Perhaps the most common kind of inductive argument is called an inference to the
best explanation. And to understand this kind of argument
we need to think way back to the first week when we discussed the difference
between justification and explanation. If somebody uses an argument to justify a
conclusion then they're trying to give a reason to believe that the conclusion is
true. And maybe you didn't believe that
conclusion before you heard the argument. But if somebody gives an argument.
To explain, the conclusion. Then they're taking it for granted, that
the thing they're explaining is true. An they're trying to, understand.
Why it's true. An the argument is supposed to help us
understand, why it's true. The weird thing about an inference to the
best explanation is it really combines these two.
It uses the argument to justify belief in the conclusion, that is to give you a
reason to believe that it's true, and yet a premise of the argument is that, that
conclusion explains a phenomenon that you took for granted.
Inferences to the best explanation are extremely common.
For example, almost every detective story uses an inference to the best
explanation. Just imagine that there are three
suspects. And you know that one of those three
suspects must have done it. Because the door wasn't jimmied open.
So, whoever got into the room must have had a key.
And there are only three people who had keys.
But one of'em couldn't have been the one who did it.
Because she has really small feet. And the footprints outside the door were
really large and so it couldn't have been her.
And the second person couldn't have done it because they have an alibi on the
other side of the town. So it must have been the third person who
did it. You notice what you did is, you can't
explain why the door wasn't jimmied by the person who got in.
Because. there were no marks, and that means that
the best explanation, that must be that the person that did it, had a key.
And the best explanation why the footprints were so large, is that it was
a large person who wore large shoes. And the best explanation of why the alibi
would place the person on the other side of town was that they were being honest.
Assuming it's not their brother or they're not the kind of person who would
lie, or so on. So the best explanation of why the jewels
are missing from the room, or why there's a dead body in the room, is that this
third suspect is the one who did it. So all the, detective stories work like
that. It's almost always an inference to the
best explanation. The best explanation is, he's the one who
did it. One implication of this, is that no
matter what Sherlock Holmes says, the form of reasoning that he was using was
inductive reasoning, not deduction, as he claimed.
It's not only detective novels. It's also science abuses inference to the
best explanation. Take for example the greatest murder
mystery in history. What killed the dinosaurs?
Well some people think that mammals eating their eggs,
not a chance. That doesn't explain why they were also
mass extensions in the oceans, where the mammals weren't eating their eggs.
Well some people think that, the best explanation is that.
There were big volcanic eruptions in Southern India.
That seems pretty unlikely too, because the volcanoes that we know didn't put out
enough material to kill things all the way around the world.
So, they think of the best explanation of what killed the dinosaurs is that a giant
meteor hit in the Yucatan Peninsula, in Mexico.
And that produced lots of soot in the atmosphere that killed the dinosaurs.
As well as many other species at the time but luckily, not mammals.
And so, we now have a best explanation in science.
And a lot a scientific theories work that way.
As a matter of fact, the point of most scientific theories is to provide, the
best explanation of the experimental data.
that has been observed by scientists throughout the world.
And of course, we also use inference of best explanation in our everyday lives,
to try to figure out what's going on around us.
Here's an example. Whoa, what was that.
A drop of water just hit my head. There must be a leak in the roof.
Now that is an inference to the best explanation.
Starts with an observation, of the water hitting my head.
Then I think about, why the water would be coming down.
And the best explanation I can come up with, is that there's a leak in the roof.
So I conclude that there is a leak in the roof.
Notice that this argument uses an explanation but it runs in the opposite
direction from an ordinary explanation. In an explanation, the premises explain
the conclusion and the conclusion describes the phenomenon that was
observed. When there is a leak in the roof, water
drops through the roof. When water comes through the roof, it
drops onto whatever is in its way. I am in its way.
Therefore, water drops onto me. This explains that.
In contrast, an inference to the best explanation works in the opposite
direction. The conclusion is what does the
explaining. The premises are what get explained, and
the point is to justify belief in the conclusion, not to explain it.
Water drops onto me. Leak in the roof might explain why water
drops onto me? No better explanation is available.
Therefore, there must be a leak in the roof.
Notice that the conclusion of the left argument is a premise, of the right
argument. And, the conclusion of the right argument
is part of a premise, of the left argument.
So, the form is different. The function is different as well.
In the explanation on the left we start out already knowing that the conclusion
is true. In the interest to the best explanation
on the right, we argue that the conclusion is probably true because it is
the best explanation of the observation in the first premise.
That's why we call it an inference to the best explanation.
Is this argument valid? Yes or no?
Right, it's not valid. Because it's possible for the premises to
be true and the conclusion false. Now does it's invalidity make the
argument bad? Yes or no?
Right. It does not make it bad, because an
inductive argument can be good, even if it's invalid.
The next question's a bit trickier. Remember that an argument is defeasible
if further information can make the argument weak.
So, is this argument defeasible? Yes or no?
Right. It is defeasible because further
information could make this argument weak.
So what? Does its defeasibility mean that this
argument was weak even before we got that additional information?
Yes or no? No.
Because inductive arguments can be strong, even though they are defeasible.
So now we know that this argument is invalid, and is defeasible but it still
might be strong and good.