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.

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In recent work I have explored the problem further with help from an unlikely source: Kant and his German idealist followers. None was a logician, in any technical sense. Still, the projects of all can be illuminated through the logocentric predicament.

This approach also clarifies one of the most vexing developments of the idealist period: the return of metaphysics. I mean that ambitious area of philosophy which strives to know God, the soul, the world. No sooner had metaphysics been declared moribund by Kant when it seemed to have revived by his idealist successors. This is especially true of Hegel with his project of Absolute knowledge and his talk of the world spirit. How could this stunning reversal in the fortunes of metaphysics occur? Some readers of Hegel sidestep this question by reading him as a less robustly metaphysical thinker, e.g. a pragmatist. I take a different tack.

The story I tell begins with Kant. Kant chooses the well-trod path of regarding the laws of logic as justified in a default way. Not that Kant’s views in logic are unsophisticated. He has an interesting “constitutivist” conception of logic’s laws: in other words he thinks logic’s laws are the ones a certain faculty in us would obey if unconstrained by any other (imagination, wish, desire). Kant’s conception of logic has been accused of psychologism: the error of collapsing logic into empirical psychology. Doing so elides the distinction between how people ought to think and how people in fact do. This accusation is unfair. Even so Kant seems fairly complacent about logic. Notoriously he praises it for having attained completion so early in its history. Unbeknownst to him logic would be revolutionized by Frege and others in the latter half of the 19^th c.

This problem in Kant cannot be easily contained, at least from the point of view of some of his idealist critics. For Kant’s view that logic is unproblematic is hard to reconcile with his project of “critique.” Critique insists that all areas of philosophy and the sciences justify themselves at the bar of reason. In Kant’s critical philosophy, all are summoned “the courthouse of reason” to defend themselves. All must prove that they do not go beyond the human mind’s proper bounds. Famously, metaphysics fails this examination (though it gets a second chance in the moral domain).

Why, then, does Kant exempt logic from critique? Why is he content to appeal to it throughout his critique at crucial junctures? To the extent Kant is complacent about logic this lapse in scrutiny is one in self-scrutiny. That is because Kant’s own standpoint relies on logic throughout: Kant’s “categories” and “ideas,” for example, derive from logic. If the standpoint of critique relies on logic, then so too will the Kantian critique of metaphysics. Logic is a point of vulnerability for Kant. That point of vulnerability is one Kant’s subsequent critics exploit.

Already in his preface to an edition of Kant’s logic lectures, Benjamin Jäsche wondered why Kant had not sought to deduce the laws and materials of logic from some more fundamental principle. Jäsche was no doubt wondering this because of J.G. Fichte, one of the first German idealists, whose reconstituted version of Kant’s system began with a deduction of the laws of logic.

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For Fichte, self-consciousness itself was bound up with the law of identity, A=A, itself a version of the law of non-contradiction: A≠-A. Kant had hinted at connections between self-consciousness (apperception) and logic but not spelled them out. Fichte did so via an argument that begins from something many have noted about logic: its curious emptiness.

Rightly understood, the logical law of identity is a conditional: if there is A, it is A. As far as logic alone is concerned, the universe is empty. Yet self-consciousness could populate this universe when it declared, like Descartes had in his cogito, “I think…I am.” Fichte belongs to a post-Kantian generation skeptical of Cartesian rationalist metaphysics and its claim to prove we know ourselves to be simple, immaterial, soul-substances. Still, Fichte employs a more modest version of the cogito, one closer to Kant’s principle of apperception (“the I think must be ably to accompany all my representations”) in his opening argument – and links it to logic. I think that Fichte’s deduction is falsely advertised, not so much a deduction of logic from apperception as a demonstration of their equiprimordiality.

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Hegel thought philosophy ought to begin elsewhere: not with the indubitable or certain but with the conceptually primitive.

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Hegel’s solution, in his Science of Logic, differs. It is both more radical in its approach to the logocentric predicament and more un-Kantian in the use it makes of metaphysics.

Though he concedes that Fichte’s post-Kantian cogito was certain, Hegel thought philosophy ought to begin elsewhere: not with the indubitable or certain but with the conceptually primitive.

To see why we should recall that certainty only applies to items with a certain sentence-like structure: for example “I think…I am.” Yet items with this structure are complex. They are composed out of concepts: “I” “thinking” “being.” Hegel’s objection to Fichte, in essence, questions whether he is justified in deploying the concepts that make up his first principle. For Hegel, even a knowledge-claim that is certain may take the meanings and uses of certain concepts for granted. To many readers a principle like Fichte’s starting point, one like Descartes’ Cogito or Kant’s “I think” epitomizes reason’s ability to reflect on and criticize itself. Yet for Hegel this starting point is unacceptably dogmatic.

Hegel’s Logic therefore begins with being. Every other concept is the concept of a being, though the reverse is not necessarily true. Being is conceptually primitive but not certain. In fact it is self-undermining, vulnerable to the form of internal inconsistency that is at the center of Hegel’s dialectical method.

To the friends of Being, like Parmenides and Spinoza, it appears something quite formidable. It is indeterminate being, not determinate. It simply is. It is not any determinate way (tall or short, black or white, bitter or sweet. Seen in this light, indeterminate being might seem like something more than all the determinate (particular) objects and properties in the world. It might seem like a massive all-encompassing thing that Spinoza called substance. Seen in this light it is a definition of God or of the Absolute. But another legitimate conclusion to draw would be that Being is actually something less than than it appears. For if it lacks any determinate properties, this much vaunted Being could just as well be nothing at all.

Unlike Fichte’s cogito, which stands firm, being self-undermines. Yet like the “fortunate fall” of Adam and Eve’s expulsion from the garden this is a loss that turns out to be a gain (Hegel was an admirer of this theological idea). This self-undermining dynamic drives Hegel’s dialectic onward into new territory. Understanding how helps us see Hegel’s solution to the logocentric predicament.

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The laws and materials of traditional logic cannot be primitive. They must be derived.

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The subject-matter of traditional logic appears late in Hegel’s Logic. Identity, contradiction, judgment, inference – all come in for consideration only in the second and third divisions of the work. This is not simply a matter of presentation. It reflects the order of argument. If that is so then the laws and materials of traditional logic cannot be primitive. They must be derived.

All of this, to me, suggests that Hegel is a partisan of the first approach to deducing the laws and materials of logic: the way of argument with its risk of vicious circularity. True to form he takes the more ambitious way. How, then, can Hegel avoid being impaled on the second horn of the dilemma?

While there is not space here to explain Hegel’s deduction in detail, I note the following. Hegel’s logic has a master-argument, one he describes in terms of a movement from “immediacy” to “mediation” to a standpoint that combines (synthesizes) both. Hegel will takes us from principles that are singular or monadic to others that are dual or dyadic and, finally, settle on ones that are triadic.

Let me explain just one phase of the argument. The monadic principles are those we consider at the start of the logic (being, nothing, becoming). Each claims self-sufficiency, or in Hegel’s terms “immediacy.” Each characterizes its object as being what it is independent of its relation to anything else. Yet this claim to self-sufficiency breaks down for the reason that, as Spinoza said, “all determination is negation” (omnis determination est negatio) All distinction requires contrast. Nothing can be what it is apart from its relation to other things.

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We thus move to a set of principles that are dyadic (cause-effect, substance-accident, whole-part), accepting that things are what they are only in relation. Yet this too proves disappointing imposing dualisms between things that render their interactions unintelligible. The stage is set for a third way.

Based on this mere sketch of Hegel’s argument we can glimpse something important about his approach to our problem. Notice that logic’s laws and materials are all absent from the first part of the logic, which treats monadic principles. Hence these early principles are available to serve as the basis for the laws and materials of traditional logic. Laws like noncontradiction and principles like the form of inference only appear later, in the dyadic and triadic parts respectively. Crucially Hegel never simply abandons the earlier in favor of the later. The later always “sublates” (transcends but incorporates) the earlier. The hard question for Hegel of course is why the problems that drive the dialectic onward are not in some covert way logical problems. I try to show that they are not in my recent book.

Hegel’s resolution of the logocentric predicament has an unexpected and un-Kantian result: it offers us a new case for metaphysics (ontology). If Being, Nothing and Becoming are conceptually prior to the simplest logical materials, like proposition affirmation, negation, judgment and inference, then metaphysics is inescapable. The rustic beginnings of Hegel’s logic ontology or theology: ontotheology (the study of the nature of being and of the highest or paradigmatic being). These beginnings lay a foundation for logic.

Readers of Hegel may find my interpretation perplexing. Hegel is famous for claiming logic and metaphysics are the same. I seem to be insisting that one depends on the other. But there is no contradiction here. My interpretation draws on narrower and more traditional senses of the terms logic and metaphysics than is common. Hegel’s system has (formal) logic depend on (traditional) metaphysics.

In placing metaphysics in this “primordial” position, Hegel is drawing attention to a different face of the enterprise. In Hegel’s retelling, metaphysics is thinking taking its first steps, thinking in its infancy and innocence. This contrast with the face of metaphysics displayed by Kant. In Kant, metaphysics is something more scholastic, inflated in its sense of what it can achieve, bold or even brazen in its use of principles like the Principle of Sufficient Reason. All of which is to say that, as his readers often emphasize, the metaphysics Hegel defends is ancient metaphysics, not modern scholasticism. No wonder then that Hegel describes the opening of his logic as coinciding with the pre-Socratic period and with Parmenides.

And there is a corresponding shift in approach to logic, which will no longer be empty or devoid of information about the world. It will be contentful.

There is more to the story, of course. Indeed the story contains an ironic reversal of the kind familiar to students of Hegel’s dialectic.  After all Hegel is the inspiration for dialetheism and paraconsistent logic, as present-day proponents like Graham Priest acknowledge. As I read Hegel a defense of the idea of true contradiction is one of his Logic’s main results. However this reformism is consistent with the basic project I have described here. One can only challenge something whose justification one already understands. Hegel’s approach nearly always combines constructive and destructive phases.

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Nobody is likely to consult German idealism for cutting-edge technical results in the field of logic anytime soon. Yet I think Fichte and Hegel have interesting perspective to offer on the philosophy of logic.  Alongside their views in philosophy of history, aesthetics and politics, the German idealists’ daring attempt to resolve the logocentric predicament deserves our attention.