The Miracle of Science: Against the Principle of Sufficient Reason

Through worlds unnumber’d though the God be known,
Tis ours, to trace him only in our own.
—Alexander Pope, An Essay on Man

I. Reason and Its Critics

To speak of a miracle is to ask an absolute question. It is to ask a question for which no answer can be finally given. For if a miracle is genuine, it could not be any sort of magic trick, the surprise of which would pass away as soon as it is exposed, but rather must be a sudden event that forever defies any possible explanation.[1] It is the mark, not of an epistemic limit, but of a singular nova of radical contingency. All efforts to prove or disprove miracles are, for this reason, essentially investigations of the events from which science begins.

Miracles were once read as signs of wonder (mirari).[2] From the transit of the stars to the flight of the birds, miraculum were interpreted as spectacular manifestations of divine and holy powers crossing the horizon of visible nature. And so long as the uppermost limits of the possible had remained porous, these signs could be investigated scientifically, not as a naïve suspension of, but rather as a heaven-sent guarantee that the world can and shall be known.

This understanding has since been dramatically reversed. Since Francis Bacon’s program of scientific research, and Isaac Newton’s discovery of the laws of nature, the mechanical forces of nature have come to be calculated with increasing mathematical precision. All events can, we expect, soon be predicted in advance. And the inexplicable event of a miracle would now appear to violate, not only the physical “laws of nature,” but also the intellectual “laws of logic.”

The testimony of miracles has thus come to be held in contempt by science. For no inexplicable event can be tolerated so long as science holds to the totalizing ambition to know the causes that are sufficient for any effect. Yet, the possibility of a miracle has been denied by the progress of science, not because the miraculous is false, but rather and precisely because science can admit nothing that cannot be explained by a sufficient reason.

This absolute presupposition of science has been called the “Principle of Sufficient Reason.” The Principle of Sufficient Reason holds that for any fact, there must be an analytic demonstration in formal logic that is not only necessary but itself sufficient to prove it to exist as true.[3] Gottfried Wilhelm Leibniz first explicitly formulated this principle: “We consider that there can be found no fact that is true or existent, or any true assertion, unless there is a sufficient reason why it is thus and not otherwise.”[4]

An argument of reason can be called “sufficient” if it can be proven by an analytic demonstration of formal logic. And such a demonstration can be called “analytic” if the combination of predicates at the conclusion is virtually contained among its premises.[5] This principle can then be postulated as the essential ground that proceeds any demonstration of existence as true.

This principle would appear to foreclose the possibility of a miracle. For as a sudden event beyond scientific explanation, a miracle can neither be directly proven nor disproven by any analytic demonstration or scientific experimentation. Yet, as a momentous suspension of the laws of nature and logic, it is nevertheless possible to argue indirectly against the possibility of a miracle: arguments for miracles affirm, while arguments against miracles deny any higher contingency beyond the essential ground of scientific necessity.

All arguments against the possibility of miracles can thus be analyzed into the Principle of Sufficient Reason: first, in an analysis from any inexplicable event to the hypothetical conditions of its possibility; second, from these hypothetical conditions to the universal laws that regulate the order of subsequent consequences; and third, from all such universal laws to the constitution of the Principle of Sufficient Reason.

The Principle of Sufficient Reason has since been absolutely presupposed to deny the possibility of a miracle. For if, as it presumes, any fact could be explained by a sufficient reason, then such a principle could be elevated to constitute the essential ground upon which stands the possibility of any subsequent demonstration. And if, to the contrary, such an explanation could not possibly be discovered, we could, with Voltaire, regard miracles as, not only a violation of the laws of nature, but of the laws of logic, and even as “a contradiction in terms.”[6]

The Principle of Sufficient Reason thus appears as a secular alternative to belief in the divine Logos. For it would seem to supplant the prior ground of divine creation with the simulated ground of sufficient reason. Yet, as Leibniz also suggests, belief in this principle is no less theological.[7] For in postulating a principle by which to analyze all facts in and from its essential ground, it leaps in an infinite reflection from the visible world to the originary source of its ultimate intelligibility. And yet, in holding this infinite reflection apart from its source, it also appears to constitute a simulacrum of the rational, or of “rationalism.” As Paul Feyerabend writes: “Rationalism is a secularized form of the belief in the power of the word of God.”[8]

We can, with equal legitimacy, also direct the weapons of skeptical doubt against the foundations of science itself. How, we can ask, can we prove the Principle of Sufficient Reason? At the risk of an infinite regress, there can be no prior sufficient reason for the Principle of Sufficient Reason itself. As a fundamental principle of reason, it can, to the contrary, not be proven by any direct argument of formal logic, but rather and only by a dialectical argument, in which all alternative arguments are destroyed by contradiction, and yet its essential ground is equally preserved to proceed in the simulated constitution of successive arguments.[9]

The successors of Leibniz had, for this purpose, first attempted to prove the Principle of Sufficient Reason.[10] Christian Wolff had, for example, argued that if, on the Principle of Identity, the subject is the “ground” of predication that is virtually identical to its inferential consequences, and, on the Principle of Non-Contradiction, such consequences could not contradict its prior ground, then nothing is true without an analytic demonstration and sufficient reason for it to be so.[11] The virtual identity of non-contradictory and analytically valid consequences could, in this way, be argued to constitute the essential ground of science.

Such dialectical proofs have, however, come to be suspected as having either circuitously presupposed or illicitly derived their content from the pure forms of reason. Immanuel Kant had, in his early essay New Elucidation of the Principles of Metaphysical Cognition (1755), objected that such a proof makes illicit use of the intuition of “nothing.”[12] He argues that, “if there is no ground, the concept corresponding to it will be that of non-being”, of “which no concept corresponds at all”, such that “the absurdity, which was supposed to follow, does not follow at all.”[13] Since the “nothing” is not a virtual product of any pure form of reason, such dialectical arguments appear to pivot upon an illicit intuition of the nothing, which, as negative, would destroy the contrary, such that nothing can exist without a sufficient reason for it to be so.

In spite of these criticisms, the Principle of Sufficient Reason has since come to be assumed as the “Mother of all Science.”[14] Although it cannot be proven, it can nevertheless be absolutely presupposed as the originary aspiration of science to know the sufficient causes for why anything at all must be so. The highest hope of science to explain the causes of all events rests absolutely upon such an unshakable belief that a sufficient reason can and should be given for any fact. And were this principle ever to be proven, it would be elevated to the essential ground from which, it seems, any conclusion of science could be proven as true.

Recent currents in continental philosophy have called this principle into question. Kant’s suspicions of Leibnizian rationalism have been radicalized among the heirs of Heidegger. If a miracle is an event for which no explanation can ever be given, we can, by definition, offer no direct argument to demonstrate a miracle. No empirical observation of natural science, and no analytic demonstration of mathematical logic could at last suffice to compel belief either for or against the miraculous. And yet, even in the absence of such a scientific demonstration, we can, nevertheless, reconstruct a dialectical argument against any purported disproof of the miraculous for the purpose, not of knowing, but of believing in miracles.

II. Critiques of the Principle of Sufficient Reason    

The Principle of Sufficient Reason has long been assumed to deny the possibility of a miracle. For if every fact can be sufficiently explained, then no event can be read as a sign of wonder. Yet skeptical criticism has recently turned against the Principle of Sufficient Reason: first, in Heidegger’s question of being that comes before the ontological construction of science; second, in Alain Badiou’s event from which to count the situations of mathematical ontologies; and third, in Quentin Meillasoux’s escape from the correlationist circle of scientific necessity to release an absolute contingency that comes before scientific necessity. We can, following the groundbreaking work of Tyler Tritten, reconstruct this dialectical subversion of the Principle of Sufficient Reason as the absolute presupposition of science, recall the radical contingency of the event, and clear the ground to search again for signs of the miraculous.[15]

A. Martin Heidegger

The question of being (Seinfrage) is, for Martin Heidegger, a question of the essential ground of science. It had, he insists, never been truly answered because the notion of being had from Plato to Hegel traditionally been treated ontically as the most immediate determination that a thing “is,” and ontologically as the essential structure of beings in relation to being.[16]

To treat being ontically is, he argues, to render being as an element of ontology, to bury the experience of being under the form of ontology, and, in so doing, to leave unasked the more originary question of “what is being?”[17] When, at the beginning of Being and Time (1927), he asks this question of being, he reflects upon the question of being, as our being reflects upon its own being, in a reflection of being upon being, a self-reflective being, or Dasein.[18]

Dasein is that being which uniquely reflects upon the question of its own being. It can, in this cycling reflectivity, “run ahead” of any other method that would follow behind the experience of being in the “analytic of Dasein.”[19] The analytic of Dasein is designed to analyze “the state of being that is constitutive for those entities that exist,” where “the idea of Being is already included” as it is presupposed in any judgment of the elementary ground of science.[20]

The “basic concepts” of science are, for Heidegger, the ontical presuppositions of any scientific research program.[21] Being must, he suggests, be presupposed before we can speak of anything at all.[22] Since all sciences presuppose such an elementary speech of being in the premises of any scientific demonstration, Heidegger can, in questioning the meaning of being, analyze so as to subvert the unasked presuppositions that constitute the essential ground of science. Yet, he hints, this analysis of Dasein is only a preparation for a greater work that “will have to be repeated on a higher and authentically ontological basis.”[23]

“Be-ing” is, in Contributions to Philosophy (1938) distinguished by a “leap” of infinite reflection over the construction of any ontology, from the first to the ‘other beginning’ of philosophy.[24] Heidegger announces this leap as the “most daring move” from “inceptual thinking” that “abandons and throws aside everything familiar, every method, and even any understanding of the analytic of Dasein.”[25] The question of being can, thereafter, only be asked by this leap from the “event” (Ereignis), which, in abandoning the basic concepts of science, is simply constituted by the self-reflectivity of Dasein.

Heidegger’s “destruction” (destruktion) of metaphysics can, in this way, be shown to subvert by questioning the essential ground of science. Since the basic concepts of science have been ontically constructed upon the unquestioned presupposition of being, the Principle of Sufficient Reason at its essential ground can be radically deconstructed, suspended, and subverted by asking this more originary question of being.[26] Since, however, this movement of deconstruction can subsequently also be directed against the construction of any ontology, including the negative ontology or « meontology » of deconstruction itself, nothing at last remains for the self-reflexivity of Dasein, except as it can be shown to leap in and from the event.

B. Alain Badiou

The “event” (événement) is, for Alain Badiou, absolutely prior to the phenomena of being. In Being and Event (1988), he advertises the event as “an intellectual revolution” in the “entirety of possible thought” that proposes “completely new tasks to philosophy”.[27] Since Parmenides, philosophers had believed unity to be prior to multiplicity and being to be united as one. Against this Platonic axiom of the One over the Many, Badiou wagers the priority of pure multiplicity.

The one is, he argues, not a simple unity, but rather a count of the multiple. For the one can only be counted in the mathematical situation of counting multiplicity as one.[28] Since, moreover, the many is not one being, not a being, but nothing at all, Badiou can “subtract” the unity of being as one into pure multiplicity before the void.[29] This “ontological subtraction” of the unity of being into pure multiplicity before the void results in a further radicalization of Martin Heidegger and Jacques Derrida’s deconstruction of ontology, semiotics, and science.[30]

Badiou then subtracts the ontology of set theory, mathematics, and logic. Georg Cantor, the inventor of set theory, had first defined a set as a multiple grouping of ontic object intuitions.[31] Badiou alternatively defines the set as the “count-as-one” of a formula’s multiple validation.[32] Yet as soon as this set of the multiple can be counted as one, then, he observes, it is equally possible to count the multiple as a one that is a multiple; to multiply its unity; and, thereby, to produce a virtual multiplicity that exceeds both analytic identity and ontological unity.[33] The foundational paradoxes of set theory can, for this reason, be observed to contradict, trivialize, and subvert the constructed ground of any mathematicized ontology.[34]

The “event” thus appears at the nova of the collapse and construction of all mathematicized ontologies. It appears, not in the simulation of counting being, but “beneath” it, “on the edge of the void,” and at the interstices between being and nothing.[35] It must, accordingly, appear “undecidable from the standpoint of the situation itself.”[36] For it to be present in a situation, we must first “verify whether it is presented as an element of itself,” which, as a paradoxical set within a set, would threaten to precipitate the collapse of any mathematical set theory, and any mathematicized ontology.[37]

At the nova of this collapse, this event appears absolutely prior to any situation of mathematical, logical, or scientific necessity. For the event comes before counting as the condition for the construction of the foundations of mathematical logic, necessary arguments, and scientific demonstrations. It cannot be counted as either united or multiple. Rather, it appears as the pivot upon which any situation of mathematics can collapse and be constructed. Hence, Badiou writes: “I touch here upon the bedrock of my entire edifice.”[38]

A mathematical situation can be called “eventual” as it counts from this nova of a prior collapse. In counting from this collapse, it counts from a negative ground, which, as negative, passes away as soon as it appears. Since, however, nothing at all can be counted except from the event, yet an event cannot be known except as it is counted in such a situation, the event can be correlated to the situation, that is, to an ‘evental situation’. And yet, since Badiou subtracts any count as one into pure multiplicity, and the event can be correlated as counted in and for this evental situation, the event appears as the pivot of the correlationist circle.

C. Quentin Meillasoux

The Principle of Sufficient Reason can, as Heidegger and Badiou have shown, be critically deconstructed. For the essential ground of mathematics, logic, and scientific demonstrations can be subverted by asking the question of being, and subtracting one as being into the multiple before the void. Yet as the foregoing exposition has also suggested, this negative movement of deconstruction can also be dialectically subverted by collapsing any construction of ontology into the event, and correlating the event to the situation.

Quentin Meillasoux has, in After Finitude (2006), defined “correlationism” as the “central notion of modern philosophy” from Descartes to Kant, “according to which we only ever have access to the correlation between thinking and being, and never to either term considered apart from the other,” as an “object ‘in itself”.[39] Since this “correlationist circle” threatens to collapse any independent objects of being into the correlata of thought, he seeks instead to chart a speculative escape from the solipsistic loop of modern philosophy by making “ancestral statements” about the “materials indicating the existence of an ancestral reality or event”.[40]

The “arche-fossil” is, for Meillasoux, the ancestral reality that is given before thought from the anterior objectivity of being.[41] It is, he argues, designed to “test the philosopher’s faith” in correlation with the decisive anti-correlationist dilemma: either the arche-fossil is real and correlationism is false or the facts of science are false. Since he absolutely presupposes the truth of science, he argues that correlationism must be false.[42] Hence, Meillasoux concludes: “There is no possible compromise between the correlation and the arche-fossil: once one has acknowledged one, one has thereby disqualified the other.”[43]

The reality of the arche-fossil cannot, he argues, be “de-absolutized” without collapsing the ancestral reality of the arche-fossil into the correlationist circle, in which any object of uncorrectable facticity can again be reflexively correlated in a closed circuit of scientific necessity.[44] Rather, he calls upon the arche-fossil to chart a path of escape from the reflexive recollection of uncorrelated facticity to the free release of absolute contingency.[45] He concludes: “The absolute is the absolute impossibility of a necessary being.”[46]

Meillasoux thus critically suspends the essential ground of the Principle of Sufficient Reason from the chaotic un-ground of absolute contingency. Contrary to Leibniz’s “principle of reason,” his “principle of unreason” holds that “there is no reason for anything to be or to remain the way it is; everything must, without reason, be able not to be and/or be able to be other than it is.”[47] It is thus designed to save the facts of science from correllationism. Since, however, even this “principle of unreason” stands upon the negation of the “principle of reason,” and the negation of this essential ground betrays a hidden subjectivity that stands opposed to objectivity, Meillasoux can only escape from so as to return into a more tightly bound correlationist circle.

Evidence for this arrested movement can be observed in Meillasoux’s description of the arche-fossil. He locates the “ancestrality” of the arche-fossil within a temporal chronology: the origin of the universe (13.5 billion years ago); the accretion of the earth (4.56 billion years ago); the origin of life on earth (3.5 billion years ago); and the origin of humankind (2 million years ago).[48] To be genuinely uncorrelatable, the anteriority of the arche-fossil should not be correlatable at all within the coordinates of space and time. Since, however, any such ancestral statement can be correlated to thinking, Meillasoux’s arche-fossils can again be re-correlated as recollected moments that continuously break from, and yet equally return in a way that is negatively opposed within an “anti-correlationist circle.”

At the culmination of these three successive critiques, this anti-correlationist circuit can now be shown to constitute a negative dialectic that destroys itself at the fulfillment of its nihilistic acceleration: the essential ground of science is deconstructed by questioning being to leap in and from the event; the nova of the event is correlated to the knowing of the situation; and the ancestral reality of the arche-fossil is correlated against but for thought. Meillasoux seeks to break definitively from the correlation between thought and being. Since, however, even this trajectory of escape from correlationism can also be re-correlated, he has succeeded in breaking from so as to return again to the correlationist circle, in an accelerating sophistic exchange, spiraling in to be released from scientific necessity to a more radical contingency.

III. The Nova of Radical Contingency

Miracles were once read as signs of wonder. Religion and science were held to begin together.[49] And miracles were regarded, not as violations of, but as the beginning of science. Yet miracles have since come to be doubted as not only false but foolish. For since in science every fact must have a sufficient reason, and a miracle has no known cause, the possibility of miracles can be dismissed as, not only naturally impossible, but logically inconceivable. Miracles thus appear to trespass beyond the iron laws, not only of nature, but of logic.

Yet the foolishness of miracles may be wiser than we know.[50] For to disprove the miraculous, we must first prove the Principle of Sufficient Reason. As a principle of reason, it cannot be proven by any direct demonstration of formal logic, but rather and only by an indirect or dialectical argument. This principle has since been absolutely presupposed as the “Mother of all Science” to deny the possibility of a miracle. Since, however, this essential ground of science has recently come to be subverted by successive philosophical criticisms, the principles of science can, in the last analysis, be no more certain than the event of a miracle.

Although it is clear that a miracle cannot be proven, we can, following recent currents in continental philosophy, nevertheless argue against the absolute presupposition of the Principle of Sufficient Reason: Martin Heidegger’s destruction of metaphysics has radically questioned it so as to subvert the basic concepts of science in every constructed ontology; Alain Badiou’s subtractive ontology has subtracted one into the pure multiplicity before the void at the site of the event; and Quentin Meillasoux’s anti-correlationism has escaped from the correlationist circle.

These successive criticisms can, as the foregoing has shown, now be recollected to dialectically subvert the essential ground of scientific necessity: Heidegger’s questioning of the basic concepts of science has shown the elementary presupposition of being to leap in and from the event; Badiou’s collapse of set theory, mathematics, and logic has shown being as multiple to be correlated to thought in the evental situation; and Meillassoux’s anti-correlationist escape from the solipsistic loop of scientific necessity has released a higher contingency.

After these criticisms of the Principle of Sufficient Reason, there nevertheless remains a nova of radical contingency. For once scientific necessity has been suspended, and a higher contingency has been released, the “absolutely contingent” event of a miracle can be read to come before even as it marks the beginning of science.[51] Hence, rather than anarchic interventions that violate nature’s laws, miracles can now be interpreted as the “sudden” event of absolute contingency that erupt prior to the postulated necessity of scientific reason.

What most of all elicits wonder from a miracle is precisely this infinite reflection that erupts from a singular and sudden event beyond understanding. For, as the foregoing suggests, thought responds to the event of the miracle by reflecting in an infinite ascent of analysis, beyond the order of scientific necessity, to float above the suspended ground of scientific explanations. In this movement of infinite reflexivity, speculative thought leaps over the point of the excessive, the uncanny, and the wonderful, as all habits of explanation fall away, and as our spirits rise to a higher contemplation (metanoia).

Upon conversion to this higher standpoint, we can look again at any event and see it differently. Rather than searching to discover a principle of scientific necessity, we can, on the contrary, recognize a reciprocal subject of free contingency. For, in this movement of infinite reflexivity, speculative thought recycles from the object in and for the subject, and ascends to the standpoint of absolute subjectivity, where, from the end to the beginning, it enjoys at last the liberty of its own free self-contemplation. At these starry heights, we can draw the curtain and acknowledge the hidden springs of divine and holy powers erupting from behind the sudden events that elicit awe, wonder, and admiration.

Miracles, once prohibited by science, can again be read as wondrous signs of a radically contingency that come before scientific necessity. The Principle of Sufficient Reason is not the essential ground of science that forecloses the possibility of a miracle. Rather, miracles are signs of wonder that announce the absolutely contingent possibility of postulating any regime of scientific necessity. As Tyler Tritten argues, “all necessity is based on the utter contingency of being as a factum brutum, the fact that there is something rather than nothing.”[52]

Miracles may thus be far more frequent than we know. As a sudden movement of understanding, miracles appear ubiquitous. Yet as a metanoia, miracles are, in contrast to Meillasoux, not a sheer rupture, but the sign of wonder, which, although not yet known, can nevertheless come to be known; the pivot upon which understanding turns; and the nova of infinite reflectivity in the progressive ascent of faith seeking understanding.

We may, after Christmas, recall the miracle that announces the beginning of science. The divine Logos is, for Christian theology, the principle (arche) not only of the first creation, but also and finally of the new creation. As the incarnate Logos, the Christ child of Bethlehem represents the singular concentration of contingency, in the gift of creation made new, and of necessity, in the principle of language, logic, and scientific reason. As John Milbank has argued, the Platonic and Pauline significance of the event can, contra Badiou, be recalled as the “sudden” instant (exaiphnes) of hyper-contingency, of a change from one category to another, and of the creation of the world, as it is recreated in Christ, and as it is recollected in the Church.[53]

The event of a miracle can, thereafter, come to be, not only believed, but even known in giving and receiving a witness that testifies to the miraculous. For in giving testimony of a miracle, these signs of wonder are displayed in a gratuitous repetition, drawn from, and yet equally given in surplus of its source. And, in receiving testimony of a miracle, we share in the accelerating mimetic reciprocity of performing such a recollection of these signs that elicit our wonder, conversion, and the satisfaction of faith in knowing.

A miracle is, we may say, an empirical confirmation that surprise is possible. The explosive significance of the sacraments is not simply the product of, but the site at which, miracles are made. Jesus’s instruction “do this in memory of me” is equally spoken of from the maker of and for the making of the miracle of the Eucharist. For in transubstantiation, the transformation of the bread and wine into the body and blood of Christ can only be known as it is believed, and only so by the recollection of the mimetic performance of the Mass, in persona Christi, of the miracle of creation made new.[54] And once announced at the Epiphany, it can ever again be celebrated in the liturgical cycle, continuing onwards from the Christmas season.

The celebration of the Christmas miracle can thus signal a momentous reversal of the secular. For after the essential ground of scientific reason has been critically deconstructed, the principles of science can no longer be held apart in a simulacrum of the rational as a secular alternative to the originary speech of creation. There can, on the contrary, be no ultimate conflict between the universal laws of nature and the absolute liberty of divine charity. Nature’s laws, no less than reason itself, testify to the absolute contingency of its creation. And once all prohibitions against the miraculous have at last been overthrown by criticism, we can, with faith and hope, begin to chart an escape from a closed understanding of a world without surprise.

A clear vista has now opened from within the crystalline chambers of long-forgotten philosophical formulae to recognize the possibility of miracles falling like raindrops of charity between the leaves of scientific reason. The buttresses and battlements of opposed metaphysical camps that had formerly held reason apart from wonder, and suffocated any genuine sense of the possible, can breathe again, as the eyes of a child open to reveal a sky of radical novelty.

We may wonder if the world is not stranger than we had ever wished to know.

[2] Thomas Aquinas, Summa Theologiae, Pars I, q. 105, aa. 7-8.

[3] Alexander Pruss, The Principle of Sufficient Reason: A Reassessment (Cambridge: CUP, 2006), 3-19.

[4] Gottfried Wilhelm Leibniz, Leibniz’s Monadology (Edinburgh: EUP, 2014), §32, 20.

[5] Gottfried Wilhelm Leibniz, “General Inquiries about the Analysis of Concepts and Truths”, Leibniz: Logical Papers: A Selection (Oxford: OUP, 1966), 47-87; “First Truths”, Leibniz – Philosophical Papers and Letters (Dordrecht: Reidel, 1969), 267-79.

[6] Voltaire, Philosophical Dictionary (New York: DuMont, 1764/1901), 272.

[7] Leibniz, Leibniz’s Monadology, §§29-30; 38-53, 19-24.

[8] Paul Feyerabend, Against Method (Verso: London, 1993), 218.

[9] Georg Wilhelm Friedrich Hegel, The Science of Logic (Cambridge: CUP, 2010), 386-417; The Encyclopaedia Logic, Part I of the Encyclopaedia of Philosophical Sciences (Indianapolis, IN: Hackett, 1991), §121, 188-192.

[10] Christian Wolff, Philosophia Prima Sive Ontologia Methodo Scientifica Pertractata, Qua Omnis Cognitionis Humanae Principia Continentur (Veronae: Ramanzini, 1736), §§56-78, 24-36; Alexander Baumgarten, Metaphysics (London: Bloomsbury, 2013), §§20-22, 104-105.

[11] Wolff, Philosophia Prima Sive Ontologia, §70, 28.  

[12] Immanuel Kant, “New Elucidation of the Principles of Metaphysical Cognition” in Theoretical Philosophy, 1755–1770 (Cambridge: CUP, 1992), 1: 392-398, 11-20; Béatrice Longuenesse, Kant on the Human Standpoint (Cambridge: CUP, 2009), 117–142, esp. 121-123.

[13] Kant, “New Elucidation of the Principles of Metaphysical Cognition”, 19.

[14] Arthur Schopenhauer, “On the Fourfold Root of the Principle of Sufficient Reason”, in Two Essays (London: George Bell and Sons, 1889), 1-27, esp. 5.

[15] Tyler Tritten, “Per Posterius: Hume and Peirce on Miracles and the Boundaries of the Scientifc Game”, Argument, Vol. 4 (2/2014), pp. 247–266; The Contingency of Necessity: Reason and God as Matters of Fact (Edinburgh: EUP, 2019), 9-16.

[16] Martin Heidegger, Being and Time (Oxford: Blackwell, 2001), 21-4.

[24] Martin Heidegger, Contributions to Philosophy (From Enowning) (Bloomington, IN: IUP, 1999), 5-7.

[26] Heidegger, Being and Time, 41-49.

[27] Alain Badiou, Being and Event, trans. Oliver Feltham (London: Continuum, 2006), 16.

[30] Ibid., 1-2, 8-10, 38, 47.

[39] Quentin Meillasoux, After Finitude: An Essay on the Necessity of Contingency (London: Continuum, 2008), p. 5.

[41] Ibid., 10, 14, 16–18.

[48] Meillasoux, After Finitude, p. 9.

[49] Plato, Theaetetus, 155d; Aristotle, Metaphysics, 982b; Ps. 33:8; Lk. 5:26.

[51] Meillasoux, After Finitude, 54-55, 62-63.

[52] Tyler Tritten, The Contingency of Necessity: Reason and God as Matters of Fact (Edinburgh: EUP, 2019), 9.

[53] John Milbank, “The Return of Mediation, or The Ambivalence of Alain Badiou,” Angelaki: Journal of Theoretical Humanities, 12:1 (2007), pp. 127-143, esp. pp. 136-140.  Cf. Plato, Parmenides, 156d-e; Acts 9:3, 22:6.

[54] Mk 14:22-25, Lk 22:18-20, 1 Cor. 11:24.