The “slippery slope” is the fallacy (if it is a fallacy – some might dispute that!) that says certain actions cannot ever be taken because they lead to other actions, which make still other actions possible, etc., leading finally to some kind of catastrophic action which can no longer be denounced or argued against because of all the little steps that led up to it and gave it permission. It is a frequent traveler with those who would argue against any sort of incremental changes to social institutions or the guarantee of civil rights. Thus, we’ve seen a great deal of slippery slope “reasoning” amongst conservatives denouncing marriage equality, with such claims being floated as, “If gays are allowed to marry, what is to prevent people from marrying farm animals, or young children?” (I’ll not link to any such claims; if the rock you’ve been hiding under these past several years has kept you shielded from such nonsense, I will not be the one responsible for breaking your bubble.)

What inspired me to write about this now was my recollection of how this fallacy relates to the famous sorites paradox: Sorites: noun so·ri·tes \sə-ˈrī-(ˌ)tēz\ The paradox (if it is a paradox) rotates around the question of how trivial actions, too small to have any consequence of their own, nevertheless can sum up to be massive and absolute distinctions. So, in a sense, slippery slope is going down the hill, while sorites is going up it.

The sorites paradox is often exemplified with a full head of hair, a beard, or even a horse’s tail. Pluck out a single hair, and you still have a fulsome head or tail. So you pluck another hair, and so on. Now, since the number of hairs on any head or tail will always be finite, eventually there will be no hairs left. But at what “point” did the head or tail become bald?

The question, as posed, is, quite honestly, rather foolish. It is playing on some assumptions of traditional logic and the use of predicative terms like “bald” to demand an absolute, black-or-white distinction between a full head/tail of hair, and a completely bald one. Speaking as a man approaching 60 years of age, whose hair line used to be much closer to his eyebrows than it is now, “bald” is an end state, but balding is a process that can go on for some time. Unlike balding, “bald” is what is known as a “monotonic” term – there is neither growth nor diminution of meaning no matter how repeatedly the term is used. Monotonic logic is easy to formalize, because there is nothing at the end that was not already at the beginning. So, for example, ((IF a IMPLIES b) AND (IF b IMPLIES c)) THEN (a IMPLIES c), is a standard rule of orthodox logic (basically, it says that “IMPLIES” is transitive.) This can be formalized thus:

((a → b) & (b → c)) → (a → c)

The monotonic “law” of transitivity says that the above can be extended without bound. Thus, according to monotonicity,

((a → b) & (b → c) & … & (y → z)) → (a → z)

with the ellipsis possibly covering many more claims then there are letters to represent them. Indeed the “law” of monotonic transitivity (let’s just call it the “law” of monotonicity) says that, given those premises collected together with those “ands” (the “&” symbols) then it is necessarily the case that (a → z) is true.

The problem with monotonicity is that it is an abstract, if not downright recondite, rule that has little or nothing to do with the actual world. Of course meangings grow and diminish; we see this all the time in our own lives, to say nothing of the documented span of human history. In order to allow reality some purchase on our reasonings, then we have to acknowledge that monotonicity is not a “law,” and it is only a usable rule of thumb under the most limited of circumstances. The non-monotonicity of the real world tells us that, even given the above premises, not only is (a → z) not necessarily true, it is quite possibly false. (For reasons I’ll not pursue here, I do not treat those two conditions as identical, the way modal laws of monotonicity do.)

Let’s bring this back now to slippery slope. Slippery slope arguments and arguers generate their grandiose “sturm und drang” from an uncritical and unqualified acceptance of monotonicity. They assume (though seldom make this assumption explicit) that if you take an infinitesimal step, then you must also take infinitely many of those steps. This is typically accompanied by a substantial amount of histrionics.

But how serious a problem is this, in the real (and really non-monotonic) world? Are dogs and cats really going to be living together? Are small children really going to have no protection from sexual predators? All because same-sex marriage is finally made legal, or some equally incremental acknowledgment of basic human and civil rights?

Such wild-eyed nonsense is predicated on the reasonless notion that thought and intelligence amount to nothing more than the mechanical application of simplistically mechanical rules. Within the entire scope of human experience (to say nothing of variously known history) there is nothing that could provide a justification for such an assumption. Yet as formal logic was rendered increasingly mechanical – by the revolutions imposed on the subject by people like Frege, Russell, and Hilbert – so too did the dogma of mechanical reasoning become further entrenched in at least some circles. To be sure, slippery slope fallacies are at least as old as human writing, so the generally unexpressed assumption of mechanical reasoning has been around far longer than the actual possibility of mechanically expressing such reasoning ever was. This fad in logic and philosophy is passing, but only slowly. The problem (as far as formal logic goes) is that talking about “things” is formally much simpler than talking about meanings. (This corresponds pretty directly to the differences between external versus internal forms of relatedness, that I’ve discussed elsewhere. Filling out this connection is, however, a task for another time.) Because talking about actual meanings is hard, most of those investigating logic and philosophy in the 20^th Century abandoned such inquiries as lacking any merit.

Leaving us with the vacuous theatricalities of persons who will say and do anything rather than deal honestly with issues of basic human rights (among other things). The thesis of monotonicity – which the slippery slope arguers embrace without qualification, or even the first clue what the term might mean – takes it for granted that neither thought nor intelligence are, in even the littlest, little way, generative or productive; for this thesis, and the people who embrace it unthinkingly, repetition exhausts rationality. Such repetition is what monotonicity means.

The reason people won’t be marrying animals or legally taking small children as their sex toys – because same sex, rational agents, capable of rational choices are allowed to do so – is because intelligence is not a machine, but a living process. Permitting rational agents the rights they’ve always had (but never were permitted) is not the same as attacking rights across the board. It is only through the thoughtlessly mechanical application of rules – rather than the living, thoughtful process of judgment – that the slippery slope ever appears to gain traction.