Trivialisation, Explosion, Incoherence and Absurdity
Let’s explore the rule of trivialisation. A notable instance of this rule is explosion, which posits that everything follows from a contradiction. Encountering a contradiction under this rule means that all propositions become true, leading us into the realm of the trivial theory—which is universally regarded as undesirable. This stringent intolerance to contradiction has driven philosophers to develop convoluted theories, which I refer to as “mailboxes” in Logic in the Wild--you'll have to read it to understand why. Increasingly, many have come to recognize that completely avoiding contradictions is an impractical aim and have consequently rejected the rule of explosion. Acknowledging that some contradictions are inevitable necessitates the abandonment of explosion, lest the trivial theory take hold.
Accepting inevitable contradictions, however, complicates logical application, particularly in deductive contexts where validity reigns supreme. The challenge arises because there are few clear alternatives to consistency as a metric of coherence in deductive logic. Yet, no one endorses the trivial theory, but how are we to know whether a given logical theory implies everything or not? If avoiding contradictions entirely through explosion were feasible, we might possess at least one candidate for a non-trivial logical theory.
Rather than merely searching for a new measure of coherence, I propose an application-oriented reformulation of trivialisation: a theory is trivial if it is incoherent. Absurdity might serve as a useful metric for trivialisation, though it is challenging to define precisely. What constitutes an absurd theory? In Logic in the Wild, I talk about Camus’ myth of Sisyphus and how, while it is not contradictory, is an absurd story which he uses as an analogy to the futile quest for the meaning of life. However, does pondering life’s meaning necessarily lead to trivialisation? That remains uncertain.
Consider other illustrations of absurdity like bringing a knife to a gunfight—a clear mismatch between action and expected outcome, or David Lewis’ resolution of the grandfather paradox in time travel theories. These scenarios are absurd but not contradictory. They don't lead to everything becoming true, but rather highlight how some scenarios, while possible, are implausible.
As I reflect on these ideas, I suggest that perhaps the generalisation of explosion that aligns with the framework of Logic in the Wild is the assertion that “incoherence is bad.” If logic serves as the guardian of coherence, then naturally, incoherence is undesirable. This view extends the understanding of explosion from mere inconsistency leading to triviality (which is bad) to considering whether absurdity itself might represent a form of incoherence. This reorientation allows us to engage with the question of trivialisation on a different plane.
