WEBVTT

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Great. We can do course analysis, we can
identify the premises and conclusions, we

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can put them in standard form. What's
next? Well, the next step is take those

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parts and put them in a certain order, and
fill in the missing gaps. We need to learn

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how to reconstruct arguments. Are you
ready? Well, there are lots of ways to

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reconstruct. When you think about
constructing a house, or a building. In

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order to construct a good building you've
got know, what the goal is, what the

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standards of a good building are. The same
thing goes for reconstructing arguments.

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In order to reconstruct an argument
properly, you need to know what the

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standards are for reconstruction. We're
trying to reconstruct it so as to meet

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those standards. Because the goal is not
to reconstruct the argument in order to

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make it look bad. The point is going to be
reconstruct arguments so as to make them

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look good. Cuz by making your opponents
look bad or silly, that doesn't do anybody

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any good. If you want to learn about their
perspective, and you want to learn from

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their views, then you need to reconstruct
their argument, so as to make it look as

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good as possible. And to do that, you need
to know about the standards for arguments.

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That is the standards that make arguments
good or bad. So what we're going to do

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this week is we're going to look first at
some standards for our arguments, validity

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and soundness in particular, and they
we're going to use those standards to

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develop a method called reconstruction or
deep analysis, I'll explain those terms

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later. And then we are going to apply that
methods to a few concrete examples, in

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order to be able to take a passage and
take those premises and conclusions and

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fill them out and get a full fledged
argument that if we've done it properly

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will be, be as good as it can be, and that
we can learn from. That's the goal. Now,

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because an argument consists of premises
and a conclusion, and the premises are

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supposed to be related in the right way to
the conclusion, there can be two main ways

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an argument can go wron g, two main vices
of argument, you might say. The first is

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there might be something wrong with the
premises. In particular, they might be

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false, or at least one of them might be
false. Second, there might be something

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bad about the relation between the
premises and the conclusion. The premises

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might fail to give a good reason for the
conclusion. Now each of these problems is

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something that we need to avoid and when
we do avoid them, we get the corresponding

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virtues mainly validity and soundness. And
those are the two notions that we want to

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discuss in this lecture and the next.
Let's begin with the relation between the

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premises and the conclusion. What kind of
relation between the premises and the

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conclusion is good for an argument or
makes an argument good? Well, that

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depends. Some arguments are deductive and
others are not. So, let's focus for a

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moment on deductive arguments. In
deductive arguments, the conclusion is

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supposed to follow from the premises, but
what does that mean? I mean, what does it

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mean for a conclusion to follow from the
premises? That's a really hard notion to

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pin down. So what logicians usually do
and, and what we're going to do, is focus

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instead on the notion of validity. And the
idea is that a deductive argument is

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trying to structure itself so that it's
valid. And we'll explain what validity is,

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but for now, I want to emphasize that
we're only talking about deductive

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arguments. There's going to be another
class of arguments called inductive

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arguments that we'll get to later in this
course, where they don't even pretend to

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be valid. They don't even pretend that the
conclusion follows from the premises. But

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just for simplicity, let's focus on
deductive arguments now, and the idea is

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that the deductive argument should be
structured in such a way that it's valid.

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Then the next question is what's validity?
Let's start with a simple example. Suppose

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that you know Mary but you don't know her
children. However you do know that she has

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one child who is pregnant. And you also
know that only daugh ters can become

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pregnant. So you have all that you need to
know in order to draw a further

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conclusion, namely, Mary has at least one
daughter. So here's the argument. Mary has

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a child who is pregnant. Only daughters
can become pregnant, therefore, Mary has

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at least one daughter. Now, if you think
about it, there's just no way, no

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possibility that both of those premises
are true and the conclusion is false. That

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is the feature that we're gonna call
validity. More generally, we can define

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validity in an argument so that an
argument is valid if and only if, it's not

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possible for the premises to be true and
the conclusion false. That is, it's not

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possible for there to be a situation where
both of those hold, that is a situation

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where the premises are true and the
conclusion is also false. Now that might

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strike you as a pretty simple notion. But
actually that little word possible is a

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problem. How do you tell what's possible
or what's not possible? Well, there's no

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mechanical solution to that and we'll
struggle with that a little bit throughout

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this course. But for now, since we're
right at the start, let's think of it this

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way. Is there any way for you to tell a
coherent story? Where the premises are

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true and the conclusion is false. Can you
describe a situation with that combination

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of truth values? That is, the premises
being true and the conclusion false in the

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same situation. If you can tell a coherent
story with that combination then it's

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possible and the argument is not valid.
But if there is no way to tell a coherent

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story where the premises true and the
conclusion is false, then the argument is

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valid. Now let's try that test on our
example. Mary has a child who is pregnant.

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Only daughters can be pregnant. Therefore,
Mary has a daughter. So is there any way

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to tell a coherent story where the two
premises are true? That is, where Mary has

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a child who is pregnant, and only
daughters can be pregnant, but the

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conclusion is false. Mary does not have a
daughter. Well, just try. Suppose Mary has

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only one child and i t's a son. There's
the conclusion that's false. Good. What

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about that? But then, is that son
pregnant? Well, if the son is not pregnant

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then the first premise's false. Mary
doesn't have a child who is pregnant. But

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if the son is pregnant somehow, don't ask
me how, but if the son is pregnant then

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the second premise's not true. It can't be
true that only daughters can be pregnant

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because this child is a son. Okay, what if
Mary has two children? Try that. Try to

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tell the story that way. Mary has a
daughter and a son. Now she's got a child

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who is pregnant, the daughter, and only
daughters can be pregnant, but she has a

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son. Wait a minute, she's got a son and a
daughter. So now the conclusion's true,

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because she does have a daughter even
though she also has a son. Oh, oh, wait.

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How about this one? What if Mary has a
child who is biologically female but sees

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himself as a male? And so she sees that
child as a male, but that child is

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pregnant, cuz after all, they're
biologically female. Now are the premises

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true and the conclusion false? Does that
story make sense? Wait a minute. Either

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her child is a daughter or her child is a
son. Now if it's a daughter and its

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pregnant, no problem. The conclusion's
true. If it's a son, because that child

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sees himself as a male, then you've got a
choice. Well, what about the first

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premise? The first premise is going to be
true. She does have a child, who is

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pregnant, but what about the second
premise, only daughters can be pregnant.

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Wait a minute. If that really is a son, if
we're gonna call that a son, then it's not

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true that only daughters can be pregnant.
So now the second premise is false. So try

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it again. Try it with, you know, sex
changes, and try it with Hermaphrodites

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tell the story any way you want about
Mary's children. And there's no way that

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both premises come out true when the
conclusion is false. That shows that the

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argument is valid. It might be just that
we can't imagine the coherent story, which

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makes it invalid. But the fact that we've
tried hard and looked at all th e

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possibilities we can think of at least
gives us a good reason to think that this

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argument is valid. Now some people like to
think of it in the reverse direction. They

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say, let's imagine that the conclusion is
false, and then, If it has to be the case,

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that at least one of the premises is
false, the argument is valid. Then you can

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define the validity as, is necessarily the
case that if the conclusion is false one

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of the premises is false, or in every
possible situation, if the conclusion's

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false one of the premises is false. We can
apply this new account of validity to the

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same old example. It's got to be the case
that if Mary doesn't have a daughter, then

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she doesn't have a child who is a
pregnant, or else there are at least some

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children who are pregnant who are not
daughters. So notice in this case you're

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reasoning back from the falsehood of the
conclusion to at least one of the premises

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has to be false. whereas in the earlier
definition you were saying it's not

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possible in the situations where the
premises are true for the conclusion to be

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false. You can look at it either way,
either direction. Just pick the one that

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works for you and go with that definition,
because in the end, the two definitions

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are equivalent. It's just a matter of
what's going to help you understand which

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arguments are valid and which ones are
not. In addition to understanding what

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validity is, it's also very important to
understand what validity is not. A lot of

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people get confused by the notion of
validity in this context, because they're

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thinking that to call an argument valid
must be to call it good, right? You call a

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driver's license valid when it's good in
the eyes of the law. But that's not what

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we're talking about here. The notion of
validity is getting used by logicians here

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as a technical notion and it's very, very,
very important to remember that to call an

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argument valid is not to call it good. For
some arguments, like deductive arguments

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the invalid might be necessary for them to
be good. But it's not enough and we'll see

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a lot of examples of that later on. The
second point about what validity is not is

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that validity does not depend on whether
the premises and the conclusion are

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actually true or false. Instead it depends
on what's possible whether there is a

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certain combination, true premises and a
false conclusion, it's even possible. So,

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whether the premise is actually true in
the actual world is not what's at issue.

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And we can see this, by seeing that some
arguments with false premises can still be

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valid. And some arguments with true
conclusions can be invalid. So let's look

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at some examples of that. Indeed there
four possibilities. Cuz remember, the

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conclusion could be true or false, and the
premises could be all true or at least one

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false. So we've got four possibilities.
And all of those are possible except for

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one. The one combination that's not
possible for valid arguments is true

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premises and a false conclusion. But if
you've got true premises and a true

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conclusion, it might be valid, it might
not. If you've got false premises and a

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true conclusion it might be valid, it
might not. If you got false premises and a

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false conclusion, it might be valid, it
might not. So let's look at some examples

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each of those possibilities in order to
better understand the relation between

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premises and conclusion that exist when
the argument is valid. It's hard to give

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examples with true premises or false
conclusion, or any these other

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combinations when the truth is
controversial. So we're going to have a

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really simple example, and we're going to
start just by stipulating what the facts

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are. We're going to assume that all Ford
cars have four tires, but some Ford cards

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do not have four doors. We're also going
to assume that Henry's car is a Ford that

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has four doors. And Jane's car is a
Chrysler that has only two doors, not four

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doors. And we're just going to take those
facts for granted and assume that that's

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the situation we're talking about, and
then we can give examples of all the

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combinations that we discussed before.
Let's begin with tr ue premises and a true

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conclusion. So, here's an example of that
sort. All Fords have four doors. Henry's

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car is a Ford, therefore, Henry's car has
four doors. Is the first premise true?

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Yes, that's what we are assuming, that's
one of our assumptions. Is the second

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premise true? Yes. That's another one of
our assumptions. Is the conclusion true?

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Yes. So they're all true and now is the
argument valid? Is it possible that all

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Fords have four doors? Henry's car is a
Ford and yet it's not true that Henry's

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car has a four doors. I mean, just think
about it. How would that happen? Well, for

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the conclusion to be false, it would have
to not have four doors. Suppose it has two

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doors. Well then, either it's not a Ford
or there's some Ford, namely Henry's Ford,

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that only has two doors and not four
doors. So, there's just no coherent story

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you can tell where the premises of this
argument are true and the conclusion's

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false. Or in reverse, if you start off
with the assumption that the conclusion's

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false. You can tell from that, that at
least one of the premises has to be false

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as well. Nonetheless. There are other
examples, where the premises are true, and

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the conclusion is true, but the argument
is not valid, instead it's invalid. Here's

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an example of that combination. All Ford
cars have four tires. Henry's car, has

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four tires. Therefore, Henry's car is a
Ford. Now, in this new argument, are all

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the premises true? Yes, the first premise
says, all Ford cars have four tires. And

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that's true by our assumptions. Second
premises Henry's car has four tires and

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that's also true by our assumptions and is
the conclusion true? Yes our assumptions

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also tells that Henry's car is a Ford. But
is it possible, is there any way to tell a

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coherent story where those premises are
true and the conclusion is false? Yes,

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absolutely. All that has to happen is that
Jane and Henry switch cars. Then the first

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premises can be true because all four cars
have four tires, and the second premise is

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going to be true, because Henry's car has
four times, of course now it's a Chrysler,

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cuz he got it from Jane, but the
conclusions can be false. Henry's car is

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not a Ford because Ford and Chrysler are
different companies. So, if he switches

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cars with Jane and he has a Chrysler then
he doesn't have a Ford. His car is not a

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Ford. Okay, so now you've got a situation
where the premises are true and conclusion

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false. It's not the actual situation but
its a possible situation. You can tell a

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coherent story with the premises true and
conclusions false and that tells you that

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the argument is invalid. Next, let's
consider an example with false premises

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and a true conclusion. Premise one, all
Fords have four doors. Premise two,

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Henry's car is a Ford. Conclusion, Henry's
car has four doors. Is the first premise

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true? No, it's not true that all Ford's
have four doors. Our assumptions tell us

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that. Second, is Henry's car a Ford?
That's true. So one of the premises is

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false and the other one's true. That means
they're not all true. And the conclusion,

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is that true? Yes, it is true that Henry's
car has four doors. But remember, the fact

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that that's actually the case doesn't tell
us wether or not is valid. So, is it

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valid? That depends on wether it's
possible for the premises to be true and a

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conclusion false. Premises aren't actually
true, but is there a possible story that

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you could tell that would be coherent
where the premises are true and the

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conclusions false? That's the test of
validity. So let's apply it to this case.

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We'll just imagine, that, the conclusion's
false, that Henry's car does not have four

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doors. It's only got two doors. Then,
there are really only two possibilities,

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either it's a ford or it's not a Ford. If
it is a Ford, then the first premise is

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false. It's not true that all Fords have
four doors. But if Henry's car is not a

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Ford, then, the second premise is false,
cuz it says that Henry's car is a Ford.

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So, there's no coherent way in which it
could possibly be true that both of these

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premises are true and the conclusion is
false so this argument's valid and not ice

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that, that shows that an argument can
valid, even though it's got a false

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premise. Now, you might be thinking to
yourself this is crazy how can an argument

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be valid when one of it's premises are
false? An argument's no good when it's

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premises are false. Notice what that does.
That confuses the notion of valid. Like in

00:19:57.268 --> 00:20:02.628
a valid driver's license where to be vaild
is good. With the technical notion of

00:20:02.628 --> 00:20:07.653
validity that we're using here. The
technical notion of validity that we're

00:20:07.653 --> 00:20:12.947
using here has to do with the relation
between the premises and the conclusion.

00:20:12.947 --> 00:20:17.905
And in particular, it has to do with
possibilities, and not with the actual

00:20:17.905 --> 00:20:23.399
falsehood of the premise. So what we have
to ask ourselves is, what would happen if

00:20:23.399 --> 00:20:29.750
it really were true? That all Fords have
four doors is not true in the actual

00:20:29.750 --> 00:20:35.815
world, but we're concerned with
possibility. And if all Fords did have

00:20:35.815 --> 00:20:43.018
four doors, and if Henry's car was a Ford,
then it would have to have four doors. So,

00:20:43.018 --> 00:20:49.382
that possibility of the premise being
true, even though it's not, is what's

00:20:49.382 --> 00:20:55.391
crucial for determining validity. Because
it's not possible for the premises to be

00:20:55.391 --> 00:21:00.634
true, and the conclusion false. That makes
it valid in our technical sense. Even if

00:21:00.634 --> 00:21:06.006
it's not valid, in the common sense notion
of validity as goodness, we're not saying

00:21:06.006 --> 00:21:11.054
that the argument's a good argument. We're
saying that it meets this technical

00:21:11.054 --> 00:21:15.973
definition of validity. That logicians
use. Now the only combination of truth

00:21:15.973 --> 00:21:21.216
values in premise and conclusion, that you
cannot get with a valid argument is to

00:21:21.216 --> 00:21:27.020
have true premises, an a false conclusion.
So here's an example of that. Premise one,

00:21:27.020 --> 00:21:36.260
some Ford cars do not have four doors.
Premise two, Henry's car is a Ford.

00:21:36.680 --> 00:21:44.334
Conclusion, Henry's car does not have four
doors. The premises by our assumptions are

00:21:44.334 --> 00:21:49.810
both true and the conclusion is false and
it's not valid because it's easy to see

00:21:49.810 --> 00:21:55.422
how it might be possible for the premises
to be true and the conclusion false. It's

00:21:55.422 --> 00:22:00.493
simple. Even if some Ford's don't have
four doors, Henry's car is one of the

00:22:00.493 --> 00:22:05.902
Ford's that does have four doors, and then
both the premises can be true and the

00:22:05.902 --> 00:22:10.971
conclusions false. So that's how you can
get an invalid argument with true premises

00:22:10.971 --> 00:22:15.592
and a false conclusion. But you don't
really even need that. Look. Every

00:22:15.592 --> 00:22:19.917
argument that has, true premises and a
false conclusion, has to be invalid.

00:22:19.917 --> 00:22:24.835
Because if it does in fact actually have
true premises and a false conclusion, then

00:22:24.835 --> 00:22:29.160
it's possible, for it to have true
premises and a false conclusion. So you

00:22:29.160 --> 00:22:34.105
can know right off the bat that every
argument with true premises and a false

00:22:34.105 --> 00:22:39.418
conclusion is invalid. What you can't know
is for the other combinations. Then you

00:22:39.418 --> 00:22:44.665
have to think of what is possible instead
of simply what is actual. So far we've

00:22:44.665 --> 00:22:50.043
only looked at arguments with all and some
and we've looked at Henry and Ford and

00:22:50.043 --> 00:22:54.705
Chrysler and so on. But the same points
are going to apply to lots of different

00:22:54.705 --> 00:23:01.505
arguments with very different forms. So
lets look at one example of that. Premise

00:23:01.505 --> 00:23:09.266
one, David, is either a swimmer or a
golfer. Premise two, David, is a swimmer,

00:23:09.266 --> 00:23:16.721
therefore, conclusion, David is not a
golfer. Okay, is it possible for the

00:23:16.721 --> 00:23:23.399
premises to be true and the conclusion
false? How could you tell a coherent story

00:23:23.399 --> 00:23:29.215
where both premises are true and the
conclusion is false? Just think about it.

00:23:29.215 --> 00:23:35.171
How could that happen? Oh I've got it! He
could be both a swimmer and a golfer, like

00:23:35.171 --> 00:23:40.721
me. I play golf, and I also swim, and lots
of people do. Now of course, if you have

00:23:40.721 --> 00:23:46.553
or, and you say something like he's either
male or female, maybe you can't have both.

00:23:46.553 --> 00:23:52.384
But with swimming and golfing you can just
be both a swimmer and also a golfer. And

00:23:52.384 --> 00:23:57.724
then the premises can be true when the
conclusion is false, which shows that this

00:23:57.724 --> 00:24:03.994
argument is not valid. Now let's try this
other example which is a lot like the last

00:24:03.994 --> 00:24:09.557
one, but it's different in an important
way. Premise one, David is either a

00:24:09.557 --> 00:24:15.805
swimmer or a golfer. Premise two, David is
not a swimmer, therefore conclusion, David

00:24:15.805 --> 00:24:21.920
is a golfer. Is there any way? Is it
possible? Is there anyway to tell a

00:24:21.920 --> 00:24:29.500
coherent story where, the premises are
true and the conclusion is false? We know.

00:24:29.940 --> 00:24:34.427
Well just think about it, the four
possibilities. Suppose that David is both

00:24:34.427 --> 00:24:39.154
a swimmer and also a golfer. Well then the
conclusion's true, right? So you can't

00:24:39.154 --> 00:24:43.163
have two premises and a false conclusion
because then in that case then the

00:24:43.403 --> 00:24:50.176
conclusion is true. Now, suppose that
David is a golfer, but he's not a swimmer.

00:24:50.176 --> 00:24:55.660
Well again, the conclusion's true. So
that's not a case where the premise's is

00:24:55.660 --> 00:25:00.141
true and the conclusion's false. but
suppose he's not a golfer but he is a

00:25:00.141 --> 00:25:04.738
swimmer Well wait a minute. In that case
the second premise is wrong, because it

00:25:04.738 --> 00:25:08.870
says, he's not a swimmer and we're, in
this story, imagining that he is a

00:25:08.870 --> 00:25:13.235
swimmer. Now suppose that he's neither a
swimmer nor a golfer. Well then the

00:25:13.235 --> 00:25:17.541
conclusion is false, and that second
premise is true. But wait a minute, now

00:25:17.541 --> 00:25:22.255
the first premise is false, because the
first premise says, he either a swimmer or

00:25:22.255 --> 00:25:27.162
a golfer. In this story it's saying that
he's neither. So, those are the four

00:25:27.162 --> 00:25:32.149
possibilities and there's none of them
where the premises are true and the

00:25:32.149 --> 00:25:36.870
conclusions false. So it's not possible
for the premises to be true and

00:25:36.870 --> 00:25:42.780
conclusions to be false in this case, so
this argument is valid. And did you notice

00:25:42.780 --> 00:25:48.087
something? I didn't make assumptions like
in Henry, and the Ford, and the Chrysler,

00:25:48.087 --> 00:25:53.593
cuz we don't need to know whether David
really is a swimmer or a golfer. We don't

00:25:53.593 --> 00:25:59.098
need to know the actual facts of the world
at all. We could tell that this argument

00:25:59.098 --> 00:26:04.375
is valid without knowing what kinds of
sports David does. And that shows you that

00:26:04.375 --> 00:26:09.174
whether an argument is valid or not
depends on what's possible, not on what's

00:26:09.174 --> 00:26:13.724
actual. Cuz you can know that the
argument's valid, even if you don't know

00:26:13.724 --> 00:26:18.897
whether in the actual world he's a swimmer
or golfer or neither or both or one but

00:26:18.897 --> 00:26:23.869
not the other. We haven't been through all
of the possibilities, but we have seen

00:26:23.869 --> 00:26:28.838
that you can have invalid arguments with
true premises and true conclusions, and

00:26:28.838 --> 00:26:34.048
you can have valid arguments with false
premises and true conclusions, and we've

00:26:34.048 --> 00:26:37.851
got a little table that shows us the other
poss ibilities.

00:26:37.857 --> 00:26:43.069
Instead of going through all of those
other possibilities myself, I think it'd

00:26:43.069 --> 00:26:48.282
be better, if. You did a few exercises,
and that'll, make sure that you understand

00:26:48.282 --> 00:26:53.828
this notion of validity before we go on
and try to show how validity is related to