Logic

Are so-called "slippery slope" arguments effectively appeals to modus tollens?

Comments

I'm not sure that there's any single standard form for a slippery slopeargument, so let's look at just one, a "sorites" or "heap": If I havea heap of stones and remove just one of them, I still have a heap. Repeating that, I will always be left with a heap. But, obviously, atleast when I remove the last stone, I no longer have a heap. Therefore...

Well, therefore, what? A heap of stones is equivalentto having no stones at all? Suppose so. That's "obviously" incorrect,so (a) the original premise or (b) some step in the argument must havebeen wrong.

Suppose (a). Then a heap of stones with one stone removedis not a heap. This does indeed seem to be an application of modustollens, which is the inference rule that says: From "p implies q" and"not q", you may infer "not p". Here, p is our original premise, q isthe conclusion of the slippery slope.

But (b) it could be that there'snothing wrong with either p or with q, but that what's wrong isrepeated application of stone-removal. In that case, it's not so clearto me that modus tollens is the best way of explaining what's going on.

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