. >> You'll remember that in the second unit
of our course, we considered the rules that we can used to evaluate deductive
arguments for validity. Now, Walter and I noticed that very few of
the submitted arguments were deductive in form.
And there's a good reason for that. Most of the arguments that we give in
everyday life are actually not deductive arguments.
But, there is a domain of reasoning where deductive arguments are common and useful.
And that is in mathematics and computer science.
In particular, in disciplines that involve a lot of precision and reasoning, we
frequently find deductive argumnets. So we're going to look at an example of
those in a moment. But first, I want to consider a submitted
deductive argument that was my personal favorite submission of all.
And that was, Rom's lecture series needs a mental health warning, submitted by
Marjorie Forbes. Now Marjorie's argument is a deductive
argument that has three smaller deductive arguments in it.
Let's look at those. Okay so, premise one.
There are over 30 million sheep in New Zealand, another 70 plus million in
Australia, a few more in the UK, and so on.
In short, there are many, many millions of sheep in the world.
Now from premise one, Marjorie draws the conclusion that there are no fields large
enough to hold all the sheep. Now, I should mention, if that conclusion
is meant to be drawn deductively from premise one, we're going to need to add
some more premises in there. In particular, we're going to need to add
premises about the largest fields that there are.
And we're going to need to add premises about the smallest condensation of sheep
that we can arrange within a particular field, right?
So, for instance, if you could condense each sheep down to a tiny little size,
then you might be able to fit them in any number of fields that exist right now.
But, given that you can't do that, and given the fields that exist on the Earth
right now, there are no fields large enough to hold all the sheep.
So I think if we add a couple extra premises into that first step, then the
first deductive argument, the first of the three deductive arguments in Marjorie's
overall argument, is going to be sound. It's going to be sound because the premise
is true. I looked into it.
And the conclusion is going to follow from the premise, plus a couple of the other
premises I mentioned, that we're going to have to add in about the limited size of
fields on the Earth right now, and about the limits to how tightly you can pack
sheep into a field. Okay, so the first of Marjorie's three
deductive arguments is sound, not just valid, but also sound.
Now, how about the second one? Well, she says, I can see sheep.
I take her word for it. Therefore, there are definitely sheep.
Now, valid, or not valid? Well, it depends on how you use the verb,
to see. Sometimes we use the verb, to see, as
what's called a success term. You can't see something that isn't there.
If I say, oh, I saw Stacy in the office this morning, you could rightly object to
me, on one interpretation of see, you couldn't have seen Stacy.
She wasn't there. She was home in bed.
But sometimes, we use the verb, to see, in a broader sense.
Sometimes we use the verb, to see when we say that someone sees pink elephants,
let's say, when they've had too much to drink.
Or Macbeth saw a dagger when he was hallucinating early on in the Shakespeare
play that bore his name. When we use see in that sense, it doesn't
follow from the fact that you can see sheep that there are definitely sheep.
But if we're using sheep in the narrower of those two senses, as a success term,
then it does follow. From the premise that you can see sheep,
it does follow that there are definitely sheep.
And so, using the verb, to see, in that narrower sense, if it's true that Marjorie
can see sheep, then it definitely follows that there are sheep.
Okay, so the second of her three deductive arguments is also valid, at least on one
interpretation of the verb, to see. And if her premise is true, it's also
sound. But is Marjorie three for three?
I'm afraid not. Consider the third deductive argument.
There's an otter at the door wearing a white coat, therefore, I need a lie down.
Now, is that argument valid, or not? Well, if there really is an otter at the
door wearing a white coat, what I should do is call a zoologist or call the news
reporter, because that would be a really one-of-a-kind event, if there was an otter
at the door, wearing a white coat. I bet it's the first time in history that
an otter has been at a person's door wearing a white coat.
Well, maybe not the first time. Maybe some practical joker has arranged it
to happen in the past. But it would be a very rare event, that
there would be an otter at the door wearing a white coat.
From the fact that there's an otter at the door wearing a white coat, nothing
whatsoever follows about what I need to do.
In fact, it doesn't even follow that I exist.
There might be an otter at the door wearing a white coat, even though I've
been vaporized a minute ago. And so, there's an otter at the doorway
wearing a white coat, but it doesn't follow that I need a lie down.
It doesn't follow that I need anything, because it's consistent with there being
an otter at the doorway wearing a white coat that I don't even exist.
But, if we interpret statement five as expressing not a fact, as reporting not a
fact, but rather as reporting a belief that Marjorie has, then we can understand
this argument as much stronger. Here's what I mean.
Suppose it seems to me as if there's an otter at the door wearing a white coat.
Or suppose I believe that there's an otter at the door wearing a white coat.
Well, if I'm in either of those two psychological states, if it seems to me as
if there's an otter at the door wearing a white coat, or if I believe that there's
an otter at the door wearing a white coat, then I shouldn't call a zoologist, and I
shouldn't call a news reporter. I should call a psychiatrist, because I
need help. So, if premise five reports a fact, then
nothing whatsoever about me follows from that fact.
But if premise five reports a psychological state that I'm in, let's
say, it's appearing to me as if there's an otter at the door, or my believing that
there's an otter at the door. If premise five reports a psychological
state that I'm in, then it might very well follow, from my being in that
psychological state, that I need to call a psychiatrist.
I need to lie down. I need to have my guns taken away from me,
and so on and so forth. So, of the three arguments, the first one
is not just valid but also sound. The second one, if the verb, to see, is
interpreted in the narrow sense, where it's a success verb, then the second
argument is definitely valid. And, if Marjorie can see sheep, it's also
sound. The third argument unfortunately, not
sound and not valid. And the reason why it's not valid is
because, from the fact that there's an otter at the door wearing a white coat,
nothing whatsoever follows about me. Because I might not even exist if there's
an otter at the door wearing a white coat. But I think what Marjorie might have had
in mind when she wrote premise five, was, it seems to me as if there's an otter at
the door wearing a white coat. And from that premise, that it seems to me
as if there is an otter at the door wearing a white coat, then something
definitely does follow about me. Of course, nothing can seem to me to be
any way, unless I do exist. And if something seems to me to be a
particularly strange way, then that suggests that I need help.
So, if premise five was intended to say it seems to me, or I believe there's an otter
at the door wearing a white coat, then that premise really does support, though
it's not clear to me at all that it entails, but it does support that I need a
lie down. So, I want to thank Marjorie for one of
the few deductive argument submissions that we got in the posts.
And now, I want to consider another deductive argument submission.