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I deeply apologise for the length; I wanted to provide (over)sufficient context while questioning my confusion and miscomprehension. Please advise if this can be improved or pruned.
Source: The Legal Analyst, Ward Farnsworth

p 176: A final example involves the use, against people suspected of terrorism, of coercive forms of interrogation—physical and mental pressure that falls short of “torture,” though obviously there is a lot of room for debate about where that line gets drawn. One argument against using any such pressures at all is an appeal to the slippery slope: if we get used to putting physical pressure on people, we will become numb to its horrors and dangers and will be inclined then to move on to more aggressive methods that would more obviously amount to torture; or we will start using torture elsewhere—against people suspected of other things, or against people convicted of crimes whom we want to punish regardless of whether they have any useful information. (The “we” here might refer to the police who do the pressuring or to the public at large.) All these things could happen, but it is hard to prove that they will happen.

176. How is the above an example of a slippery slope? Farnsworth submits that 'All these things could happen', so why does it matter whether they will happen or not? Aren't these all truly cogent, coherent reasons, regardless of their probability of occurrence? What's "slippery"?

p 177: A path of this kind, with the right to die expanded in each case, was followed by courts in the Netherlands. The first decision by itself might not have seemed to imply the last one, but each step between them turned out to be slippery. This might have been so because norms of equality—of treating like cases alike—made it hard to draw lines between any two of them; in that case we might question whether it was a true slippery slope or just a case where the implications of the first decision weren’t fully appreciated until later. But it’s also possible that distinctions between these cases are available and plausible yet hard to draw in practice: each case presents heart-rending facts, and judges may not have the stomach or, perhaps, the moral confidence to say that any two of these situations are different enough to deny relief. If so, the result could amount to a true slippery slope: a case where decision two really was not thought to follow from decision one when decision one was made, but did follow from it after all.

177. If in actuality, decision 2 did follow from decision 1, then how's this a slippery slope?

As an addendum, I thought to link to https://philosophy.stackexchange.com/a/4683.

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The argument to a 'slippery slope' lies precisely in the inevitability which is claimed for the final undesirable outcome. Once you step onto such a slope its slipperiness is so great that you cannot achieve the traction or friction which would be needed to stop at some point along the way: you must continue all the way to the bottom.

In 176, "All these things could happen, but it is hard to prove that they will happen" is an argument against the slippery slope: the end is not inevitable, the slope is not so slippery that we cannot stop at some point short of the bottom.

In 177, "decision two" represents the bottom of the slope and "decision one" its top. Even though it "was not thought to follow from decision one when decision one was made", it did in fact "follow from it after all". Once decision one was made, decision two followed inevitably: that is "a true slippery slope".

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The previous two answers are correct and basically answer it. I do want to put a fine point on it, however.

Slippery slopes are typically fallacies. This means that it is not necessarily true, for example, that "if you legalize alcohol" then "everyone will become drunkards."

Slippery slopes rely on a supposed connection between an 'if' and a 'then'. The point the speaker is trying to communicate is that if A happens then B will follow and B is not a desired result. So, we shouldn't do A.

What people fail to realize is that this type of reasoning is typically unsound or that it is typically presented in an unsound way. Because A happens does not necessarily mean that B will happen. While they are trying to prove their argument, they are actually undercutting their own argument and showing that their argument is not sound. People using rhetoric (politicians) or untrained in logic (everyone besides philosophers or mathematicians) typically make this mistake. They neglect to provide additional evidence to support why B will result from A.

There is a caveat however. You CAN use a slippery slope argument soundly. This is possible. It is only possible, however, if you provide a secondary argument that shows how B is a result of A.

If someone said "if we legalize alcohol" then "everyone will become drunkards" and then provided a secondary argument, such as, "and this would happen because alcohol is highly addictive and many people have a genetic weakness to become addicted to alcohol." That would be a very strong argument, indeed. Incidentally, it is the underlying argument that AA programs use to promote abstinence for recovering alcoholics.

The newer version has something that most slippery slope arguments don't have -- it has some evidence. So, the slippery slope might be true. The task, now, is to defeat the secondary argument. If we do that, then we show that the slippery slope is a fallacy.

The argument, however, as stated, is still false. Simply because some people have a genetic disposition to become alcoholics does not mean that all people will become alcoholics -- that's just basic predicate logic.

The next few paragraphs will rehash what other people already said, but I'll tie this up.

The first paragraph is a criticism of the argument, saying that the speaker is using a slippery slope fallacy and that the connection between 'we shouldn't torture' and 'becoming desensitized to torture' are not connected. Additionally, there is no secondary argument to support that 'we shouldn't torture' is connected to 'becoming desensitized to torture'. The author's shorthand way of saying there is no connection is by using the term 'slippery slope' (fallacy).

The second paragraph is saying that Netherlands, indeed, went down this path and each successive court case seemed to allow more torture or, perhaps, weakened prohibitions against torture. The author poses a question, then, that even though the argument was phrased as a slippery slope (in a fallacious way), without additional supporting argumentation, that it might have been the correct argument.

In my humble opinion, I'd say that the desensitized argument could have been strengthened and avoided the 'slippery slope' criticism. By saying that if we don't define exactly what torture is or isn't beforehand, then it will be the case that successive court cases may have to define what torture is ad hoc. That may lead to courts possibly authorizing interrogation techniques that go beyond simple physical or mental pressure.

Sources:

Wikipedia provides a decent definition. I'm unsatisfied with it because it talks around the slippery slope fallacy (and its sound version) without giving details and examples of the fallacy (or, by contrast, of its sound version). It also doesn't talk about why slippery slopes are typically fallacies.

P.S.: Another poster used the example of "A House Divided" speech. You will notice that Lincoln uses a slippery slope argument. It makes a strong argument because Lincoln provides reasons why the country will either become all free or all slave. It's implied but the implication is that, because of the incessant political fighting in Congress and within the States, the fighting among the territories, Dred Scott, the Nebraska doctrine, and the occasional bloody armed skirmish, tensions were escalating drastically and the country was turning into a pressure cooker. It was conceivable that the fighting would result in the pro-slavery faction ending the conflict by making slavery legal across the United States and its territories or that abolitionists would do the same.

To further strengthen his own conclusions, Lincoln then offers examples and more arguments of why the slippery slope is a cause for concern -- he isn't simply just stating the slippery slope. I'll leave it to you as an exercise to reconstruct those arguments.

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Over the last 75 years, several organizations have used "slippery slope" strategies to achieve their goals. Looking back, it is obvious that many of these groups did this deliberately.

Their opponents tended to point out the slippery slopes, usually when opposing the intermediate steps. In almost every case, the proponents yelled "slippery slope fallacy", and tried to make their opponents look like paranoid reactionaries. Ironically, the opponents were right about the slippery slopes -- but still lost politically. In a few cases, dire consequences (predicted by the opponents) not only occurred, they undid the "desirable" effects sought by the proponents.

Sometimes, there are slippery slopes acting in opposite directions simultaneously. A modern American example is efforts to register/regulate/buy back/prohibit various kinds of guns, versus efforts to allow most adults to carry concealed weapons. An older example was the expansion of slavery, versus the abolition of slavery, in mid-1800s America. Abraham Lincoln's "A House Divided" speech analyzes the slippery slope of expanding slavery; his "Cooper Union" speech discusses measures to restrict slavery.

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