Christ is a walking contradiction. He is both fully human and fully divine. Indeed, he is both mutable and immutable. According to classical logic, the existence of a true contradiction would imply that everything is the case, no matter how absurd. And so, theologians and Christian metaphysicians have worked for centuries to conceptually make sense of Christ’s dual nature in a way that avoids contradiction.
Philosopher and logician Jc Beall argues that these efforts have been motivated by a naive understanding of logic. There are “subclassical” logics – that is, logics weaker than classical logic – in which contradictions do not entail every arbitrary conclusion. And these aren’t ad-hoc constructions. Beall argues that one subclassical logic – called First Degree Entailment (FDE) – is, in fact, the correct account of logical consequence, for reasons independent of the Christian problem. Beall covers the basics of how FDE works and why it is the universal or “basement-level” consequence relation. This allows us to have our cake and eat it too: we may take Christ to be, quite literally, both mutable and not mutable, at the same time and in the same respect. This isn’t just appealing for its simplicity. Beall suspects that it is essential to Christ’s role that he be literally contradictory.
If you’re interested in Jc Beall’s work and non-classical logic, check out my interview with Greg Restall (part 1 and part 2) on the book Logical Pluralism, co-authored by Beall and Restall.…
In Part 1, we disambiguated between the logic that we intuitively use (hereafter “intuitive logic”) and systems of logic. Systems of logic codify a set of rules of entailment. That set of rules may or may not accurately represent the rules involved in intuitive logic. Logic selection is the process of finding a set of rules that does.
You might think of it this way: there are many systems of geometry. There’s traditional Euclidean geometry, but there are also various non-Euclidean geometries. No one of them is any more a geometry than any other. To choose between these geometries, we need to match up their rules against what happens in the type of space we want them to represent.
So it is with logic. To choose a system of logic, we need to match its rules of entailment against the rules of intuitive logic.
Of course, the process of logic selection cannot be a merely logical one. That would presuppose what we’re looking for. We can (must) use intuitive logic in the selection process, as we use it in all our reasoning. But we can’t use any formal system of logic. So, what do we use?
The selection criteria
Logician Graham Priest presents a theory of logic selection in this video. Priest argues that the process of theory selection is always the same, whether you’re selecting a theory of logic, physics, or economics. The selection criteria are as follows:
Agreement with data
Power (how much data it accounts for)
Relevance (avoidance of the ad-hoc)
Agreement with data is always the most important criterion.…