Placeholder Image

Subtitles section Play video

  • (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

(intro music)

Subtitles and vocabulary

Click the word to look it up Click the word to find further inforamtion about it