Complex Conditions

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From the course by Duke University

Think Again III: How to Reason Inductively

111 ratings

Duke University

Think Again III: How to Reason Inductively

111 ratings

How to Reason Inductively Think Again: How to Reason and Argue Reasoning is important. This series of four short courses will teach you how to do it well. You will learn simple but vital rules to follow in thinking about any topic at all and common and tempting mistakes to avoid in reasoning. We will discuss how to identify, analyze, and evaluate arguments by other people (including politicians, used car salesmen, and teachers) and how to construct arguments of your own in order to help you decide what to believe or what to do. These skills will be useful in dealing with whatever matters most to you. Courses at a Glance: All four courses in this series are offered through sessions which run every four weeks. We suggest sticking to the weekly schedule to the best of your ability. If for whatever reason you fall behind, feel free to re-enroll in the next session.We also suggest that you start each course close to the beginning of a month in order to increase the number of peers in the discussion forums who are working on the same material as you are. While each course can be taken independently, we suggest you take the four courses in order. Course 1 - Think Again I: How to Understand Arguments Course 2 - Think Again II: How to Reason Deductively Course 3 - Think Again III: How to Reason Inductively Course 4 - Think Again IV: How to Avoid Fallacies About This Course in the Series: Think Again: How to Reason Inductively Want to solve a murder mystery? What caused your computer to fail? Who can you trust in your everyday life? In this course, you will learn what distinguishes inductive arguments from deductive arguments and then how to analyze and assess five common forms of inductive arguments: generalizations from samples, applications of generalizations, inference to the best explanation, arguments from analogy, and causal reasoning. The course closes by showing how probability can be used to help us make decisions of all sorts. Suggested Readings Students who want more detailed explanations or additional exercises or who want to explore these topics in more depth should consult Understanding Arguments: An Introduction to Informal Logic, Ninth Edition, Concise, Chapters 8-12, by Walter Sinnott-Armstrong and Robert Fogelin. Course Format Each week will be divided into multiple video segments that can be viewed separately or in groups. There will be short ungraded quizzes after each segment (to check comprehension) and a longer graded quiz at the end of the course.

From the lesson

Causal Reasoning

<p><b>CONTENT</b>: This module will focus on how to decide what causes what. Students will learn how to distinguish necessary conditions from sufficient conditions and how to use data to test hypotheses about what is and what is not a necessary condition or a sufficient condition. Then we will distinguish causation from correlation (or concomitant variation) and explain the fallacy of post hoc ergo propter hoc. It is sad that some diners had to die to make this lesson possible, as you will see.</p> <p><b>LEARNING OUTCOMES</b>: By the end of this week’s material you will be able to do: <ul> <li> analyze causal reasoning</li> <li>distinguish necessary from sufficient conditions</li> <li>determine what is necessary or sufficient for what</li> <li>separate causation from correlation</li> </ul> </p> <p><b>OPTIONAL READING</b>: If you want more examples or more detailed discussions of these topics, we recommend <em>Understanding Arguments, Ninth Edition</em>, Chapter 10.</p>

Negative Sufficient Condition Tests9:28

Positive Sufficient Condition Tests10:09

Negative Necessary Condition Tests4:36

Positive Necessary Condition Tests6:51

Complex Conditions11:39

Meet the Instructors

Dr. Walter Sinnott-Armstrong
Professor
Philosophy
Dr. Ram Neta
Professor
Philosophy

Last time, we ended with a bit of a mystery.

We concluded that fish still might be necessary and not sufficient for death,

and red wine might be necessary, but it's definitely not sufficient for death.

The question is, well, if neither of those is sufficient, what is sufficient?

To answer that question, we've got to look at complex conditions.

Now, complex conditions are just conditions, or features, or candidates,

that are combinations, of other candidates, or features or conditions.

It might be a negation; not having fish.

It might be a disjunction; having either fish or beef.

But we're going to look at conjunctions. That is, having some combination

of two or more of the food and drink at the banquet.

And we're going to understand these in exactly the same way

we understood the simple, or atomic conditions, or features, or candidates.

So, for example, we're going to use the same definition of a sufficient condition.

F is a sufficient condition for g. Well, what that means is

that whenever f is present, so is g.

And then we're going to have a negative test for a sufficient condition.

This is just reminding you of a couple of lectures

ago, that x is not a sufficient condition of y,

that is of a certain target, like death, if there's

any case where x is present and y is absent.

Now notice since we used x and y

as variables, you can stick anything in for them.

So, to get a conjunctive condition, we're going

to simply substitute in the conjunction w and x.

So, w and x, that combined conjunctive candidate, is not

a sufficient condition for y, if there's any case where both w and x are present,

and y is absent.

Just like in the other cases, but we're just using a conjunction to replace one of

the variables. And we can

look at our data

from before

to determine

which conjunctions

are, and are not,

sufficient

conditions

for death? So,

are there any

conjunctions

that still

might be

sufficient

conditions

for death? What

about tomato

soup and chicken?

Maybe, when you

have tomato

soup and chicken

together,

that will

kill you. Nope,

that can't

be, why not?

Which case

rules out the

conjunction

of tomato soup

and chicken as

a sufficient

condition

of death? Ann does, because

Ann had tomato soup and chicken but she didn't die.

What about red wine and cake? Is red wine and cake together, as a

combination, as a conjunction, is that sufficient for causing death?

Is leek soup and fish necessary for death? No.

Well who shows that?

Barney, because Barney died without having leek soup and fish.

Is there any other case that shows that? Yeah, Emily shows that, because she died.

Without having leek soup and fish.

So that combination is not necessary, for death.

Okay, so, Barney and Emily, show that leek soup and fish is not necessary for death.

What about tomato soup and fish?

They both had tomato soup and fish, so

maybe tomato soup and fish Is necessary for death.

Does that work?

No, because of Fred.

Fred dies without having tomato soup and fish because he has leek soup and fish.

So

Fred shows us that the combination tomato soup and fish is

not necessary for death because you can die without that combination.

If you have leek soup and fish instead.

So neither of those combinations is necessary.

What might be necessary, which combination is not ruled out.

As necessary.

[SOUND]

Or here's one, fish and red wine.

Fish and red wine might be necessary for death because

everybody who died at this banquet had fish and red wine.

There was nobody who died without having fish and red wine.

So fish and red wine is not ruled out as a necessary condition of death.

But wait a minute.

Fish and red wine was also not ruled

out as a sufficient condition for death because everybody

who had fish and red wine together died. That means that this particular

combination, fish and red wine, is both necessary and also sufficient.

For death, at least given the data that we have so far.

I won't go through developing the positive test for conjunctions, because it's

going to be just like the positive necessary condition test and the positive

sufficient condition test that we went through in previous lectures.

You just substitute conjunctions for variables and you get those tests.

But it looks like for the data so far we've got at least some reason to

belief that fish and red wine is necessary

for death and also sufficient for death, great.

Now we know which combination meets those tests, but what does that tell us?

We don't know any mechanism, right? Why would fish and red wine cause death?

Well, obviously, these people died of bad taste.

The chef, who worked all afternoon on the

fish, can't stand the fact that people might

eat his beautiful fish And have red wine

which is going to destroy the taste of the dish.

So anybody who ordered red wine with the fish, he poisoned them.

That would be the mechanism for why everybody who had fish with red

wine died.

You know, there might be some other story about how some chemical in the fish

interacted with the red wine, but If you

can rule that out from background knowledge, we've

got a pretty good reason to believe

that somebody back there in the kitchen, probably

the chef, or someone who was mad at them, poisoned them, they died of bad taste.

Now we need more research to be sure. We need lots

more candidates, we need to test various

combinations, but that's just an inductive argument.

Inductive arguments never make you absolutely

certain that the conclusion is true.

they're defeasable. They're not valid.

We know all that.

But at least, we have some evidence to believe that

fish and red wine is necessary and sufficient for the death.

That's what caused these people to die.

And it's the chef that ought to go to jail.

We've gone through one example in some detail, but, like many other things in

this course, the best way to learn

this material is to practice, practice, practice.

So let me give you a little hint.

You can create all the exercises you would ever want.

Just by taking the chart that we've looked

at in the last couple of lectures that goes

from Ann through Harold and change what each of them had

in the soup course or what each of them had in

the main course or what each of them had in the

wine course or what each of them had in the dessert course.

Or change which ones lived and which Which ones died.

And you can create more examples to practice

the necessary condition test and the sufficient condition test.

And if you want to

know whether you got it right bring your chart and your answer to the discussion

forums and the other students in the course can help you out by telling you.

Whether they agree about what's necessary and

sufficient in the set up that you created.

So if all you students out there in Coursera land practice,

practice, practice by changing the banquet to meet your own specifications,

then you'll all learn better.

How to distinguish necessary and sufficient conditions and

how to test for necessary and sufficient conditions.

So go off and have some fun with it.

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