Justin Khoo 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 2 of the series on conditionals, Justin discusses some of the challenges facing the material conditional theory.
Speaker: Dr. Justin Khoo, Assistant Professor, M.I.T.
Speaker: Dr. Justin Khoo, Assistant Professor, M.I.T.
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- Would "I think, therefor I am" be considered a conditional statement? If so, when I use it in a truth table it seems not to make sense on the third line. I think(false) ---> Therefor I am(true)= True? Is it true because in the statement saying "I am" is true, makes it true?(1 vote)
- Any argument may be rendered into a conditional - read a book on logic to find out.
The argument ''I think. Therefore I am'' can be rephrased into a conditional as IF I think, THEN I am.
Look at the meaning of this conditional. It asserts: given ''I think'' is true, ''I am'' MUST BE true.
Note the conditional statement does NOT assert anything about the situation ''I think'' is false. Therefore, any situation in which 'I think' is false lies outside the claim of the conditional. Thus all situations in which ''I think'' is false CANNOT falsify the conditional. Well, if something CANNOT be false, it MUST BE true. Thus, the situation you describe: I think (false), I am (true) makes the conditional true. This is how I understand it. Does it work for you?(5 votes)
- There is a problem with the coding in the captions. You probably put the <br> element in the part that shows the captions.(1 vote)
- Im confused about the material conditional theory; with the two parts to it. Im confused about using "and" and using "or"(1 vote)
- Concerning the section beginning at4:40:
I've been thinking about the suggestion of a paradox in the Material Conditional Theory. Essentially, what Justin's argument boils down to is "If A, then not A". I believe he errs in assuming that this statement is false; consider that we assume not A. Then, logically and from our truth table, if we assume our antecedent to be false, then regardless of the truth value of our consequent, we must conclude that our statement as a whole is true. So, essentially, I see an error in Justin's reasoning that the initial "f, then" statement is false. If we assume "God does not exist", then our antecedent is false, which makes our "if, then" statement true (and therefore contradicts the suggestion that the statement is false. I think a better statement would have been "EITHER our statement is FALSE (and therefore our antecedent is TRUE, as shown in this video), OR our antecedent is FALSE". And so it is shown that our antecedent may be either true or false, which does not create a paradox nor argue either way for the existence of a god.
Does anyone else have thoughts on this matter or can anyone clarify, refute, or argue for the presented paradox? I'm not sure I've worked through the reasoning properly (I'm new to using logic in the philosophical sense!).(1 vote)
- I think you're mistaken at the last part of your argument. P = god exists; -P = god doesn't exist. You're correct that if P is set to F in the truth table, then "P -> -P" is set to T.
However, we also know from reasoning that P -> -P can not be set to T. P -> -P intuitively is F.
Therefore, we have to accept a situation where P -> -P is set to F, and the only situation where that happens according to Material Conditional Theory is the one where P is T and -P is F. And if P is T, then God must exist.(1 vote)
(intro music) Hello, my name is Justin Khoo, and I'm an assistant professor[br]of philosophy at MIT. This is the second part of[br]our series on conditionals. Recall our question from last time: "What do conditional[br]sentences, like (1), mean?" "If the safety net needs[br]repair, I will fix it." In the first video, we considered the answer to this question given by the material conditional theory. According to that theory, a conditional "if A, then B" is true just if either A is false or B is true. Equivalently, it is true[br]just if it's not the case that both A is true and B is false. Thus, according to this theory, when Romney utters (1), he tells us that either the[br]safety net won't need repair, or that he will fix it. Equivalently, he tells[br]us that it's not the case that the safety net will need repair and he won't fix it. We can consult our truth table to help us better understand[br]what's meant here. The first two lines of the truth table tell us what truth value[br]the conditional has when the safety net needs repair. In particular, line one[br]tells us what truth value the conditional has when both[br]the safety net needs repair and Romney fixes it. Notice that it says that the conditional is true in this case. Line two tells us what truth[br]value the conditional has when the safety net needs repair and Romney doesn't fix it. It says that the conditional[br]is false in this case. Reflect on your intuitions. Romney has uttered the conditional (1). Is what he says true, in a situation in which the safety net needs repair and he fixes it? I say, "Yes." Is what he says false, in the situation in which the safety net needs repair and he doesn't fix it? I also say, "Yes." So far, the material conditional theory makes the right predictions. Let's turn now, to the[br]third and fourth lines of the truth table. Together, they represent the condition that the safety net doesn't need repair. The table says that[br]the conditional is true in that case, no matter what else happens. Does this seem right? Is what Romney says true, if the safety net doesn't need repair, regardless of what else happens? If you're like me, you may[br]be unsure what to think. That's okay, maybe we need to turn to another example. Since the material conditional theory is a theory about the meaning[br]of every conditional sentence, we can change the sentence slightly to see if we have clearer intuitions. Here's a different, made-up conditional. (2): If the earth is flat, I will win the lottery tomorrow. Again, the material conditional theory doesn't care about what the antecedent and consequent of (2) mean, just what their truth values are. The truth table tells us everything there is to know about the meaning of (2), according to the theory. Again, let's focus on rows three and four of the truth table. They represent the condition[br]that the earth is not flat. Let's just assume, for[br]the sake of conversation, that if the earth is not[br]flat, then it's round. So, in the condition[br]that the earth is round, the theory says that (2) is true. That is, since the earth in fact is round, the conditional "if the earth is flat, I will win the lottery tomorrow" is true. Does this seem right to you? If you're like me, you'll[br]be inclined to say, "No." Why is this? Well here's a simple answer. It seems that the lack of the right kind of connection between the[br]antecedent and consequent of (2) is what makes it false. There's just no connection between the earth being flat and my winning the lottery tomorrow. But notice that the[br]material conditional theory just doesn't care at all[br]about this missing connection. Rather, it only cares[br]about the truth values of the conditional's[br]antecedent and consequent. According to the material[br]conditional theory, if the antecedent's false,[br]the conditional's true. Here's another way to see the same problem from a different angle. I'm about to give you a simple proof of the existence of God. It has one premise. The premise is this: it's false that if God exists, then God doesn't exist. Conclusion: God exists. This proof is valid, given the material conditional theory. Here's why. According to the theory, a conditional "if A, then B" is false only on the condition that its antecedent, "A," is true and its consequent, "B," is false. You can verify this by[br]seeing that it's false only on the second line[br]of the truth table. Thus, according to this theory, the conditional embedded in (3), "if God exists, then God doesn't exist," is false only if God exists. That is because only in that case is its antecedent true[br]and its consequent false. So on our material conditional theory, the premise entails that God exists. Hence, according to the theory, this proof of God's existence is valid. What's paradoxical here is that everyone, it seems, should accept the premise (3), whatever their theological leanings. But no one should, merely on that basis, accept its conclusion that God exists. Of course, one way out of this paradox is just to reject the[br]material conditional theory. So, I've just put forward, I think, one reason for rejecting the[br]material conditional theory, namely, that in doing so,[br]we avoid this paradox. What's underlying both of these issues is the following problem. The material conditional theory provides too few opportunities for conditionals to be false. Alternatively, it makes it too easy for conditionals to be true. Now, defenders of the[br]material conditional theory are definitely aware of these problems, and they have responses to them. Their main line of defense is to hold that in uttering a conditional, one communicates more information than just what it means. And this extra information may underlie the special connection between the antecedent and consequent that seems missing from their theory. This is usually understood[br]as an implicature, a component of what a speaker communicates by uttering a sentence that is not part of what it means. If you're interested in that way of defending the material[br]conditional theory, I recommend that you check out the Wi-Phi lectures on implicatures and the following papers by Paul Grice and Frank Jackson. However, in the next video, we won't pursue that line of defense. Instead, we'll look at a different theory of what conditionals mean, according to which they[br]mean something stronger than what the material[br]conditional theory says they do. In other words, the next[br]theory we'll look at provides more opportunities[br]for conditional sentences to be false. See you then! Subtitles by the Amara.org community