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Language: Conditionals, Part 1

Justin invites us to think about conditional sentences ("if P then Q"). Perhaps surprisingly, the question of what these sentences mean has vexed philosophers for thousands of years. In part one, Justin motivates the question and introduces one of the oldest answers to it, the material conditional theory. 

Speaker: Dr. Justin Khoo, Assistant Professor, MIT.
Created by Gaurav Vazirani.

Video transcript

(intro music) My name is Justin Khoo, and I am an assistant professor[br]of philosophy at MIT. Today we are going to[br]look at conditionals, which are a class of sentences that have puzzled philosophers[br]for thousands of years. Here's an example of a[br]conditional sentence from a speech by former presidential[br]candidate, Mitt Romney: "If the safety net needs[br]repair, I will fix it." Conditional sentences, like[br](1), consist of two parts: an antecedent ("the[br]safety net needs repair") and a consequent ("I will fix it"). Our question today is "What do conditional[br]sentences, like (1), mean?" In other words, by uttering this sentence, what has Mitt Romney told us? Here's a way to think about[br]questions of meaning like this. When I say, "The cat is on the mat," I tell you that the cat is on the mat, rather than not on the mat. This is because the meaning of (2) is that the cat is on the mat. Okay, that's pretty easy. What about our conditional sentence (1)? What has Mitt Romney[br]told us by uttering it? One way of figuring out[br]what Romney has told us is to get clear on what[br]he has not told us. He hasn't told us that the[br]safety net needs repair, and he also hasn't told us that[br]he will fix the safety net. Rather, what he said is that[br]there is some connection between the safety net needing[br]repair and his fixing it. But what connection? Here's a simple answer. By saying the sentence (1), Romney has told us that it is not the case that the safety net needs[br]repair and he won't fix it. Equivalently, he said that either the safety net doesn't need repair, or that he will fix it. Let's call this theory the[br]"material conditional theory." Philosophers at least as far back as the Hellenistic philosopher Philo of Megara have been[br]attracted to this theory about what conditionals mean. In order to state the[br]material conditional theory more precisely, we will[br]make use of a device from logic called a "truth table." A truth table is a way of representing how the truth of a complex sentence, in this case, the conditional (1), depends on the truth values of its parts, in this case, the antecedent[br]and consequent of (1). Let's start with a simple[br]example of a conjunction. Take this sentence: "The cat is on the mat,[br]and the cat is fat." Naturally, someone who says[br]this tells you two things: that the cat is on the mat,[br]and that the cat is fat. Thus, the sentence (3) is true if both the cat is on the[br]mat and the cat is fat, and false if either the[br]cat isn't on the mat or the cat isn't fat. We draw this dependence of the truth value of the whole sentence on its parts in our truth table as follows, noting "T" for true when[br]the sentence is true, and "F" for false when[br]the sentence is false. Notice that, since we want to represent how the truth value of (3) depends on the truth values of its parts, the first two columns contain[br]every possible combination of assigning either "T" or[br]"F" to the parts of (3). Furthermore, notice (3) only has a "T" in the row where both[br]of its parts have "T"s. This captures the fact[br]that conjunctions are true only if both of their conjuncts are true, and false otherwise. It also captures the fact that (3) tells us both that the cat is on the mat and that the cat is fat, since that is the only condition[br]under which it is true. Okay, so now what about our[br]conditional sentence (1)? According to the material[br]conditional theory, one tells us that it is not the case that the safety net needs[br]repair and Romney won't fix it. So, in our truth table, we assign "F" to the conditional only on row two, where it is true that the[br]safety net needs repair and false that Romney will fix it. We assign "T" to it on all other rows. This assignment of[br]truth values, therefore, entirely captures the meaning[br]of the conditional (1) according to the material[br]conditional theory. Now, although the material[br]conditional theory has been endorsed by many philosophers, it faces several difficult challenges. You might have noticed that,[br]according to the theory, the sentence (1) is true in all rows besides the second. Does this seem right to you? In the next video, we will[br]explore some challenges facing the material conditional theory, and see how some other theories about what conditionals[br]mean may fare better. Subtitles by the Amara.org community