>> You'll remember that in the second unit of our course, we considered the rules
that we can use 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 in reasoning, we
frequently find deductive arguments. 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 Ram'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 sheet 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 into 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 added 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 3 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 Stacey in the office
this morning. You could rightly object to me on one
interpretation of see. You couldn't have seen Stacey, 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 her third deductive argument.
There's an otter at the door wearing a white coat, therefore, I need to 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 door wearing a
white coat, but it doesn't follow that I need to lie down.
It doesn't follow that I need anything because it's consistent with there being
an otter at the door wearing a white coat that I don't even exist.
But If we interpret statement 5 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 that I believe that there is an otter at the door wearing a white coat.
But if I'm in either of those two psychological states, if it seems to me
that as if there is an otter at the door wearing a white coat or I believe that
there is 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 5 reports a fact, then nothing whatsoever about me follows from
that fact. But if premise 5 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 5 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 5, was it seems to me as if there is an otter at the
door wearing a white coat. And 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
anyway, 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 5 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
to 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.