The Slippery Slope Argument: a contrived example
 

There are two argument types that are attributed with the name Slippery Slope, causal type, and semantic type. In this post, by Slippery Slope argument, I am referring to causal type.

Some claim the Slippery Slope argument is inherently a logical fallacy. (Most scholars do not make this claim.) However, this is easily demonstrated to not be the case. Like any logical argument, if used improperly, the Slippery Slope argument can lead to a fallacious conclusion. But when used properly, it is perfectly sound and cogent.

To disprove the assertion that the Slippery Slope argument is inherently a logical fallacy, I have to find one example in which the method is used accurately and logically. For brevity and conciseness, I will create a simplified version.

Let's say Bob is a skydiver who is about to make his tenth skydive of the day. Bob has had a long day and is tired from packing his parachute nine times today, but he wants to get one more jump in. For Bob, like many skydivers, there is nothing like seeing the sunset from 13 000 feet above the ground. About ten minutes before he is supposed to board the airplane, Bob sees an old friend walk into the hangar. He walks over, and they shake hands and begin to catch up on what has happened in each others' lives since they last met. Before he knows it, Bob hears manifest call for jumpers to board the plane. He grabs his helmet, goggles and altimeter and runs to the boarding area, and is soon laughing and joking with 22 other skydivers in the Shorts Skyvan as it lifts off from the runway.

Thirteen minutes later, the tailgate of the aircraft is open and the pilot has given the green light for jumpers to exit. First out is a group of eight. A few seconds later, a group of six follows them. A few seconds after that, a group of five leave. After them, a group of three are gone. Bob isn't really interested in freefall this jump. He has already accumulated nine minutes of freefall today. He wants to deploy his canopy up high and enjoy the cool air and the view of sunset as he slowly descends back to earth.

What Bob doesn't realize is that, in the excitement of seeing his old friend just before loading, he completely forgot to grab his parachute rig. If Bob jumps, he will fall from his current altitude of 13 000 feet to an altitude of 12 999 feet. From there, he will continue falling to 12 998 feet. When he reaches that altitude, he will fall to 12 997 feet. He will continue to fall, inch by inch, foot by foot, until he reaches ground level at 0 feet, at which point he will impact at about 120 miles per hour, and die.


We can logically conclude that if Bob exits the plane and falls that first foot, he will die. Yet, it's not the exit that kills him. It's not the first foot he falls. But he must fall through the first foot before he can fall through the second foot. And must fall through the second foot before he can fall through the third foot, etc. Thus we have a logically valid form of causal type Slippery Slope argument. Jumping won't directly kill Bob, but if Bob jumps he will ultimately die from his action.

Thus, the Slippery Slope argument is not inherently a logical fallacy.

Of course this is a contrived example, designed not to be realistic (although people have inadvertently jumped without parachutes and did in fact die), but rather to show that, structured properly, a Slippery Slope argument can be used to logically predict future consequences of an immediate decision. And it was easier than trying to explain the Calculus necessary for a rigorous mathematical proof. :eek:

I think you need to look at the definition of "Slippery Slope Fallacy" more closely. You will find that you made a critical mistake in your example.

OK. I may be going down a slippery slope here:D...but J Christopher, I have been thinking about your tag line "Life is a fractal sine wave."

I have been able to wrap my (very small) brain around life either being a fractal pattern, or a sine wave, but have difficulty picturing a fractal sine wave. Can you provide a picture of this so I can get some sleep tonight?

Well I started writing out a post about how this is a poor example of the slippery slope. Then I did some more reading and found some other examples of this casual slippery slope. I've come to accept that yes this is a slippery slope argument.

The fallacy is that showing that there are valid slippery slope arguments does not prove that all slippery slope arguments are valid.

Granted you don't state that premise, and at times explicitly state that the slippery slope is not automatically a fallacy. So in the end I'm confused as to your goal. (Lose a debate recently? ;)) Anyone who believes that all classifications of fallacious arguments are always fallacious hasn't put the effort into examining the argument at hand. In fact I'd say that that's why the countering argument would begin by stating that a particular statement was a "Fallacious Slippery Slope". Arguing a countering point by identifying the type of argument will not win you many debates.

Feel free to expound. (If you are referring to falling through 12 999 causes Bob to fall through 12 998, that's the contrived part. Technically valid, but admittedly designed to highlight the continuum of events, and not the events themselves.)

Slippery Slope:
A increases the probability of B, B increases the probability of C, C increases the probability of D, … , Y increases the probability of Z, therefore A increases the probability of Z.

The causation need not be direct, nor certain, one event just needs to increase the probability of the next event.

See the "Help Recording Keystrokes to monitor guest accounts" thread in System. :) This thread is an attempt (likely in vain) to un-hijack that thread.

Imagine a graph of a sine wave. Now imagine zooming in on a tiny interval of that graph. The sine wave should appear to be very similar to a straight line on that interval. But what if, instead of looking like a straight line, it looked like another sine wave? And zooming in on a tiny interval at that level revealed, not anything close to a straight line, but another sine wave. And zooming in at that level revealed, not anything close to a straight line, but another sine wave. And zooming in…

Does that make any sense? I hope so, as I would hate to feel responsible for you losing sleep. :)

There is nothing inherently fallacious about a slippery slope argument. One could argue that if you're going to temporarily misappropriate $11.37 from the collection plate to pay for your lunch, you're distinctively if marginally more likely to consider borrowing $2800 from the church operations fund to pay your rent. In both cases you have every intention of paying it back. The reason for not doing it, in both cases (aside from the risk of getting caught at it, of course) is the principle of the thing. Once you've violated the principle in a small but real way, it's just a matter of scaling.

Or...

"Would you sleep with someone, let's say it was me, if I had Bill Gates' fortune and offered you 250 million?"

"Well duh! Take my kisses and call me missus."

"So will you sleep with me for $20?"

"I get it. I'm supposed to say 'How dare you, what do you think I am?' and then you say 'We've already established that, now we're just haggling about price'. Well, it take a lot more oil than you've got in your toupee to slide down the slippery slope from $250 million to twenty bucks!"

The main problem with slippery slope arguments is equivocation. Where rather than "x" and "y" both being valid examples of the same phenomenon, with "x" merely being a milder form that can easily lead to "y", there's actually something more compelling about the difference than there is about what they have in common.

"Don't jaywalk. It's against the law. If you're fine with jaywalking you could be a murderer tomorrow." Equivocation. The restriction against jaywalking is not a law of moral or social necessity, it's a rule of convenience.

"You can't wear white after labor day! If you don't care enough to abide by accepted rules, you'll end up going naked or going dumpster diving to get your clothes and you'll live out your days as an asocial recluse because you don't give a crap about what others think!" Equivocation. Ceasing to care what any of the people think at all times to the point that it dictates your choice of apparel is a very different phenomenon from ceasing to care what anyone thinks any of the time to the point that you disengage from the rest of the species.


Sometimes a slippery slope argument can have a grain of truth but not the beachfront that its proponents try to claim for it:

"You're smoking marijuana, an illegal drug? Four years from now you'll be shooting up heroin. Why not? They both feel good, they're both illegal, and you're convinced you know better than the folks who run society, because ooh, it's YOUR body, blah blah blah..."

Yes and no. Marijuana is not an addictive drug, nor does it incapacitate in the same way as heroin. On the other hand, yes, I would assume that someone who has questioned the loudly touted wisdom about the evils of drug user enough to experiment with marijuana might conclude that everything we've heard about the other drugs is a pack of lies, too. Which is an equivocation on the part of the drug user. The info supporting the claim that heroin is an addictive and dangerous drug is of a very different calibre than the party-line "just say no" propaganda about marijuana. Similarly, experience with recreational substances that do not foster tolerance and generate withdrawal effects don't teach you much about the possible experiences with those that do.

@AHunter3

Thanks for covering the semantic version of the slippery slope! :)

In addition to Al's excellent examples of how the slippery slope argument is only useful to extremists with no sense of balance:

If Bob the skydiver had done what all jumpers should do and touch all three handles* at least once on the way up, or looked at his shoulder, he would have realized his error. That final step may be 12000 feet high but it's still only one step in the chain - once his foot leaves the ramp he's a dead man. He (or any of the other 20+ people on the plane) could have stopped the slippery slope any time before that.

The statement that "it's not the exit that kills him" is rather absurd. The exit in this example begins an irrevocable action that ends with Bob making a dent** on the ground. The slippery slope ends at the door, not the ground. Although the ground is directly responsible for Bob's demise, unless he's owed a big favour by some major deity*** there's not much he can do to change things.

Pure logic arguments fail in real life because real life is not logical. This whole thing got started because A wanted to do something that B didn't agree with, so B et al create some examples about why A's idea was unacceptable at ANY time. They didn't consider A's complete situation (little hard to do in online forums) or what he would do after the fact (where, I agree, things can get dicey). That's where balance comes in. Most modern governments have balance. If they didn't we'd have Jack Bauers running the place and dictators giving them free reign (1930's Germany for example) Every modern government has some Jack Bauers working wor them, but on a short leash.
However, a balanced government is an inefficient one - a benevolent dictatorship is the most efficient. No modern examples of those come to mind, but Saudi Arabia is fairly close. If you have an ethical, smart, sensible absolute-power dictator running the place I'll happily move there. (Saudi Arabia isn't close enough)

So, my reply to these "logical reasons" is - Have you considered ALL the variables in this situation? If not, kindly shut up.

----------------------------

* note to non-jumpers - a sport parachute has three operating handles: one to open the main parachute, one to release it if it doesn't work, and one to open the second chute. If the handles are covered in folds of clothing or pushed too far into their pocket they're a little hard to use when you need them.

** second note to non-jumpers - bodies impacting non-pointy surfaces usually don't leak much.

*** old parachuting joke:
Bob is going for his first jump. His instructor told him, "If everything goes wrong, say, `Help me, Buddha oh Buddha' and you will be saved."

Bob got so scared that he forgot to pull his rip cord. So he said, "Help me, Buddha oh Buddha," and a giant green hand came out of a cloud and saved him.

He said, "Oh, Thank God," and the hand dropped him.

The slippery slope fallacy, aka the fallacy of the beard or the fallacy of the continuum, is the argument that small differences in a continuum of change between two extremes are inconsequential. For example, in your example of falling, a simplified beard fallacy argument might go like this:

A millimeter is a very small distance, yes? And certainly, to fall one millimeter would not do one any harm. If you increased the distance to two millimeters, would your health, upon landing, be any worse than it would be for one millimeter? Of course not. How about three millimeters? I think it’s safe to say that you would come to no harm. Indeed, you could keep adding millimeters to the distance you fell, and you could be certain that, upon landing, you would be okay. So, how can you call one distance "long," and the other distance "short?" Certainly, such a distinction would be arbitrary. Therefore, falling from a "long" distance would not harm one any more than falling a "short" distance.

Similarly, in your example, what you seem to be essentially arguing is that falling one foot is no different from falling 13,000 feet. And that, of course, is incorrect.

I know all about emergency procedures. Look Reach Look Reach Arch Pull Pull turns into "Oh" *pull rightside (soft)* "Sh!t" *pull leftside (silver)* turns into "Not" *cutaway* "Again" *reserve*. I've gone for the silver handle over the years more times than I care to remember. And handle checks can absolutely save lives in such a situation, to the extent that such deaths are statistical anomalies among skydiving incidents. However, I was not not writing to a skydiving audience, I was writing to a Mac using audience. So I'm sure you'll forgive me for not coming across as the local S&TA. (Would it have been better if I had used a dart or shuttlecock analogy?)

I used an extreme example because it made it eliminated all extraneous stuff so that only the basic structure of the argument strategy is highlighted. I wanted to avoid maths, because this isn't a maths forum, either. While my goal was to make the example as extreme as possible (I stole a bit from Zeno; I hope he doesn't mind. I removed the paradox.), to eliminate unnecessary variables. If used properly the slippery slope strategy can be a cogent argument in the real world as well. It just has to be used correctly. Like any logic strategy, if used improperly, Slippery Slope can lead to an fallacious conclusion.

The logic does not break down, the people do. :) People do not always act rationally and logically. But some situations do. So we need the logic. We just need to use it properly.

I considered all the variable of the problem. My goal was never to save Bob's life. He could could only have one choice, and it had already been made for him. He was destined to die from the very beginning.* I thought about giving him a rig and short chain of problems where the statistically correct choices was actually the incorrect choices in his actual situation. But that seemed like a lot of work to explain, so I just took his rig away and made him tired instead. It's also pretty unlikely 22 people would have let him get on the plane without a rig, if we're picking nits.

I sure hope no one was doing 270's in the main landing area! :eek: ;)

Not the way I heard it, but I think I like your version better.




*BSBD Bob. Now go get on a big-way with my friends.

What you are describing is semantic slippery slope. What I described was causal slippery slope. They are similar concepts, hence the same name, but there are significant differences.

In causal, one event along a continuum of events increases the probability of the next event along a continuum. (For simplicity, I increased probability to one.) Therefore, the first event increases the probability of the last event, at the other end of the continuum.

In semantic slippery slope argument, one argues the two things are really the same thing, since any distinction between the two, real or imagined, is arbitrary.

Ah, I see what you’re saying.

Certainly that’s not fallacious; I think we can all agree of the inevitability between the steps involved ;) :).

Of course you weren't. What, realistically, were the chances of you finding another jumper (+ master rigger) on a computing forum??

Doesn't matter. As the original purpose of this discussion involved people it makes no difference WHY the argument fails. It still fails. As people do not behave logically it is therefore logically impossible to use logic to explain them. :confused:

Fine. but your example fails when you say the first foot fallen leads to the second foot etc. Exit to impact is a single event as it is unchangeable once begun.

Happened in the early 90's. You can dig the details out of USPA. Cameraman had a chest-mounted recorder and was sitting in the rear corner of a Porter* with his back to the wall.

People still do toggle hook turns? Front risering is so much more controllable. I've always liked "learn from the mistakes of others, you won't live long enough to make them all yourself." Still, it's an efficient way to reduce the annoying Skygod population.

* if you don't know, picture a Cessna 180 on mega-steroids. 8-way to the top in about 10 minutes

Side Thread....
 

I think it's very appropriate; life is, in fact, a fractal sine wave. At the largest scale:

More like a cosine, I suppose, but sinusoidal.

Then on smaller scales we have respiration, heartbeat, etc. I like it.

Here's an example from the Scopes trial made by Clarence Darrow

I was able to envision this on the way to work today, so I am not surprised by the description. However, I am still struggling with the math (now remember, I am an admitted simpleton looking to my peers for insight).

In theory, I can envision the picture described (it's a nice mental exercise that reminds me of an intro to an episode of The Simpsons that has the whole universe in Homer's brain)...My issue is that the math of fractal shapes seems incongruous with that of a sine wave. In other words, when I try to move beyond simply imagining the quoted example as a static picture to trying to apply fractal logic, I keep seeing the actual result as a fractal curve - not being able to retain the continuous shape of a sine wave.

Help me out here. Point me at the "Fractal Sine Waves for Dummies" math explanation.

Regarding fractals and sine waves, I have to recommend this book.

It’s an excellent read.

I think Seeker777 is imagining Mandelbrot patterns. Squish that down to one dimension, i.e. imagine taking a slice through it and looking at it from the side.

well, hmmm... I'm not certain this actually describes a fractal; sounds more like an odd sort of Fourier expansion. if I remember correctly, fractal attractors are everywhere non-differentiable, which would never apply to sine curves. I mean, I can see the analogy to a Koch snowflake, I just don't think it flies (the basic element of the snowflake is non-differentiable at three points, but that approaches total non-differentiability as the line length approaches 0...).

I'll point out, in passing, that this is a variation on Zeno's paradox - arguing that an arrow can never hit a target, because first it has to get half way there, and before that, it has to get halfway to that halfway point... the classics are always the best. :-)

that being said, though, problems only occur with these kinds of arguments when the relational chain between objects or events is improperly specified. it's really a question of proper vs. improper induction, and as such it can't really be called a fallacy. it's just a theory that's subject to examination and/or refutation.

Fairly high on a Mac site. Skydivers aren't all that rare, and , based on my observations, freefall videographers use Macs at a rate that is higher than the population as a whole.


If you want to believe that, you are certainly entitled to do so. However, for the purposes of this particular discussion, why the argument fails or doesn't fail IS the topic of discussion. I only needed one example, no matter how unrealistic and contrived (my example was admittedly both), to show that it is misuse, not use, of the slippery slope strategy that leads to a fallacious conclusion.

That's the whole point of the Slippery Slope argument. The first step implies the last step, hence the name slippery slope. (It can also be valid if the first step just increases the probability of the last step, provided that is all that is asserted.)

I've seen more than one cameraman board without a rig. Those damn helmets can be quite distracting. I know of at least one (beginning) skysurfer who did it also. He was most of the way to altitude before anyone noticed. Usually when they check their handles and find they are not there, they become aware of the problem.

Regretfully, I've yet to attempt to find the actual mathematics of the pattern. It was actually by studying Taoism that I thought of it in those terms. But should you come across said mathematics, please let me know. :)

From what little I've read of Chaos Theory, there seems to be a distinction between mathematical fractals and natural fractals. You make a very valid point about the differentiability. I just use the term fractal to represent the self-repeating aspect of the appearance, no matter how closely one zooms in, much like the Mandelbrot set. (If I recall correctly, the Mandelbrot set has only a finite number of "dimensions.")

Yes, I did steal Zeno's process, but eliminated the (since resolved) paradoxical aspect.

True. In the previous thread in System, I mentioned how one can use division improperly to prove that 1 = 0, but it's the improper use of division that creates the fallacy, not division itself.

all fractals have finite dimensions, though generally they are fractional (that's where the name 'fractal' comes from - a corruption of 'fractional dimension'). basically that means that the set is infinite without filling an entire dimension - Mandlebrot, if I remember correctly, is around 1.3 dimensions, meaning it's more than a line but less than an entire plane. also you have to distinguish between the computer enhanced patterns which you see and the attractor, which is more of a mathematical abstraction. for instance, with the Mandelbrot set, the attractor is the set of all points C on the complex number plane such that iterations of the equation Z=Z^2+C never exceeds 2. 2 is not arbitrary or chosen, that's just the way it happens to work out - if it exceeds 2 the equation heads off to infinity. when you see Mandlebrot images, the Mandlebrot set is always in black - colors are generated for points outside the set, according to how quickly Z passes 2 for that value of C.

fun, hunh? :)

they resolved Zeno? seems I missed something. :) what was the resolution?

J Christopher-
It was not my intention to create a math test. I enjoyed the thought exercise, as I too believe in the patterns of nature providing insight into life. I am trying to find my path on the Way.

IMHO the definitive translation of the Tao Te Ching was done by R.L. Wing. If you have not seen it, I highly recommend checking it out at your book store.

Calculus (limits, geometric series, the understanding of instantaneous velocities, etc.)

The Tao that we can speak of is not the eternal Tao.

:D

I will have to track that version down and read it. Thanks for the heads up.

No worries about the maths test. I enjoy maths. No matter how much I learn, I wish I knew more.

ah... that. :rolleyes:

there is no definitive translation of the taote. there is only the tao, ineffable and serene, and the maunderings of old men entranced by its beauty...

that being said, though, I'll look it up. :D

One problem with Zeno's paradox, and probably a problem with the OP's example, is that what actually exists is a continuum; the divisions into smaller parts is imposed by the observer and are artificial, not intrinsic to the situation at all.

That's exactly what the slippery slope argument is meant to highlight.

Having said that, Zeno was one clever fellow, IMO, but I'm more inclined to accept Einstein's conclusions (which built on Newton's work) about motion. :)

Nicely spotted. There's an old joke about a male Engineer and Mathematician being offered the services of a lissome lass standing unclad before them provided only that they approach her by halves. The mathematician declines because he knows he'll never get there, but the engineer accepts eagerly because he knows he'll get close enough.

lol - that joke is almost too true... :)

tw-

Good point.

Perhaps I should have said that I found it to be the most insightful and resonant translation I have read. Have a peek and let me know what you think.