1 The Cosmological Proof for the Existence of God and the Principle of Sufficient Reason

Cosmological proofs for the existence of God, regardless of how one determines their function with regard to faith (whether foundational or explicative), traditionally require the principle of sufficient reason as a presupposition. Why? Because, in short, every contingent being, in accordance with the well-established and customary rules of human reasoning, demands a causal explanation for its existence and nature. This is what the philosopher of religion Friedrich Hermanni states in his response to Nicholas Rescher from 2016, titled „Why is anything possible at all?”^[1] – a position that is already found in a similar form in his Metaphysics. If the principle of sufficient reason holds, then „from it, as well as from the unproblematic assumption that contingents exist, it will necessarily follow the factuality, and thus also the possibility, of a necessarily existing being.”^[2] Even if the chain of explanations were to be infinitely extended within the world, „the question of why a world exists at all and why it is specifically the factual one would remain unanswered.”^[3] Hermanni draws the following contrapositive from this: „If it [i. e., a necessarily existing being] were impossible [...], then the statement of the principle of sufficient reason could have no validity.”^[4] Why? Because then, at the very least, the entire world as a contingent entity would no longer have a causal explanation.

Under the crucial condition of such a contraposition, two possibilities arise for determining the relationship between the principle of sufficient reason (PSR) and the assertion of a necessarily existing being (NEB). It is either an implication from PSR to NEB or an equivalence relation. In the first case, the implication, the assertion of a necessarily existing being would hold even if the principle of sufficient reason did not apply. Therefore, a proof of God’s (i.e., a NEB's) existence could, but would not have to, be based on the principle of sufficient reason. In the second case, the equivalence, the assertion of a necessarily existing being would hold if and only if the principle of sufficient reason also applied; if the principle of sufficient reason were to be discarded, then the assertion of a necessarily existing being would likewise collapse. Thus, a proof of God’s existence could be limited to proving the principle of sufficient reason; and similarly, a proof of the principle of sufficient reason could be limited to proving God’s existence.

If, on the other hand, the contrapositive construed by Hermanni does not hold, then two other possibilities will arise.

In the case of a conjunction, the principle of sufficient reason and a necessarily existing being would indeed occur together, but only contingently. In the case of a projection function of NEB, the assertion of a necessarily existing being would be true, regardless of whether the principle of sufficient reason applied or not. In both cases, therefore, a possible proof of God’s existence would have to forgo the principle of sufficient reason.

This brief overview can be summarized as follows: in a cosmological proof of God’s existence, the principle of sufficient reason is relevant in two cases – namely, when one (as Hermanni seems to do) assumes PSR→NEB or PSR↔NEB. Below, however, I introduce an author who disputes the contraposition drawn by Hermanni – one who denies that the falsity of the principle of sufficient reason and the denial of a necessarily existing being must coincide: Charles Sanders Peirce. Hermanni might well agree with Peirce – who notably influenced Hermanni’s interlocutor, Nicholas Rescher, particularly in the field of non-standard logic – that „[i]t is a damnable absurdity indeed to say one thing is true in theology and another in science.”^[5] Furthermore, Peirce is oriented towards an author to whom Hermanni also feels committed: Gottfried Wilhelm Leibniz.^[6] Two centuries after Leibniz (1646–1716), though, Peirce (1839–1914), who shares Leibniz’s interest in universal semiotics and logical notation systems, maintains the reality of an Ens necessarium without ascribing universal validity to the principle of sufficient reason. Rather, Peirce seems to claim a projection function for the thesis of the reality of an Ens necessarium: the Ens necessarium is real regardless of whether the principle of sufficient reason holds or not.

In the following, I will outline in four brief steps how Peirce departs from the paths paved by Leibniz and thus arrives at a position that also deviates from Hermanni.

2 The Concept of Signs

For both Leibniz and Peirce, thinking takes place through the proper use of signs.^[7] For both, the proper use of signs can – in order to grant „relief from the hardship of thinking”^[8] – be formalized, controlled, and accelerated, especially through the employment of logical notation systems, including those of a graphical kind. However, whereas for Leibniz the function of signs primarily consisted in analyzing relations of identity and inclusion, especially of an intensional nature, Peirce expanded his concept of signs at an early stage.

Firstly, according to Peirce, anything that captures attention in a given situation functions as a sign. This ultimately means that all processes of consciousness, or all processes of orientation undertaken by an organism, can be described as processes of sign interpretation. The results of such processes of sign interpretation may manifest as feelings, as volitions and actions, as well as concept-using thought, including perceptual judgments. In this way, the use of signs does not merely enable combinatorics and the handling of logical calculi; rather, it interweaves the organism of the interpreter with the physical world. Ultimately, for Peirce, the entire world of experience is constituted through the interpretation of signs.

Secondly, Peirce posits that all forms of sign usage – however diverse – share one and the same basic structure, which is both capable of and requires differentiation. Unlike Leibniz, Peirce does not distinguish between the signum (the perceived sign) and the signatum (that which is not perceived but has to be signified) – that is, between the sign and what it signifies, whether this be a concept (conceptus), an idea (idea), or a thing (res).^[9] Instead, Peirce identifies three elements, connected by a triadic relation: the sign, the object, and the interpretant. These three are not connected by two or even three dyadic relations (sign-object, sign-interpretant, object-interpretant), but by a single triadic relation. The interpretant mediates between a newly emerging sign and an object that is already known or presupposed. In more complex cases, the interpretant assumes a representational function: it represents not only the sign and the object – each individually – but also the relation between them. This can be illustrated by the example of a judgment: the interpretant – namely, the judgment – represents the sign through the predicate term, the object through the subject term, and additionally makes explicit the relation between them, including its modality. For example: if one trusts the Wikipedia entry on Friedrich Hermanni, then one of the interpretants that arises is the judgment that Friedrich Hermanni (object) was in fact – or contingently – born in Schwelm (sign), and not not in Schwelm.

Thirdly, in the final decade of his life, Peirce refined his distinctions between sign, object, and interpretant by analyzing the various manifestations of signs according to their possible internal structures, doing the same for objects and interpretants, while also classifying the relations between them by type. Of relevance here is that Peirce recognizes not only signs, objects, and interpretants of a regular, law-governed kind, nor only strictly logical and thus necessary relations between them like those central to Leibniz’s philosophy. Instead, Peirce systematically embraces indeterminacy and vagueness at every level, alongside physically situated individuals and unique events that occur in space and time. For example, an icon is a sign that, although it appears in a regular form and thus possesses recognizability, refers to its object by virtue of an attributed similarity, allowing it to potentially denote a broad spectrum of objects. Consequently, an icon neither possesses informational value nor permits reliable intersubjective communication: a painted circle might represent the sun to one person, and a well opening to another. A symbol, such as the word ‚blue,’ which relates to its object through a regulated convention, can still signify a turquoise shade to one person and an ultramarine tone to another, with neither hue clearly distinguishable from neighboring colors. Similarly, it may denote for one individual the concrete occurrence of blue in the Chagall windows in St. Stephen’s Church in Mainz, and for another, the occurrence of blue on the ceramic columns at the Hundertwasser House in Plochingen – and so forth. While Leibniz also addressed the phenomenon of qualities, he considered the associated concepts deficient insofar as they are clear but not distinct.^[10] Peirce, by contrast, allows vagueness and indeterminacy, as well as the actual, individual, and unique, to shape not only certain classes of symbols that are interpreted through concepts, judgments and rationales but also less elaborate signs that are nonetheless the indispensable foundation for those types of symbols ultimately employed in logical reasoning. So, while Leibniz’s focus lies primarily on symbols, Peirce extends his inquiry into the broader realm that precedes symbols. This is why Peirce’s classification of signs carries both descriptive and normative implications: descriptive implications regarding those less elaborate signs processed through emotions, volitions, actions, etc., and normative implications regarding the rules for transforming symbols into interpretants of a conceptual nature.

Fourthly, from the fact that the use of signs is by no means confined to necessary relations of implication, it follows that in most cases interpretants are not fully congruent with the signs they process. Such perfect congruence occurs only with deducent signs – that is, judgments that allow deductive justification from a given set of premises. All other signs are transformed into interpretants that display a semantic surplus in relation to the signs from which they arise. According to Peirce, this is precisely the mechanism by which new knowledge is generated.^[11] Interpretants are thus, for the largest part, synthetic in nature – and this holds not only for judgments in general,^[12] including those concerning the reality of God, but also for true judgments in particular. In contrast, for Leibniz, true propositions are analytic, insofar as the subject concept necessarily contains the predicate concept. As Sibylle Krämer explains, this holds even for contingent truths, „only that their logicality is revealed solely to God’s eye, but not to human proof practices, insofar as these would have to extend into infinity. This means that although Leibniz clearly distinguishes between truths of reason and truths of fact epistemologically, ultimately – that is, sub specie aeternitatis, in God’s perspective – he concedes the reducibility of factual truth to logical truth.”^[13]

Unlike in Leibniz’s philosophy, the concept of God, for Peirce, cannot be derived analytically. Rather, it is the result of a complex web of interpretive processes that are ultimately rooted in experience and eventually culminate in a vague concept of a benign Creator. This web of interpretive processes not only cannot ultimately be clarified,^[14] but may also differ significantly from one individual to another: it may incorporate perceptions, even feelings, as well as metaphysical reflections on the fundamental structures underlying reality. The justification Peirce offers for the God-concept that thus evolves is therefore not substantive but formal: according to Peirce, it results from abductive processes – that is, processes which, although inferential in nature, link premises and conclusions only loosely, and which in this way open up possibilities of thought, even though they terminate merely in hypotheses. Indeed, Peirce’s God is, as he himself puts it, „strictly hypothetical”.^[15] However, it is in the course of a person’s life that the God-hypothesis may gain increasing validation, and Peirce includes within this validation the individual’s engagement with the experience of evil. Accordingly, the problem of theodicy leads Peirce to interpret the encounter with evil (as a sign) in such a way that it reshapes the concept of God (as object), ultimately permitting the Creator to be conceived also as the Reconciler.

3 The Principle of Sufficient Reason

It is as conspicuous as it is in need of explanation that Peirce, despite his sympathy for Leibniz, makes hardly any reference to the principle of sufficient reason. Leibniz employs the principle of sufficient reason as a criterion for truths of fact, which are to be distinguished from truths of reason. In Leibniz’s formulation, the principle states „that no fact can be true or existent, and no statement correct, unless there is a sufficient reason why it is thus and not otherwise, although such reasons are in most cases unknown to us.”^[16] As is well known, the principle of sufficient reason in Leibniz binds together an ontological and a logical axiom. The ontological axiom reads: everything that is the case has a determining cause – not only with respect to its that (its occurrence), but also with respect to its how (its manner of occurrence). Every fact thus presupposes another fact as its determining cause. Conversely, it follows that what has no determining cause is not a fact. The logical axiom reads: every factual statement requires, in order to be regarded as true, another factual statement as its rationale. Conversely, a factual statement that cannot cite such rationale cannot be regarded as true.

Peirce, by contrast, separates these two axioms and assigns them to different scientific domains. The ontological thesis concerning the causal concatenation of facts belongs to metaphysics. Metaphysics, however, is grounded – within the framework of his theory of the sciences – on presuppositions established by semiotics; and it is semiotics that constitutes the proper domain of the logical thesis regarding the sequence of justification between factual statements. Thus, in Peirce’s view, the logical thesis takes precedence over the ontological one, rather than standing on equal footing with it.

Regarding the logical justification of factual statements, Peirce analyzes these statements, on the one hand, as interpretants. They thus arise from one’s own observations, memories, etc., or from trust in the testimony of others. As with all interpretants, they process signs and objects; in this case, however, the signs and objects processed do not themselves take the form of judgments but are instead represented by mere terms functioning as predicates and subjects. Factual statements, understood as interpretants, are therefore not based on inferences in Peirce’s view. Rather, they neither require nor permit justification through inferences from other factual statements; instead, they call for confidence in one’s own reliability or in the credibility of others. Consequently, the principle of sufficient reason does not apply here.

Factual statements, however, can also function as signs and as objects. Only in such cases do they require justification through inference or serve as justifications themselves. Yet even then, they do not necessarily fall under the principle of sufficient reason. Peirce, after all, distinguishes three kinds of justification or explanation: abductive justification, which merely reveals possibilities; inductive justification, which gathers individual cases to establish general laws; and deductive justification, which applies general laws to determine specific cases. Since all these forms of reasoning – though each requires mediating concepts to link premises with conclusions – follow different rules, the principle of sufficient reason lacks the precision to adequately account for any of them.

These semiotic structures find their counterparts in Peirce’s metaphysics, developed under the influence of 19th-century evolutionary theories. Metaphysics encompasses not only time and space,^[17] which are invoked in semiotic interpretation processes once a certain level of complexity is reached, but also (1) uniformity or generality, derived from signs such as symbols and deducents, (2) compulsion, individuality, or diversity,^[18] derived from signs such as indices and inducents, and (3) absolute chance, derived from signs such as icons and abducents. The principle of sufficient reason does not apply to chance, which operates in the world.^[19] It may, however, apply to the realm of interacting and mutually responsive individual things – that is, to what Leibniz terms the contingent. Yet according to Peirce, it is no longer sufficient to fully account for the regular and the uniform – that is, what appears as the instantiation of law, because the effect of lawfulness consists in coordinating all future instances, all would-bes. This is what renders such regularities real. For this reason, Peirce, who described himself as a „scholastic realist of a somewhat extreme stripe,”^[20] considered Leibniz to be a „modern nominalist par excellence.”^[21]

4 The Principle of Non-Contradiction

By applying the principle of non-contradiction, Leibniz holds that truths of reason can be identified. A truth of reason („Vernunftwahrheit”) is characterized by the fact that its opposite must be regarded as impossible.^[22] Accordingly, the principle of non-contradiction states that „we,” as Leibniz puts it, „consider everything that involves a contradiction to be false, and everything that is contradictorily opposed to the false to be true.”^[23] This already indicates that truths of reason are analytic truths. The concept of a NEB, too, is for Leibniz an analytic one. Since it includes actual existence, it also includes possible existence; and thus, it cannot contain anything that would exclude existence.

Peirce approaches the law of non-contradiction in a divergent way, using it – again with reference to semiotics – to construct three distinct realms of logic and, derived from these, three corresponding realms of metaphysics, that is, of reality. In the first of these three realms, the law of the excluded middle holds, but the law of non-contradiction does not. The only applicable truth value is that of ‚possibly true.’ Metaphysically, this realm is governed by the both-and of overdetermination: both p and not-p can be the case. In the second realm, which is familiar to us from everyday practical experience, both the law of non-contradiction and the law of the excluded middle hold. The two truth values that apply are ‚true’ and ‚false.’ Metaphysically, the disjunctive either-or prevails: either p is the case or not-p is the case. In the third realm, the law of non-contradiction holds, but the law of the excluded middle does not. Three truth values apply: ‚true’, ‚false’ and ‚indeterminable’. Metaphysically, this realm is governed by the neither-nor of underdetermination: neither p nor not-p must hold.

In theology, the construction of such non-standard worlds can be traced back to late antiquity. For example, the non-standard world of both-and could be, and indeed was invoked for a concept of God that embraces all possible opposites within itself. This notion also appears in Luther, specifically with regard to the doctrine of the two natures in Christology: that Christ was both God and not-God (a contradictory opposition), that is, divine and human, is something that, according to Luther, is accessible here and now only through faith, but one day – in regno gloriae – will also be accessible through reason.^[24] The non-standard world of neither-nor, in turn, can (in my view) be found in the concluding sections of Luther’s De servo arbitrio, where he addresses the problem of theodicy. There, Luther suggests that God’s iustitia iustissima, which can be grasped only in lumine gloriae, surpasses the two lower types of justice: both the social justice of suum cuique, which is revealed in lumine naturae, and the unmerited justice through faith, which becomes thematic in lumine gratiae.

5 The Ens necessarium

According to Leibniz, the claim that a being exists actually – and therefore possibly – whose existence is necessary will constitute a truth of reason („Vernunftwahrheit”) if denying the possible existence of such a being leads to a contradiction. Hermanni, however, shares Kant’s critique of the ontological argument for the existence of God, which, as is well known, consists in the claim that existence cannot be regarded as a property among others, as a conceptual determination, a real predicate, or perfectio.^[25]

Peirce raises this objection as well, though with a different focus. Existence is that which judgmental interpretants express; and since judgmental interpretants – by relating signs (represented as predicate terms) to objects (represented as subject terms) – are fundamentally synthetic in nature, existence cannot be claimed analytically as a component of a concept. Peirce understands existence as a dyadic relation: an encounter between two entities (in the broadest sense, including qualities or possibilities) at a specific coordinate of space and time.^[26] The existent is that which could be observed or interacted with, were one present at that coordinate. That which exists thus always falls within the domain of the empirical, the individual and the contingent, not within the domain of what is necessary in thought. This is why Peirce considers the attribution of existence to God to be a category mistake.^[27] Existence cannot be predicated of God. To do so would be to represent God as a finite and immanent entity, located in time and space, a possible subject to the actions of other beings.

Rather, it is reality that must be ascribed to God. Peirce conceives of reality as a triadic relation that mediates between two events through a regularity – a habit or a law. The real governs particular instances, producing uniform effects that persist over time. It is in this continuity that the mark of the real is found: it is what it is, independently of how it is conceived in any given instance. Unlike that which merely exists, the real reveals itself persistently through its effects, has revealed itself in the past and will continue to do so in the future: while an individual apple that falls to the ground merely exists, the law of gravity, which has caused apples to fall and will continue to do so, is real. In this sense, God too, according to Peirce, must be regarded as real: He produces effects, always and unceasingly, in the manner of a creatio continua.^[28]

As the real manifests itself as a coordinating regularity or law, it can be adequately represented only through argument-like interpretants, for these alone establish connections between individual statements or facts, such as observations. This is why Peirce, in his seminal 1908 text „A Neglected Argument for the Reality of God,” posits a conditional relationship between the reality of God and the capability of that reality to be justified: If God is real, Peirce argues quite consistently, then it should be expected that an argument for God’s reality could be found.^[29] Between the claim that God is real and the claim that God’s reality can be justified, there exists an equivalence rather than a mere subjunction, for Peirce rules out the possibility that God might be real without there being any justification for God’s reality, on the grounds that what is real will make itself known through the effects it evokes (a position that aligns with his long-held thesis of the ultimate knowability of the real).^[30] Such a justification, according to Peirce, can – and indeed will – be found through a process of reflection that begins freely and playfully, and then gradually becomes more focused: a process he calls musing. The justification that the metaphysician Peirce presents as his own focusses on the metaphysical structures of what he calls the three universes of experience: three persisting, structurally distinct, and phenomenologically accessible modes of reality – ideas,^[31] matter, and mind.^[32] According to Peirce, these cannot be reduced to one another, nor can they be dissociated from one another. Rather, they interpenetrate and mediate one another. The striking and explanation-worthy tendency toward uniformity that emerges both within each of these three universes and between them^[33] – especially what Peirce refers to as „growth,” a progression toward greater richness in variation, diversification, and complexity^[34] – makes the hypothesis of a Creator God not merely plausible but compelling.

This Creator God, thus inferred – or even self-disclosing – is described by Peirce as „pure mind”^[35] in the sense of being structured according to the sign-object–interpretant matrix of interpretation: a God who is distinct from the world, not immanent within it, but rather situated beyond time and space. In the manner of a creatio ex nihilo, God brings reality about by creating – that is, by thinking – a continuum of indeterminate possibilities (or qualities), that stretches infinitely into an increasingly diffuse past. As Peirce puts it: „We cannot ourselves conceive of such a state of nility; but we can easily conceive that there should be a mind that could conceive it, since, after all, no contradiction can be involved in mere non-existence.”^[36] From this continuum, particular possibilities suddenly spring into existence, manifesting as singular qualities, and eventually give rise to regular patterns.^[37] In this sense, Peirce’s view aligns with what Hermanni, following Leibniz and Augustine, maintains: „[...] God [is] not only the ground for the being of the actual but also the ground for the being of the possible [...]. Even prior to and apart from their actualization, possibilities possess being, namely, in that they are thought by God.”^[38] However, Peirce’s critique of Leibniz lies in the assessment that in Leibniz’s system, God’s thought – „by making its knowledge Perfect and Complete” – is deprived of the possibility of development and expansion.^[39]

For Peirce, God is Ens necessarium not in a logical sense. The concept of an existing God is neither logically necessary, as in an ontological proof, nor can it be derived as a necessary conclusion from the contingent taken as a premise. Rather, God is Ens necessarium in a metaphysical sense. He is conceived as the necessary precondition for the world – for its very existence and the specific mode of its existence: that is, for the three distinct universes of experience, which, being irreducible, do not emerge or develop successively out of one another but are co-original, as well as for the strikingly uniform structural features of these universes: „[...] the three universes must actually be absolutely necessary results of a state of utter nothingness.”^[40] As Jon Alan Schmidt succinctly summarizes, „[...] the Reality of God as Ens necessarium is indispensable to both the origin and order of our existing universe of Signs.”^[41] It is certainly no coincidence that Peirce’s commitment was not to a unitarian but to a trinitarian conception of God – a position shaped by his doctrine of the three differentiated universes of experience and, ultimately, by the irreducible triad of sign, object, and interpretant.

That the Reality of the Creator God, from a metaphysical perspective, constitutes the necessary precondition for the world^[42] – both for its existence and the mode of its existence, both its that and its how – cannot, as mentioned, be logically secured by appeal to the principle of sufficient reason. For although Peirce, as previously mentioned, does not commit himself definitively or exclusively to any specific content in justifying the God hypothesis – other observations might equally serve as its basis, in place of the structural congruence among the experiential universes – he does commit to its logical form, and thus to the mode of its validity. The God hypothesis is justified abductively, and in such a way that aesthetic qualities play a role.^[43] In this sense, what is sought is not the disclosure of a sufficient reason for the world, but merely an „adequate cause.”^[44]

Unlike William Kingdon Clifford, Peirce (like William James) does not hold that „it is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence.”^[45] On the contrary, anything not ruled out as impossible – any hypothesis that spontaneously arises, including the hypothesis of God’s reality – may initially serve as the basis for a belief, that is, a conviction that guides action and forms habits. Such hypotheses, however, must subsequently be subjected to testing. With regard to the hypothesis of God’s reality, I suggest that Peirce – contrary to his explicit statements and unlike the approach taken in the „Neglected Argument” – ought to have referred to the method of qualitative induction, by which something is identified as something through the gradual accumulation of relevant characteristics.^[46] The attributes that the muser ascribes to his hypothetical God, Peirce indicates, resemble qualities that manifest themselves in the world process, in the course of history – a history that, under divine governance (gubernatio), will, over the long term, tend toward increasing order, coordination, and, in this sense, love. In this light, one might understand Peirce’s observation that the muser – the reflective inquirer – who has begun revering and „adoring his strictly hypothetical God,”^[47] that is, the idea of God, develops the desire „to shape the whole conduct of life and all the springs of action into conformity with that hypothesis.”^[48] With respect to the problem of theodicy, this means that the muser, in light of the God hypothesis, becomes capable of interpreting the evils encountered as expressions of divine goodness – however hidden or obscure that goodness may be, and always from a first-person perspective. In this way, the musing individual transforms the God hypothesis into a (weak) kind of inductively tested claim: one that no longer grants to God’s reality merely the status of possibility but recognizes it as an actual, though not logically necessary, fact.^[49] This world is not the best of all possible worlds in the mind of God; rather, it is the only world. It does not come into being through a value-based or rational selection among alternatives by God, but from sheer chance, disorder, and chaos. Yet it evolves – over a vast span of time – toward improvement. God is the causa efficiens of the world – not by having absorbed every detail of its unfolding into his thought, but by creating the structures along which it can develop, including through spontaneity. At the same time, God is also the causa finalis of the world – not by having predetermined a certain end from eternity, but by seeking, from each given state, to realize the best possible outcome from that point, without forcefully imposing this aim upon the world.^[50] The world follows, step by step – albeit with unsettling interruptions again and again – „God’s purpose.”^[51] It is meant to become the best world.

6 Summary

Certainly, I have not been able to demonstrate the validity of the principle of sufficient reason, from which the reality of an Ens necessarium could be inferred. And certainly, I have not been able to show that Peirce, despite his restriction of the validity of the principle of sufficient reason, rightly insists on the reality of the Ens necessarium. However, what I hope to have illustrated is that proofs of God’s existence, whether cosmological or ontological, rely on far more underlying assumptions beneath the surface than are visible above it. It is precisely these invisible yet crucial governing assumptions, especially in terms of logic and semiotics, that require discussion and therefore deserve at least as much attention as the proofs of God’s existence based on them.