[Music]
Scientists often gather data through
observation experiments, archival studies
and so on. But they are rarely satisfied
with data alone. Scientists want to draw
conclusions from those data. They want to
use the data to show that certain
theories are right and others are wrong.
To understand science, then, it will be
important to understand when it is
legitimate and when it is illegitimate
to draw a specific conclusion from what
we already know. We need to understand
arguments; and that is why, in this
the difference between good and bad
lecture, we will take a look at logic--the
study of argumentation. Let us first
introduce some terminology. An argument
consists of two parts: the premises and
the conclusion. The premises are the
things we presuppose and the conclusion
is what we conclude from those premises.
So let's look at an example:
No medieval King had absolute power over
his subjects. Louis 7 of France was a
medieval King. So Louis 7 of France did
not have absolute power over his
subjects. Here the first two lines are
the premises and a final line introduced
by the word "so" is the conclusion. In this
argument we assume that medieval kings
did not have absolute power and that
Louis 7 was a medieval King. And we
conclude that he did not have absolute
power. As a second piece of terminology
we will make a distinction between valid
and invalid arguments. A valid argument
is an argument in which the conclusion
really follows from the premises.
Our example about Louis 7 is an example
of a valid argument. The conclusion
really follows from the premises. It
makes sense to draw this conclusion from
these premises.
As an example of an invalid argument we
can take this: No medieval King had
absolute power over his subjects. Louis
seven of France was a great horseman. So
Louis seven of France did not have
absolute power over his subjects. We just
can't draw that conclusion from those
premises. So this argument is not valid.
It's invalid. Note that whether an
argument is valid or not
has nothing to do with whether the
premises or the conclusions are true.
Perhaps Louis 7 really was a great
horseman. Then all the premises and the
conclusion of that argument are true and
yet the argument is invalid because the
conclusion just doesn't follow from the
premises. On the other hand it's also
possible to have false premises and a
valid argument. For instance: No medieval
King had absolute power over his
subjects. Victor Gijsbers was a
medieval king. So Victor Gijsbers did not
have absolute power over his subjects.
This argument is perfectly valid even
though the assumption that I am a
medieval King is, as far as I know, false.
We can now introduce our final piece of
terminology: The distinction between two
kinds of arguments. Deductive arguments
and inductive arguments. A deductive
argument is an argument in which the
truth of the premises
absolutely guarantee the truth of the
conclusion. It's just not possible for
the premises to be true and the
conclusion to be false.
Returning to our original example, we can
see that this is a deductive argument. It
is true
the medieval Kings did not have absolute
power; and if it is true that Louis 7 was
a medieval King, then it must be true
that he did not have absolute power.
Or, in other words, if he did have
absolute power then one of those two
premises must be wrong. I'll come to the
definition of inductive arguments in a
moment, but first I want to point out two
interesting features of deductive
arguments: First, if you use deductive
arguments you can't make any new
mistakes. The only way for the conclusion
of a deductive argument to be false is
if one of your assumptions is false, so
if you already believe something false
then your conclusion may end up being
false. But if your assumptions are true
your conclusions are guaranteed to be
true as well.
So deductive arguments never introduce
falsehoods if they weren't already there.
And that makes them very strong and good
arguments to use, because they're not
very risky. Second, logicians found out
already more than 2,000 years ago--and
Aristotle played an important role here--
that whether a deductive argument is
valid or not can be determined just by
looking at the form of the argument and
ignoring its content. Even if you know
nothing about medieval kings and Louis 7
you can still see that our example
argument is valid. How? Because there's
this form: No A is B. C is A. So C is not B.
Where A is "medieval King," B is "someone
with absolute power," and C is "Louis 7" But
we can put anything we like in the place
of those letters and the argument will
remain valid. For instance, let's choose A
"Is a Dutchman" B "is humble" and C "is Victor
or Gijsbers" Then we have: No Dutchman
is humble. Victor Gijsbers is a
Dutchman. So Victor Gijsbers is not
humble. Which is another valid argument.
Although of course the first premise is
false and so is the conclusion. So we can
see whether a deductive argument is
valid simply by looking at its form
without knowing anything about its
content. And that is really important
because that means that we can see
whether something is a good argument
without making any prior theoretical
assumptions about the content matter. If
we believe that scientists first
collect data and then come to a
conclusion about which theories are
right and wrong, this is exactly what we
would expect. We only need the data and
some valid arguments which can be shown
to be valid independent of any theories
or ideas, and then we draw our
conclusions. It would be great if science
worked like that. Unfortunately, and I bet
you saw that coming,
science doesn't work like that. And it
doesn't work like that because the most
important arguments in science are not
deductive. They are inductive. Remember
that a deductive argument is an argument
such that the truth of the premises
absolutely guarantees the truth of the
conclusion. An inductive argument is an
argument where the truth of the premises
gives good reason to believe the
conclusion but does not absolutely
guarantee its truth. Again let's look at
an example:
None of the medieval texts we have
studied argues against the existence of
God, so no scholar in the Middle Ages
argued against the existence of God.
That's a valid argument if it's true
that none of the texts we have makes
this argument, and we have a lot of texts,
and it's quite plausible that nobody in
that time actually made this argument.
But it's indeed only plausible. It could
be that the argument was made but
somehow it wasn't transmitted to us. So
in an inductive argument. The truth of
the premises makes the conclusion likely,
but it doesn't guarantee it. And that's
generally the case in science. We have
some limited data. We want to draw a
general conclusion from those, and our
data makes the conclusion likely but
they don't make it certain. So, in science,
we are continually making inductive
arguments. And, as we will see in the next
lecture, induction is a lot more
problematic than deduction.