So two days ago, I discussed a bit about formal logic. Today, as I continued with Teller's Logic Primer, I came across an interesting lesson that I think will help clarify some things from yesterday. As discussed previously, I'm currently learning about sentence logic, which allows you to take different phrases, transcript them into a formal notation, and then find things that are true or false about those premises. Logic allows you to see things cleanly and pricely. Yet, as I learned today, that precison comes at a cost. As Teller explains, we lose a bit of expressiveness with formal logic notation. The "and" used in formal logic doesn't translate exactly to the "and" we use in everyday speech. The same goes for "or". For example, a sentence like "I prepared a sandwich and ate it", transcribing it would lose some meaning. Sure both parts of the sentence could be true and can have a true or false value, but I'm also saying that one happened before the other. I couldn't have eaten a sandwich before preparing it. That aspect is lost when if I wrote it using formal notation. In English, "and" doesn't just have a "truth functional" purpose, that is, it's a function that takes a true or false value. It can be used in other ways as well that can't be translated as cleanly. I think this was an interesting lesson in terms of precision and the precise nature that logic requires. Anyhow, I hope you enjoyed that. Until next time!
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