modifications of the sentences. The two statements stand as they are. They don’t modify each other. “The next sentence is false.” Fine. The sky is blue. It’s just a statement.
I think that this kind of writing, to popularize technical fields, risks using simple concepts that are fundamentally wrong and thereby do the field a disservice.