(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!
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