that we're going to look at is slippery slope.

Here's a pretty extreme example of a slippery slope fallacy.

A high school kid's mom insists that she study on Saturdays.

Why?

Because if she doesn't study on Saturdays,

her grades will suffer, and she won't graduate high school

with honors.

And if she doesn't graduate with honors,

then she won't be able to get into the university

of her choice.

And, well, the rest isn't clear, but the result of all this

is that she'll end up flipping burgers

for the rest of her life.

And surely, she doesn't want that,

so she better darn well get serious and study.

I've actually heard a version of this discussion between two

wealthy mothers who were talking about which preschool

to send their kids to.

The gist was that if they didn't get their kid

into a prestigious preschool, then

they'd be disadvantaged from that point

forward in ways that could ultimately threaten

their future life prospects.

So this was not a decision to be taken lightly.

I did not envy those kids.

Here's the schematic form of a slippery slope argument.

It's a series of connected conditional claims

to the effect that if you assume that A is true

or allow A to occur, then B will follow.

And if B follows, then C will follow, and if C follows,

then D will follow.

But D is something nasty that we all want to avoid.

So the conclusion is that if we want to avoid D,

we need to reject A, or not allow A to happen.

Now, note that as stated, the logic of this argument is fine.

In fact, this is a valid argument form

that we've seen before.

We've called it hypothetical syllogism,

or reasoning in a chain with conditionals.

Slippery slopes are fallacious only if the premises

are false or implausible.

Everything turns on whether these conditional relationships

hold.

Sometimes, they do.

And if they do, it's not a fallacy.

But very often, they don't.

And when they don't, we've got a slippery slope fallacy.

Now, there's a caveat to this way

of analyzing slippery slopes.

It's usually the case that slippery slope arguments

aren't intended to be valid-- that is, they're not intended

to establish that the dreaded consequence will follow

with absolute certainty.

Usually the intent is to argue that if you assume A,

then D is very likely to follow.

So what's being aimed for is really a strong argument.

And that means we shouldn't really

be reading the conditional claims as strict conditionals

with every link in the chain following

with absolute necessity.

We should be asking ourselves, how likely is it

that D will follow if A occurs?

If it's very likely, then the logic is strong.

If not, then it's weak.

So in a sense, we're evaluating the logic of the argument.

But it turns out that in cases like this,

the strength of the logic turns on the content of the premises.

So in the end, we are evaluating the plausibility

of premises, which makes this a content fallacy, and not

a logical or formal fallacy.

For our example, the chain of inferences looks like this.

Now, this argument is obviously bad at every stage

of the reasoning.

It's possible that not studying on Saturdays

could make a difference to whether the student gets

on the honor roll, but there's no evidence

that this is likely.

Yes, if you're not on the honor roll, then

maybe this will affect your chances

of getting into a top university.

But without specifying what counts as a top university,

one of the factors may or may not

be operating-- like, for example, whether the student is

a minority or an athlete.

They might be eligible for non-academic scholarships

of various kinds.

Then it's impossible to assess the chances in this case.

The last move, from failing to get into a top university

to flipping burgers for a living,

is obviously the weakest link in the chain.

This is just widely pessimistic speculation with nothing

to support it.

So each link in the chain is weak, and the chain as a whole

simply compounds those weaknesses.

By saying this, we're saying that premises 1, 2, and 3 are

not plausible, and so the inference from A to D

is not possible.

We have no reason to think that this slope is not slippery.

Now, there's another obvious way that one can attack

a slippery slope argument.

You might be willing to grant that the slope is slippery

but deny that what awaits at the bottom of the slope

is really all that bad.

This would be to challenge premise 4,

the not D. Not D says that D is objectionable in some way,

that we don't want to accept D. But this

might be open to debate.

Put away to the bottom of the slope

is "and" then you die a painful death,"

or "and then all our civil rights are taken away."

And sure, just about everyone is going

to agree that that's a bad outcome.

But it's not as obvious that everyone

will find flipping burgers objectionable,

or whatever this notion stands for-- working in the service

industry, or working in a low-paying job or whatever.

What's important in evaluating a slippery slope argument

is that the intended audience of the argument

finds the bottom of the slope objectionable.

So this is another way to criticize a slippery slope

argument-- by arguing that the outcome of this chain of events

really isn't as objectionable as the arguer would

like you to think.

So just to summarize what we've said so far--

there are two ways of challenging a slippery slope

argument.

The first one is to challenge the strength

of the conditional relationships that the argument relies on.

When people say that a slippery slope argument is fallacious,

they usually mean that the chain of inferences is weak.

By the way, I hope it's clear that slippery slope

arguments don't have to have only three links.

My argument schema could've been longer or shorter.

Now, second, you can also challenge a slippery slope

argument by challenging the objectionableness of whatever

lies at the end of the chain.

If it's not obvious to the intended audience

that this is actually a bad thing,

then the argument will fail to persuade, regardless of how

slippery the slope may be.

Before wrapping up, I'd like to make a few points

about assessing the plausibility of conditional chains.

Fallacious slippery slope arguments

often succeeded at persuading their audience

because people misjudge the strength

of the chain of inferences.

They're prone to thinking that the chain is stronger

than it actually is.

It's important to realize two things.

First, a chain of conditional inferences

is only as strong as its weakest link.

The weakest conditional claim-- the one that

is least likely to be true-- is the one that sets the upper

bound on the strength of the chain as a whole.

So even if some of the inferences in the chain

are plausible, the chain itself is only

as strong as the weakest inference.

Second, weaknesses in the links have a compounding effect,

so the strength of the whole chain

is almost always much weaker than the weakest link.

To see why this is so, you can think of conditional claims

as probabilistic inferences.

If A is true, then B follows with some probability,

and this probability is usually less than one,

or less than 100%.

So the probability of D following

from A, the probability of the whole inference,

is actually a multiplicative product

of the probabilities of each of the individual links.

Now, the odds of a coin landing heads on a single toss

is one half, or 50%.

The odds of a coin landing heads twice

in a row is one half times one half, or one quarter,

which is 25%.

Conditional inferences compound in a similar way.

So if the odds for each link in the chain were,

let's say, 90%, then the odds of the whole chain being true,

of D actually following from A, would only be 0.73, or 73%,

and this number would go down further

with each additional link in the chain.

People in general are very bad at estimating

compound probabilities and will tend to overestimate them.

Here's the calculation if one of the links

is weaker than the rest-- say, 0.6, or 60%.

The probability of D following from A

actually drops below 50%, a very weak inference.

But very few people will read the probabilities this way.

Their attention will focus on the highly probable bits

of the story, and their estimate of the overall odds

will be anchored to these bits, especially if they're

either at the very beginning or the very end of the chain,

since these make the biggest impression.

So human beings in general are quite

vulnerable to slippery slope reasoning,

and knowing these facts should motivate

you to be more critical when you encounter

these kinds of arguments.