The laws of logic are believed to be the basis of rational thought. But what grounds logic itself? Surely logic cannot be grounded in logic, for that would be circular reasoning, and therefore illogical. Yale Professor Jacob McNulty argues there is no logical foundation for logic. Instead we should look to Hegel for a solution to this dilemma, according to which logic is derived from metaphysics.

Consider logic, the area of philosophy traditionally tasked with identifying the most basic inviolable laws of rational thought: for example the law of noncontradiction; or modus ponens (“if p, then q” “p” therefore “q”). What justification could one give for logic? The question leads to a dilemma.

One horn of the dilemma is vicious circularity. Suppose the justification we give takes the form of an argument. But logic’s laws are presupposed by every rational argument. Hence, any argument we might give for them would be viciously circular.

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One thing is clear: the law of noncontradiction is not self-evident.

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The other horn is complacency. Having abandoned the way of rational argument we might pursue an alternative form of justification: the way of self-evidence or brute fact. This is essentially the method Aristotle tried. He suggested that we could simply dismiss anybody who questioned the law of noncontradiction. This second approach is by far the more common in the history of philosophy (and today). Yet this type of justification also leaves something to be desired.

Aristotle may not have known of serious challenges to the laws of logic, but we do. Paraconsistent logicians and dialetheists (believers in true contradiction) insist that the law of noncontradiction admits of exceptions: among them commonplace phenomena like motion and thresholds. They also employ nonclassical logics to resolve paradoxes. They further reject the idea of “explosion,” which warns that from a true contradiction anything follows.

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The problem that has arisen here is sometimes called “the logocentric predicament,” the problem of how to justify logic without already relying on it.

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Whether the paraconsistent logicians are right or not, one thing is clear: the law of noncontradiction is not self-evident. Not to them anyway. So much for this second approach.

The problem that has arisen here is sometimes called “the logocentric predicament,” the problem of how to justify logic without already relying on it. The logocentric predicament is important to early analytic philosophy, particularly to Frege and Wittgenstein.