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Use and Mention of Words
For myself, as I said everyone knows something for sure or has an interest and experience in life; my interest is in mathematics and logic. There is a verse in the Qur'an which says: "This a scripture whose verses are perfected and then expounded."(11:1) Which tells me that there are no wasted words in the Qur'an; that each verse is perfected and then it is explained. It could not be in a better form. One could not use fewer words to say the same thing or if one uses more words one would only be adding superfluous information. This directed my attention to a particular mathematical subject, a logical subject, and I examined the Qur'an to see if I could find something of what I knew to be the case. A revolution in logic has occurred in the last one hundred years, primarily over the difference between use and mention of words. A structure of logic seemed to be in danger of collapsing about a hundred years ago because it came to the attention of the people who studied these matters that the structure was not quite sound. The issue involved 'self-reference' and the use and the mention of words which I will explain briefly. Aristotle's law of the 'excluded middle' was the statement that every statement is either true false. About a hundred years ago, somebody pointed out that the law of the excluded middle is a statement and is therefore not a law after all. It could just as well be false as well as true. This was a tangled knot for the logicians to untie until they came to understand the difference between the use and the mention of a word. When we use a word, we consider its meaning. When we mention a word we are discussing the word itself. If I said Toronto is a large city, I mean Toronto, that place, is a large cit. If I say Toronto has seven letters, I am talking about the word 'Toronto'. In the first case I used the word and in the second I mentioned the word. You see distinction. |