From Analogy to Paradox: Toward a Metaphysics of Intelligence

Introduction

At least since Aristotle, and especially Thomas Aquinas, analogy has been one of the primary tools of metaphysics. It allows us to avoid both univocity and equivocity. But is it sufficient to account for the way in which the intellect accesses metaphysical realities?

For do not the greatest metaphysical truths first present themselves in a paradoxical form? Such as the paradox of the common being shared by the absolute and the contingent, or the coexistence of unity and multiplicity, of identity and otherness…

We will therefore propose to supplement analogical knowledge with paradoxical knowledge. But moving from analogy to paradox does not mean abandoning the former in favor of the latter: rather, it is a matter of discovering that the paradox was already embedded at the heart of analogy and that, from the perspective of knowledge, it reveals its deepest significance.

Since the question of analogy was significantly revived in the^20thcentury, we will draw in particular on the comprehensive works of Jean Borella. ¹

On Analogy

This is a fundamental question, since “the nature of analogy concerns the very possibility of metaphysical knowledge”². The Greek term analogia combines logos—word, thought, reason, relationship—with ana, whose meanings evoke, in particular, elevation and return. Analogy thus embodies the idea of a vertical relationship between what is “above” and what is “below,” the latter being, in a certain sense, like the former³.

On Symbolic Reality

This verticality first appears in the symbol. A visible reality is “thrown together with” (sýn-bállō) an invisible reality. Unlike the metaphor or the allegory, the symbol does not merely illustrate an external idea: it makes present an essential, intelligible, semantic reality. Its meaning is therefore never exhausted by a particular interpretation⁴.

This symbolic presence can span radically different degrees of reality. The symbol of water, for example, can evoke the primordial waters, informal or formal possibilities, as well as bodily water itself. These levels are not ontologically comparable, but a single symbolic essence runs through them like a semantic transversal.

On Analogical Knowledge

Analogy thus resembles the symbol without being conflated with it. It is by taking on a perceptible form that it becomes a symbol; conversely, the deciphered symbol reveals the analogy that constitutes it. “Analogy provides the key to the symbol”; it is its “meaning” ⁵.

Consequently, if “the symbol is the key to ontology,” ontology itself appears to be fundamentally analogical; moreover, “being reveals itself as analogal” ⁶. Analogy thus becomes the locus of unity and distinction, of essence and existence, of identity and otherness. Its metaphysical foundation ultimately points beyond being, to a meta-ontology of Relation, all the way to the supreme Identity which, beyond Being and Non-Being, is “pure Analogy.” We thus find this unity of being and knowing that Borella refers to as ontonoesis. ⁷

Analogy and its symbolic medium thus admirably describe the structure of reality. But they do not yet fully describe the way in which our intellect discovers this reality. Yet the great metaphysical truths almost never present themselves initially as analogies: they appear to the mind as paradoxes.

This is why a metaphysics of analogy may call for a metaphysics of paradox.

On the Paradox

That contradiction accompanies human experience, in action as well as in knowledge, is an ancient insight: “What is contrary is useful, and it is from what is in conflict that the most beautiful harmony is born,” says Heraclitus.

In what sense is contradiction a source of knowledge, whether scientific or philosophical? Is not all knowledge, to a certain extent, paradoxical? The paradoxical nature of what presents itself to be known—humanity, the world, God—might correspond to a paradoxical nature of knowing itself.

If being presents itself to the intellect in a fundamentally paradoxical structure, approaching it is necessarily paradoxical as well. This paradoxical nature, however, does not yet prejudge Ultimate Reality itself: we shall see that it may belong less to the Absolute than to the mode by which the intellect accesses it.

The Three Types of Paradoxes

Very different situations are grouped under a single term. For our purposes, we can distinguish three main types. ⁸

Paracosmia is a cognitive paradox: the reasoning is valid, but two aspects of reality appear incompatible. Scientific paradoxes provide the best-known examples: Olbers’ paradox, wave-particle duality, or even Schrödinger’s cat—a thought experiment designed to highlight an ontological or interpretive difficulty in the theory.

Paralogy, on the other hand, stems from flawed or specious reasoning. The premises may be correct, but the conclusion does not follow. It becomes a sophism when an intent to deceive is added to the logical error.

Finally, a paradox arises when the data and reasoning are valid, but no rationally satisfactory conclusion can be reached. This is the dilemma proper, of which the Liar’s Paradox is the quintessential example. ⁹

Paradoxes of Reason

Each of these three types teaches reason something.

Paracosmies first remind reason that it is subject to its object. The contradiction between theory and experience is not merely an obstacle: it is one of the driving forces of scientific progress. But the scientific paradox is normally resolved within a new theoretical framework. Science thus remains true to its function: to construct rational and operational knowledge of the world.

Paralogies, secondly, remind reason that it is subject to logic. They become particularly instructive when discourse turns endlessly in on itself, detached from any ontological anchor. Tarski, for example, establishes that the truth of a sufficiently rich language cannot be fully defined within that same language. Without attributing more to this result than it formally states, we can philosophically view it as a sign that truth transcends any procedure that claims to define it entirely from within.

Paralogies thus function like road signs: they warn reason of the risk of transforming its own functioning into the totality of what is knowable.

The paradoxes go even further. Because they remain unsolvable on the level where they arise, they reveal that “infinity of things that surpasses it” of which Pascal speaks ¹⁰. We might conclude, with Kant, that what transcends reason is unknowable. But it is precisely this transition from the limits of reason to the limits of knowledge that seems questionable to us.

One of Kant’s cosmological antinomies illustrates this. To conceive of a world that had a beginning, Kant assumes a “prior time” when the world did not exist. But if a time precedes the beginning of time, then that time is, by definition, no longer a beginning. Similarly, a finite space need not be contained within a larger space: time cannot be limited by another time, nor space by another space. The fallacy thus seems to be already present in the rational formulation of the very terms of the antinomy ¹¹

Here, the paradox acquires its philosophical significance: it can free reason from its claim to constitute the ultimate horizon of the knowable. In the same vein, Gödel’s second incompleteness theorem demonstrates that a sufficiently powerful formal system cannot, under the required conditions, prove its own consistency from within. This points to a non-contradiction that ultimately stems from intellectual intuition and, more broadly, from the contradiction inherent in any project of epistemic closure of the concept¹².

The Paradox at the Heart of Analogy

One might have contrasted two modes of thought: thinking by resemblance—that is, analogically—or thinking by opposition—that is, paradoxically. But this distinction holds only as a first approximation.

If analogy is ultimately a “dissimilar resemblance,” paradoxical opposition is frequently a compatible dissimilarity. The two are therefore less two competing paths than two aspects of the same intellectual operation.

The Platonic doctrine of analogy is paradoxical

Analogy simultaneously expresses difference and unity, otherness and identity. If there is analogy, there is necessarily something other than the Same; but if this other is analogous to it, its distance from the Same is not absolute. Analogy precisely measures this distance ¹³.

The paradoxical dimension appears with particular clarity in *The Sophist*. There, Plato acknowledges that “non-being is, in a certain respect, and that being, in turn, in some way, is not.”

Parmenides’ “parricide” consists in understanding that non-being is not the absolute opposite of being, but the other of being. A man is a man, but he is also not a cat, not a stone, not an oak, and so on indefinitely. Otherness does not destroy his identity; it contributes to its determination. “Identity is inseparable from otherness, and vice versa.”¹⁴

No being, therefore, can be confined to an absolutely closed definition. To be is to be oneself, but also to enter into an indefinite network of relationships with that which one is not. The identity-otherness paradox thus already proves to be constitutive of ontological analogy.

The paradox at the heart of Platonic dialectics

The Line in *The Republic* expresses this same structure through different degrees of reality and knowledge: sensible images, sensible realities, intelligibles grasped on the basis of hypotheses, and finally dialectical knowledge rising to the unhypothesized principle. ¹⁵

The lower degree itself refers back to the higher one. The reflection calls for the model; the image, the paradigm. No sensible reality can therefore be “taken at face value” or isolated in its singularity: even its slightest reality already reveals the analogical structure of the real and invites us to transcend it.¹⁶

Thus, there is no need to choose between analogy and paradox. Since analogy unites a resemblance with a dissimilarity and combines identity and otherness without abolishing either, it is paradoxical in principle. The paradox is therefore not the opposite of analogy: it constitutes one of its dimensions.

Dialectics: Transcending the Limits of Reason

The history of dialectics can thus be read as the history of the tension between reason and intelligence.

Heraclitus observes the presence of opposites at the heart of reality and speaks of a “hidden harmony” that transcends the apparent.

With Plato, this intuition becomes a method: dialectics elevates the intellect from contradictions and hypotheses to the Forms and, ultimately, to the Good that transcends them. The paradox “ ” is therefore no longer merely a difficulty: it may signal that a shift in the level of knowledge is required.

Aristotle marks a turning point. His doctrine of the intellect remains close to Plato’s, but dialectic becomes primarily reasoning based on probable opinions. With logical formalization, the concept tends to close in more tightly on its object. Borella sees this as an initial “logical closure” that, together with modern science, will pave the way for the epistemic closure of the concept.¹⁷

Kant takes this trend much further: the antinomies become proof that metaphysical reason illegitimately exceeds its domain. Where we see a limit to discursive rationality, Kant concludes that there is a limit to the knowable.

Hegel, on the other hand, attempts to reopen access to the Absolute and to conceive of a rationality attuned to the movement of reality. But his ambition to integrate and transcend all contradiction within the unfolding of the Concept maintains the preeminence of the system. This is his own paradox: recognizing the irrepressible openness of meaning while claiming to bring it to completion within a closed system.

Yet authentic dialectics should precisely not abolish all contradiction. As Jacques d’Hondt writes, it “does not promise deep repose, but demands restless vigilance and tireless effort”¹⁸. The true paradox may be irreducible; seeking to resolve it at all costs might amount less to overcoming it than to fleeing from it.

Far from being an accident of dialectics, the paradox is rather what prevents authentically metaphysical dialectics from closing in on itself as a system.

In Defense of Aporia

The Greek term aporia literally denotes the absence of a passage, an impasse. But the halting of reason does not necessarily imply the halting of knowledge.

For Plato, aporia is a fruitful moment: Socrates brings his interlocutor into contradiction with himself in order to help him discover the inadequacy of his opinions and move beyond doxa. In the *Meno*, he acknowledges that his own doubts enable him to sow doubt in others. ¹⁹

For Aristotle, aporia is also a stage in the process of inquiry: it leads to diaporia—the examination of possible solutions—and then, eventually, to euporia. Pierre Aubenque has thus demonstrated how Aristotelian metaphysics remains a body of knowledge still being sought rather than a definitively established system.²⁰

Contemporary thought has rediscovered the fruitfulness of aporia. Heidegger may call the analogy of being “the harshest aporia”; Derrida refuses to see it as mere paralysis. Rodolphe Gasché characterizes it as amechanon, irreducible by any means whatsoever.²¹

It is this irreducibility that interests us. To accept the aporia without being satisfied with it is not to recognize a limit of the knowable, but a limit of the rational. Where reason finds no further passage, intelligence is not necessarily condemned to stop along with it. Aporia may constitute the threshold where explanation gives way to understanding, where conceptual knowledge discovers its own limits and opens itself to a form of knowledge that no longer possesses its object: a state of not-knowing.

From Paradox to nescience

The paradox, therefore, does not merely mark the limits of reason; it accompanies metaphysical knowledge to its very end.

Mysticism provides a prime illustration of this. Presence and absence, life and death, emptiness and fullness, transcendence and immanence cease to be merely terms that must be rationally reconciled: they become polarities whose coexistence must be understood—or experienced.

But the paradox is already inherent in the basic act of knowing. According to Aristotle, “the soul is, in a certain sense, all beings” (Aristotle, On the Soul, III, 8, 431b20). In knowing, the intellect becomes, in a certain sense, what it knows, without thereby becoming, ontologically speaking, the thing known: “it is not the stone that is in the soul, but only its form.”²²

Knowing therefore paradoxically consists in becoming what one is not. The intellect transcends the limits of its individuality by intelligibly embracing that which is other than itself. The knower and the known unite without merging.

Metaphysics takes this situation to its logical conclusion. It necessarily employs concepts, but only to direct the intellect toward that which transcends the concept. The concept accompanies the intuition of the real; it cannot replace it. Metaphysics is therefore transconceptual: it recognizes the ontological openness of the concept and refuses to confuse the means—the concept—with its end—the real.²³

This is perhaps the ultimate metaphysical paradox: true knowledge leads to its own transcendence.

Gnosis, understood as the perfection of the cognitive aim, thus presupposes what Borella calls a “transforming absorption of the conceptual form into its own transcendent content.”²⁴ The concept is not rejected; it disappears into its own fulfillment.

We can then understand the term “nescience.” It in no way denotes a return to ignorance, but rather a knowledge that has become aware of the impossibility of conceptually possessing what it knows. Pascal admirably describes this movement through the “two extremes” of the sciences: after having explored the limits of human knowledge, great minds rediscover an ignorance that is no longer that of the beginning.²⁵

This is also the learned ignorance of Nicholas of Cusa. The intellect, having fulfilled its function, can “close its eyes,” according to Dionysius the Areopagite, to that which is “above the eyes,” according to Malebranche. Borella speaks of “ontological ignorance”; Saint Paul allows us to speak of an epignosis, a super-knowledge.²⁶

The path that begins with analogy, uncovers the paradox that structures it, leads to aporia, and calls for nescience must therefore not be understood as a sequence in which each term abolishes the previous one. It is a process of deepening: analogy reveals that reality unites resemblance and dissimilarity; the paradox shows that what is opposed according to reason can be conceived together; aporia establishes that reason cannot resolve this tension; and nescience finally acknowledges that this irreducibility itself can be known.

The metaphysics of the paradox is therefore not opposed to the metaphysics of analogy: it may well constitute its epistemological culmination.

If ultimate reality appears paradoxical, its paradox is not a temporary deficiency that a higher form of knowledge would eventually resolve. Rather, it signals that reality transcends all conceptual determination. Ultimate metaphysical knowledge therefore does not consist in eliminating the paradox, but in knowing it without reducing it.

It should be noted, however, that the ultimate reality is not paradoxical in and of itself: the paradox here is an ultimate mode of knowledge, not an attribute of the Absolute.

Beyond Being: The Ultimate Dissolution of Analogy and Paradox

The paradox accompanies metaphysical knowledge all the way to nescience. But does this mean we must regard it as the final word of metaphysics?

While the paradox remains irreducible as long as thought remains within the ontological order, it could cease to be so once the intellect rises to that which lies beyond being.

In the ontological order, the principle of non-contradiction remains intact: a thing cannot simultaneously be and not be in the same respect. But supra-ontological Reality cannot be limited by the very opposition of being and non-being. Borella speaks in this regard of the “Non-contradiction of a Reality that cannot be contradicted by anything,” because it eludes any position, including ontological affirmation itself. ²⁷

The perspective of the Possible—and thus, in this respect, of knowledge—therefore transcends that of being. An ancient aporia from the *Sophist* regains its full force here: if to know is to act upon the known, how could the immutable Being be known without being affected?²⁸

Knowledge cannot come to Being from the outside; but if it arises within it, it would seem no longer to be immutable. We must therefore transcend the opposition itself, toward an Identity that transcends both change and the immutable and contains them supremely. Knowledge no longer comes to it: it is eternally present.

It is above all here that analogy definitively converges with paradox. Both are, in their verticality, anagogical: they lead upward.

The effect recognized as an effect is analogous to its cause. Analogy thus appears as “the cosmic reverberation of the Logos.”²⁹ But it itself compels us to go higher: essences cannot constitute their own analogical principle.

Otherness thus appears as the inverse analogue of Identity, and the affirmation of Identity as its direct analogue. At this level, identity and otherness cease to constitute truly opposable terms. “The Other is Other, and is nothing other than the Same”; the supreme Identity, “beyond essences, beyond Being and Non-Being,” is its own analogue: it is pure Analogy.³⁰

The paradox, then, may not be the ultimate reality, but rather the ultimate form in which human intelligence can intuit what transcends it. As long as thought distinguishes, it encounters identity and otherness, being and non-being, transcendence and immanence, knowledge and ignorance in paradoxical form. But beyond being and its determinations, the opposition that constituted the paradox no longer exists.

The end of the paradox is thus doubly its end: its goal, because it leads the intellect to that threshold; and its conclusion, because beyond that threshold there are no longer two terms to be reconciled paradoxically.

To summarize: analogy uncovers the paradox at its very heart; the paradox leads to an acceptance of aporia; aporia opens the way to nescience, which leads to the superintelligible; and, in the superintelligible, analogy and paradox are both abolished in their Principle.

Conclusion. From Paradox to Silence

At the end of this journey, the paradox appears less as an anomaly of thought than as one of the signs of its openness. The paradoxes of reason reveal its limits; those of intelligence indicate that a reality can transcend the categories within which reason seeks to confine it.

Reason is therefore by no means rejected. It is restored to its proper function and, by that very act, freed from any claim it might have to constitute all knowledge on its own.

Analogy has allowed us to go further. Analogy and paradox are not two competing paths: analogy is itself paradoxical, since it unites without identifying and distinguishes without separating; paradox, by holding together terms that reason tends to mutually exclude, possesses an analogical structure and an anagogical power of its own.

The culmination of this movement is the point at which the philosophy of knowledge becomes gnoseology, where knowledge concedes to nescience, and where the intellect discovers that knowing no longer consists in constructing before oneself an object that is possessed.

When thought seeks to express this knowledge, its language becomes almost necessarily paradoxical.

John Scotus Eriugena can thus describe the visible as “the appearance of that which is not apparent,” the intelligible as “the intelligibility of the non-intelligible,” and the temporal as “the temporalization of the timeless.”³¹ These are not mere linguistic games: ordinary oppositions are pushed to the limits of their capacity to signify.

Dionysius the Areopagite likewise invites us to rise “in ignorance” toward the One who is “beyond all essence and all knowledge”; his “Darkness more than luminous of Silence” expresses what knowledge becomes when light and darkness cease to be merely contradictory.³²

Nicholas of Cusa articulates the same transgression through the coincidentia oppositorum: in intellectual intuition, the One in which all things are and the Whole in which the One is coincide.³³ Structurally comparable formulations are also found in other metaphysical and mystical traditions.³⁴

From one tradition to another, therefore, the same difficulty persists: how can one describe, without rational contradiction, that which precisely transcends the order in which contradictions are mutually exclusive?

We asked at the outset whether analogy was sufficient to account for metaphysical knowledge or whether it needed to be supplemented by paradoxical knowledge. The question was still too binary.

Analogy leads to paradox because it carries within itself the difference within the resemblance; paradox leads to nescience because the intellect refuses to enclose within a concept what it glimpses; nescience ultimately leads back to the Supreme Analogy, beyond all determination.

To say that ultimate metaphysical knowledge is paradoxical does not, therefore, mean that ultimate Reality is itself contradictory or paradoxical. The paradox still pertains to our way of approaching it. It arises when the intellect—always compelled to distinguish in order to think—glimpses what precedes or transcends distinction. Beyond being, identity and otherness, being and non-being, transcendence and immanence no longer need to be artificially reconciled: it is their very opposition that ceases to be ultimate.

Thus, the paradox is both a path and a threshold. It halts reason where it claims to be self-sufficient; it opens the intellect to what transcends it; and then it disappears itself once its purpose is fulfilled. The end of the paradox must therefore be understood in both senses of the term: its purpose and its completion.

The paradox is not the last word in metaphysics; it is perhaps the last word that the intellect can utter before silence.

Footnotes

1. Jean Borella, *Penser l’analogie*, Ad Solem, 2000, reprinted by L’Harmattan, 2012.[↩]
2. Ibid., p. 32.[↩]
3. Ibid., p. 23.[↩]
4. Jean Borella, *Le Mystère du signe*, pp. 218–228; see also Bruno Bérard, *Jean Borella, la Révolution métaphysique*, L’Harmattan, 2006.[↩]
5. Jean Borella, *Penser l’analogie*, pp. 209–210.[↩]
6. Ibid., p. 127, and Jean Borella, Symbolism and Reality, p. 33.[↩]
7. Jean Borella, Lumières de la théologie mystique, p. 112; Penser l’analogie, esp. pp. 210–214.[↩]
8. For the history of the term and a detailed typology: Bruno Bérard, *Métaphysique du paradoxe*, vol. I, *Paradoxes et limites du savoir*, L’Harmattan, 2019, pp. 25–29; see also Yannis Delmas-Rigoutsos, “Les paradoxes et le savoir” [“Paradoxes and Knowledge”] (abstract of his doctoral dissertation), online, URL: http://delmas-rigoutsos.nom.fr/travaux/these/resume.html).[↩]
9. See, in particular, Mark Sainsbury, *Paradoxes*, Cambridge University Press, 1988.[↩]
10. Blaise Pascal, *Pensées*, Section V.[↩]
11. Kant, Critique of Pure Reason, trans. A. Tremesaygues and B. Pacaud, Paris: Alcan, 1905, notably pp. 377–389 and 444; see also Bruno Bérard, *Metaphysics of the Paradox*, vol. I, appendix 6. “The beginning is eternal.”[↩]
12. Jean Borella, *History and Theory of the Symbol*,^3rded., L’Harmattan, 2015, p. 99; *La Crise du symbolisme religieux*, L’Harmattan, 2009, pp. 303–304.[↩]
13. Thinking Analogy, p. 163. On “dissimilar resemblance,” see René Roques, The Dionysian Universe, Paris: Aubier, 1954, p. 201, n. 2.[↩]
14. Plato, Sophist, 241d, 247e, 255d, 257b, and 259a; Jean Borella, *Penser l’analogie*, p. 157.[↩]
15. Plato, *The Republic*, VI, 509d–511e. See the diagram in Appendix A.[↩]
16. Jean Borella, *Penser l’analogie*, pp. 167 and 268.[↩]
17. Jean Borella, *La Crise du symbolisme religieux*, pp. 122–123; *Amour et vérité*, L’Harmattan, 2011, pp. 151–157.[↩]
18. Jacques d’Hondt, “Can Dialectics Still Break Bricks?”, Grand Dictionnaire de la philosophie, 2003, pp. 284–285.[↩]
19. Plato, *Meno*, 80d.[↩]
20. Aristotle, Topics, I, 2, 101a34; cf. Pierre Aubenque, *The Problem of Being in Aristotle*, PUF.[↩]
21. Martin Heidegger, Gesamtausgabe, vol. 33, p. 46; Jacques Derrida, Apories, Galilée, 1996; Rodolphe Gasché, “The Aporetic Experience at the Origins of Thought,” Études françaises, vol. 38, nos. 1–2, 2002.[↩]
22. Ibid., 431b29.[↩]
23. Jean Borella, *History and Theory of the Symbol*, particularly on the “ontological openness of the concept.”[↩]
24. Ibid., pp. 98–100.[↩]
25. Pascal, *Pensées*, fragment on the “two extremes” of the sciences.[↩]
26. Nicholas of Cusa, *De docta ignorantia*; Dionysius the Areopagite, *Mystical Theology*, 997 B; Malebranche, *On the Search for Truth*, II, II, 3; Jean Borella, *Love and Truth*, p. 131, and *Thinking Analogy*, p. 189.[↩]
27. Jean Borella, *The Crisis of Religious Symbolism*, n. 225, p. 88.[↩]
28. Plato, *Sophist*, 248e; Jean Borella, “Gnosis and Gnosticism in René Guénon,” Dossier H: René Guénon, L’Âge d’Homme, 1984.[↩]
29. Thinking Analogy, pp. 193–214.[↩]
30. Ibid., pp. 210–214; verbatim: “only the supreme Identity, which is beyond essences, beyond Being and Non-Being, is its own analogue; It is pure Analogy.”[↩]
31. John Scotus Eriugena, *Periphyseon*, III, 633AB; cited notably by Bernard McGinn, “John Scotus Eriugena: An Introduction,” *Les Études philosophiques*, vol. 104, no. 1, 2013.[↩]
32. Dionysius the Areopagite, *Mystical Theology*, ch. I, § 1 and 997 A–B, trans. Maurice de Gandillac, Aubier, 1943.[↩]
33. Nicholas of Cusa, *De Filiatione Dei*, III; see Jean-Michel Counet, *Mathematics and Dialectics in Nicholas of Cusa*.[↩]
34. For example, the Kulayarāja Tantra: “In the time when I did not yet exist, there was not yet an essence that produced phenomena. […] In the time when I did not exist, there was, from all eternity, nothing like an assembly. Adamantine spirit, let no doubt arise within you! For within yourself, great hero, you are an emanation of my essence.”[↩]