| Logic is mostly not about the semantics of natural languages, because even very simple sentences depend on a large amount of implicit information. Consider the case of computer vision, and how no one gives a formal definition of objects that should be recognized. Instead, they throw lots of data at a neural network and hope it learns the right thing. If you really want to apply formal reasoning to philosophical issues, you will need an understanding not only of elementary propositional logic, but also of higher order quantification, formal language semantics and probably modal logics and probability theory. If that doesn't discourage you, let me try to help you over the bump that is material implication. Consider the statement "If it's raining, the sky is cloudy." (And ignore any counterexamples that come to mind.) Everyone seems to get stuck on the case where it's not raining, and the statement is true regardless of the presence of clouds. Now treat the statement as a general rule instead, and make it's time-dependence explicit: "If it's raining on a certain day, the sky is cloudy on that day." On Monday, it rains and the sky is cloudy. You look at the rule and see that it agrees with reality. The opposite rule "If it's raining on a given day, the sky is not cloudy on that day." is wrong. (Hopefully that's obvious.) On Tuesday, it doesn't rain and the sky is still cloudy. You look at the rule and realize that it doesn't have anything to say about your situation. That means it can't be wrong, so the rule must be true in this instance. The opposite rule is also right in this instance, because it doesn't say anything either (but it has been wrong before). On Wednesday, it doesn't rain and the sky is not cloudy. Both rules are also right about this day. Now, when we state a rule, we usually mean that it always holds. (This is called universal quantification and you will learn about it when you continue studying.) Since the first rule has been correct in every instance so far, it is simply called true. The second rule has been wrong once, so it is disqualified forever, since a rule that's sometimes right and sometimes wrong doesn't give you any certainty. And what about rules like "If [something impossible], then [something ridiculous]."? Since their conditions are impossible, they never tell you anything. They are the same as saying "". That's useless, but not wrong. EDIT: If something I wrote is incorrect, or you think it's not helpful, or not expressed clearly, please tell me! I really want to get better at writing explanations. |