The Liar Paradox and Presuppositional Apologetics
So Pat Mefford has raised an objection (here, here, and here) to Chris Bolt’s presentation of VanTilian Presuppositional (sometimes voguely referred to as Covenantal) Apologetics. Chris asked Pat for clarification, then responded here and here. Pat raises the “Liar Paradox” as an objection to Chris’ account of logic, specifically the Law of Non-Contradiction (LNC), as grounded analogically in the divine thoughts.
(His original objection was that Chris was “smuggling” classical binary logic into his account of logical laws – something which Chris’ opponent may not be willing to grant. Instead, Mefford proposed the adoption of Kleene’s ternary logic, which is paracomplete (it denies the Law of the Excluded Middle (LEM), not the LNC). Then he presented the Simple Liar Paradox (i.e. “This sentence is false.”) as the basis for adopting a (presumably paraconsistent) multi-valued logic (MVL). Initially, it was unclear which objection Mefford was proposing: the adoption of Kleene’s MVL (denying the LEM) or the acceptance of the Liar Paradox (denying the LNC). His follow-up posts have focused exclusively on the Liar Paradox, possibly because I pointed out that Mefford’s original argument was self-refuting, since he argued for denying the LEM via disjunction – a philosophical solvent which dissolves itself.)
Laying all of that to the side, I must admit that (despite Mefford’s clarifications) I’m still not sure what the substance of the objection is. To quote Mefford:
In what way does Chris’ simulacrum of God’s divine system answer this paradox? In what way are we thinking God’s thoughts after him when think (sic) of this scriptural passage that was at the top of my original post?… This proposition exists. It is a contradiction. How does it stand in relation to the Triune God? How is this proposition grounded in Almighty God? How does Chris account for it?
To my reading, it seems that Mefford is merely asking for an account of the Liar Paradox from the perspective of the Presuppositionalist (specifically one who holds to a classical, binary logic as Chris does). I don’t see how this is a very significant objection, but that may be a reflection of my poor reading skills rather than Mefford’s argumentation.
For example, Mefford believes Tarski’s semantic conception of truth solves the Liar Paradox. So Chris might say (arguendo, at the very least) that Tarski’s hierarchy more closely reflects God’s thinking with respect to the Liar. (I might suggest to both of them that Saul Kripke’s partial predicate T-schema seems to be a less problematic resolution. Kripke’s construction seeks to maintain classical binary logic with the Liar falling into a “truth-gap,” rather than outside of Tarski’s overly-restrictive semantic hierarchy.) Does this result in some wholesale denial of classical logic? Hardly. It simply provides a semantic “extension” of classical logic which “subsumes the binary apparatus into the new system” (to use Mefford’s own terms). Whether Tarski’s or Kripke’s or some other account is best is irrelevant to answering Mefford’s objection, since the Presuppositional Apologist is only committed to viewing human logics as analogs of divine “Logic” anyway.
Further points to consider:
Mefford’s treatment of Titus 1:12-13 is superficial. To prove this is a biblical example of affirming the Liar Paradox would require Mefford to establish that Paul intends to say that “absolutely every Cretan lies every time he speaks.” It seems much more natural to interpret Paul as hyperbolically generalizing about Cretans, citing one of their own poets as an authoritative source. Chris made this point quite clearly.
For the sake of argument, however, let’s assume Mefford’s interpretation. So Paul says the Liar Paradox is true. This would simply be a proto-affirmation of Graham Priest’s contention that there are true dialethias. This interpretation would put Christians in the minority in the history of Western philosophy, but dialetheism is not as easily refuted as some might like to think. So the Christian might just say that a paraconsistent, non-explosive logic is the most accurate way of thinking God’s thoughts after him. Mefford’s objection is again refuted.
Mefford seems to think that the adoption of a non-classical logic would dull the sharpness of the Classical Presuppositionalist’s double-edged Thesis-Antithesis approach to apologetics. However, he’s never demonstrated why this must be the case, and I’m not interested in doing the heavy lifting for him. To the contrary, the adoption of a classical-logic-with-truth-value-gaps may serve to strengthen the Presuppositionalist’s case in certain ways, a la Peter Strawson‘s conception of presupposition.
However, my intent is not to elaborate on that point right now, but rather to show that Mefford’s dilemma is hornless. Chris could defend classical, binary logic (hardly a losing proposition in my mind) or adopt a non-classical, multi-valued logic without losing any ground to his interlocutor. In my estimation, a VanTilian apologetic could comport with the more classical monaletheism or with a robust form of dialetheism, having a well-formulated paraconsistent logic.
If I get the time, I may attempt to present a reasoned defense of classical logic in this context – or Chris may beat me to the punch; I’d be willing to give it a shot, if others would find such an endeavor useful.
Finally, I find it interesting that Mefford sees the Liar Paradox as “rooted in epistemology and metaphysics,” but does not mention ethics. Being a good tri-perspectivalist, I think there must be some ethical aspects to any explanation for the Liar, which I may also consider at a later date. Remember, lying is a sin…