It is certainly disturbing to see how many people prefer a convenient lie over a disquieting truth. But more importantly, we should make note of how many people will flee in abject terror to the warm, terroristic embrace of a convenient lie when confronted with an indisputable uncertainty, the unavoidable knowing that you do not know. I should get that tattooed somewhere … somewhere where no one will ever see it …

There is a formal structure to at least some kinds of disruptive uncertainty, and that structure is not all that hard to understand. I’ll mostly be discussing that logical structure, which often requires a kind of patience with inconsistency. But I will turn to the psychological issues of those who embrace inconsistency without thought at the end. What I wish to address here are kinds of inconsistency, most importantly noting that there are genuinely and importantly different kinds. I’ll mainly draw on investigations by Nicholas Rescher and Robert Brandom, coupled with developments by Jon Barwise and John Perry.

A few words need to be said up front about the idea of “inconsistency” &/or “contradiction.” These occur when a person variously and simultaneously asserts some proposition, call it “P,” and that proposition’s negation, “~P.” When they are simultaneously asserted, one has “P & ~P”, and traditional logic (going back at least as far as Aristotle) holds that this is absolutely unintelligible, while more contemporary formal logic has a proof that from a contradiction one gets a catastrophic “explosion” where one can prove any arbitrary claim (regardless how nonsensical) whatsoever. The problem with this position is that people can and do entertain inconsistent claims all the time without ever collapsing into nonsense or believing any arbitrary notion whatsoever This is not due merely to psychological laziness &/or slovenly logic; rather, this is an actual, and even essential, component of any logically defensible (such as in “scientific”) inquiry. But it does invite misunderstanding.

For one thing, the dogmatic “explosion” account of inconsistency is much more in the way of a “just so story,” than an actual account of how people reason (much less how they ought to reason.) For example, through the 18^th and much of the 19^th Centuries, the account of the infinitesimal calculus – developed independently by Sir Isaac Newton and Gottfried Wilhelm (von) Leibniz – required that one swallow a particularly gross contradiction about the nature of infinitesimals. That contradiction required that one simultaneously accept that infinitesimals were too small to have any meaningful, additive effect (“P”), but yet they could, with infinite additions, add up to just such effects (“~P”). Graham Priest and Bryson Brown analyze this situation using the above mentioned tools of Rescher and Brandom (See, “Chunk and Permeate, a Paraconsistent Inference Strategy. Part I: The Infinitesimal Calculus.” Unfortunately, this is behind a paywall, so unless you’ve access to a research library, I cannot help you.)

The basic idea is that you have a proposition “P” that is true in a “world” (more on this shortly) “w1”, while “~P” is true in world “w2.” Normally these “worlds” would be separate representations of ways things could be possible, or possibly true. But suppose in this instance w1 and w2 overlap a little, specifically at P and ~P?

Well before going further I must pay off my debt, and explain a little bit more about what these “worlds” – more precisely, “possible worlds” – really are. As originally postulated by Saul Kripke, “possible worlds” was just a figure of speech for complete and consistent formal models (collections of propositions that include all of the logical deductions from the base set of propositions, and are fully consistent such that if P is a member of the collection then ~P is excluded, and vice versa) that provide a fully developed, logically robust picture of a way the world might be. One could vary one or another of the basic propositions (switch a P to a ~P, or a ~Q to a Q) and then build up an alternative model, a different “possible world.” These various models could themselves then be embodied in a “meta-model” (my term) in a number of different ways, each variation of such connecting and relating in turn developing a different set of deductive relations around the nature of “modality” (possibility/necessity). (Some people argued that we should take this talk of “possible worlds” literally, rather than figuratively, a move that has always struck me as the most fatuous nonsense-on-stilts imaginable. But in philosophy we’re supposed to show respect to all ideas, even when they are galactically stupid.)

So Rescher and Brandom in an abstract setting (and Bryson and Priest in a more concrete one), postulated that these “worlds” might intersect, and that intersection could comprise a contradiction. But they further argued that such contradictions could be manageably “quarantined” so that the “explosion” mentioned above does not occur. And, as Bryson and Priest show, such a quarantine actually occurred, and held in place for some 150+ years, while scientists continued to refine the nuances of Newtonian mechanics all within the contradictory paradigm of infinitesimals.

But “worlds” are too big for this kind of consideration – “worlds” are totalities which, in themselves, have no gaps nor any overlaps. Trying to force such things upon “worlds” implies the existence of a “meta-world” which is the “real” totality, making all the “world” talk both distracting and superfluous. What we need is something smaller, and this is where Barwise and Perry come in. Rather than “worlds,” let us talk about “situations.” Situations need not be complete, nor need they be consistent, especially if the elements of the situation break out in “sub-situations” in a variety of ways, many of which ways will depend on perspectives and purposes. “Situation” is a technical term not only for Barwise and Perry, but for John Dewey, as he details in his 1938 Logic: The Theory of Inquiry. In the pursuit of an inquiry, an inconsistency need not lead to a catastrophic explosion, but rather to a creative tension. This last is actually a moral term, one that Dr. King was fond of:

“(T)his is the very purpose of direct action. Nonviolent direct action seeks to create such a crisis and foster such a tension that a community which has constantly refused to negotiate is forced to confront the issue.” (My emphasis.)

It is worth noting that, according to King, inquiry is the first step in any direct action campaign, to determine if a real injustice was present. In inquiries more broadly construed (and recall that logic is the theory of inquiry), such tensions as are found in inconsistencies are not catastrophes to be denounced and swept away, but opportunities and demands for further inquiry to resolve the source of the tension. This is, in abstract, what a direct action campaign is in concrete.

Thus, the tension around infinitesimals did not prevent the science of Newtonian mechanics from developing, even though it took 150 years for the Cauchy-Weierstrass ε/δ (“epsilon/delta”) method of taking simultaneous limits to come along and set the contradiction aside, and another hundred years after that for Abraham Robinson’s model-theoretic approach to show that, properly understood, there was never a “real” contradiction in the first place. The inconsistency quarantined, inquiry proceeded until multiple – and irreducibly different! – solutions were found.

Which brings us back to foolish consistency. People do like to misquote and misunderstand Emerson on this point, but that is an argument for another day. Right here, the foolishness can be found in two forms: That which panics at the mere thought of inconsistency, and that which sanguinely accepts inconsistencies without ever permitting them to create the tension that will lead to further inquiry. This latter is the far more disturbing, because it is the method of the fascist and the authoritarian; it is the method of the Butthurt-Baby Elect, and his Blackshirt enthusiasts. For these people, no lie is so extreme that they won’t cheerfully “reconcile” it with their inconsistent ideology. At no point will the thought of engaging in further inquiry ever occur to such people, because at no time does thought of any kind occur to them. This is not just a breach of logic, it is a moral violation of the possibility of intelligence.