Figleafing and informal \(\omega\)-inconsistency

content warning: racism.

Liam Kofi Bright identified an interesting informal fallacy a couple of years ago he called 'informal omega-inconsistency'. In committing this fallacy, the speaker claims that there are things satisfying a certain property \(\phi\) but consistently denies that particular members of the domain satisfy \(\phi\). An example he gives is the speaker claiming that there are bad drivers in Pennsylvania, but denyies that any particular case of putative bad driving in Pennsylvania you present to them is down to a bad driver.

Until the speaker exhausts the domain (claims \(\neg\phi x\), for all \(x\in D\)), they are not inconsistent. The fallaciousness comes not from actual inconsistency but a sort of potent inconsistency: from its being 'apparent that this is a matter of policy, that this is how the person always responds to apparent instances of the general claim being made' (Bright). (We can think of it in terms of the conditional if the speaker were to evaluate \(\phi x\in D\), she would claim it's false.)

I want to highlight an interesting way of committing this fallacy. In the case of informal \(\omega\)-inconsistency, the reasoner prototypically wants to assent to an existential claim without assenting to what it entails (that some particular member of the domain satisfies the property): \[\not\omega_\Sigma := \exists x.\phi x.\land\neg\phi d_1\land\neg\phi d_2\land\neg\phi d_3\land\ldots\]

But one can also commit this fallacy by seeking to deny a universal claim without assenting to the presence of counterexamples to it:\[\not\omega_\Pi := \neg\forall x.\phi x.\land\phi d_1\land\phi d_2\land\phi d_3\land\ldots\]

Due to quantifier interdefinition the two formulations are biconditional,¹ but they have distinct rhetorical characters. A particularly interesting example of \(\not\omega_\Pi\)² comes from Donald Trump's infamous remark about immigrants to Usonia from Mexico:

When Mexico sends its people, they're not sending their best ... They’re bringing drugs. They’re bringing crime. They’re rapists. And some, I assume, are good people.

Trump assigns to Mexican immigrants the property \(\psi\) of bringing drugs or bringing crime or being a rapist. The absence of a quantifier raises ambiguity – in isolation, we'd normally take this to be claiming that all Mexican immigrants satisfy \(\psi\). But he then claims 'and some, I assume, are good people' – so \(\exists x.\neg\psi x\), which is flatly inconsistent with \(\forall x.\psi x\). Trump thus implies that \(\neg\forall x.\psi x\) but generally \(\psi x\). (This is equivalent to \(\not\omega_\Sigma\) with respect to \(\neg\psi\) on the same domain.)

Presumably, for each particular \(x\in D\), he would assent to \(\psi x\). He would then meet our conditional test for \(\not\omega_\Pi\), here if the speaker were to evaluate \(\psi x\in D\), she would claim it's true. So here Trump commits the fallacy of informal \(\omega\)-inconsistency in its universal form.

Jenny Saul has analysed the sort of remarks above in terms of figleafing, a device by which the speaker supplements otherwise overtly racist (&c.) remarks with a remark which raises ambiguity, doubt, and/or ensures plausible deniability (a 'figleaf', which only just covers the racism). One of the simplest (and least effective) examples is 'I'm not racist, but ...'.

Nigel Farage on BBC claiming he isn't racist, but ...

The Trump example above is a highly sophisticated one. Trump isn't merely supplementing overtly racist remarks with the claim that he isn't racist (or something meant to imply it), but is implicitly denying the racist claim he at first seems to be making (that Mexican immigrants (qua Mexican immigrants) all satisfy \(\psi\)). The figleafing is being deployed at the logical level – it is integrated in the very claims it seeks to cover.

Informal \(\omega\)-inconsistency, then, can constitute a very sophisticated figleaf by allowing the speaker to in effect appear to have it both ways. They can make a claim³ without really having to assent to it. (In the Trump case he claims that \(\neg\forall x.\psi x\) but isn't bound by its implication that there's some particular \(x\in D\) which doesn't satisfy \(\psi\).)

An interesting connexion Bright notes is to the 'no true Scotman' fallacy: (\(\not\omega_\Sigma\)) of course there are Scots who might commit brutal murders as the English do, (but Nicola Sturgeon, Carol Ann Duffy, ... wouldn't)

Notes

1. Demonstration left as an exercise!
2. Bright's example of \(\not\omega_\Sigma\) is racism (do read his blog post).
3. In \(\not\omega_\Sigma\) an existential claim; in \(\not\omega_\Pi\) a universal one.