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Chapter Two, Tutorial Four SL
Symbolization We have already seen that symbolization of English statements into SL can be less than straightforward. It is time to look at a few more of the complications. Conjunction In Tutorial 2.1, we saw that there were a number of different ways in English to express a conjunction. Just to remind yourself, look at the following list, and pick out the one connective which does NOT express conjunction: (Click on the connective which canNOT be symbolized by the ampersand, '&'.) Good. The words 'and' and 'both' are often used to express conjunction. When you see them, you should expect to use the ampersand, '&', to symbolize. Just as reminder, our first example, was: 1. Agnes is to attend law school and, as well, her husband Bob will attend law school. which we symbolized with: A&B Now, we didn't have to pick 'A' for "Agnes is to attend law school". We could have picked any capital letter. As long as you (or I) decide in advance which "atomic" sentences of SL are used to represent which simple sentences of English, there will be no confusion. But, of course, it is often easiest to be mnemonically correct and choose a capital letter corresponding to the subject or a verb of the English sentence to be represented. Think about a different example. Suppose we need to symbolize 2. Agnes will attend law school but her husband Bob will not. Here the connective is 'but', the first component will be symbolized by 'A' and the second by '~B'. So a first approximation is: A but ~B. We just need to express the 'but' with a connective. Which one? None seem to fit at first. But think about truth conditions. 2 is true if Agnes does what? and Bob does what? You should have answered: Agnes attends law school AND Bob doesn't. Make sure you see why! So, 2 needs to be symbolized as follows. A&~B and "but" is just another word for "and". Does this seem right? It may not at first. But as far as the truth conditions go, "and" and "but" are synonymous. Thus, both can be symbolized with the '&'. Still, there is a difference. "But", unlike "and", indicates a contrast. We say that one thing is true, but (in contrast) another is not. Now, from the following list, click on all other words that are much like "but" and can be symbolized by the '&'.
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