Paul Studtmann

We present a philosophically motivated framework for modelling moral agency. In addition to choosing strategies, agents in this framework choose among an appropriate exogenous set of moralities that depends on the context of the game. Further, agents can use mixed strategies to choose their degree of morality. We present two models to demonstrate the framework. In the first model, agents choose between empathy and selfishness while playing prisoner’s dilemma. In the second, agents choose between Kantian universalizing and selfishness while playing a public goods game. For both models, the degree of morality gets determined endogenously rather than assigned parametrically.

This paper revisits the classical use of Nash bargaining to model the social contract by addressing the two central objections of John Rawls: the influence of threat advantage and the multiplicity of bargaining solutions. We introduce an innovative framework that applies an optimific moral rule, termed Pure Strategy Deontarianism (PSD), to the Nash Bargaining Game. PSD is a synthesis of Kantian deontology and utilitarian altruism. By applying PSD to the Nash bargaining game, we demonstrate how rational agents can normatively select maximal disagreement points as rights, thereby equalizing bargaining power and aligning with Rawls’ first principle of justice. Furthermore, we derive the Kantian solution (KS) for surplus division from PSD, and prove that KS satisfies five key axioms of fairness - symmetry, Pareto optimality, scale invariance, strong monotonicity, and contraction consistency. We argue that KS is an ideal solution, since it does not always lie in the feasible set and so serves as an ideal benchmark that practical approximations like the Nash Bargaining Solution can approach. This synthesis not only offers a robust theoretical resolution to Rawls’ objections but also provides a structured methodology for integrating moral considerations into game-theoretic models of justice.

This paper presents a large-scale simulation study evaluating the relative success of competing moral theories in strategic interactions. Rather than relying on abstract philosophical argumentation, we adopt a game-theoretic framework in which agents governed by distinct moral principles interact across the entire range of symmetric 2-player, 2-strategy, normal form games, including the Prisoner’s Dilemma, Stag Hunt, and Hawk-Dove. We analyze 32 moral theories, including five foundational frameworks—average consequence utilitarianism, Kantian deontology, selfishness, maxi-min, and empathy-based morality—as well as 26 synthesized moralities formed by combining these base theories. Through Monte Carlo simulations, we determine which moral rules yield the highest expected material payoffs, both in homogeneous interactions (where all agents follow the same rule) and in mixed populations that include selfish agents. Our findings reveal that synthesized moralities systematically outperform their foundational counterparts, highlighting the practical advantages of moral autonomy. In particular, the synthesis of utilitarianism and deontology (UD) emerges as the 'optimific champion', achieving the highest payoffs under the assumption of universal adherence. However, in mixed societies where agents must coexist with selfish individuals, a different moral rule, what we call the 'realist’s champion', prevails: the synthesis of deontology and selfishness (SD). These results have significant implications for moral philosophy, challenging the traditional focus on isolated moral theories and suggesting that moral rules are best understood in relation to their interactive success. The study also underscores the essential role of deontology in viable moral syntheses, raising fundamental questions about the evolutionary robustness and practical viability of moral systems.

We present a cosmological model (RL+) that offers exact predictions for the Hubble constant, the cosmological constant, the total energy density of the universe, and a curvature that matches current observational constraints. The model predicts a cosmological constant energy density that constitutes approximately 64% of the total energy budget, in agreement with current estimates from the standard LCDM model. Furthermore, the model addresses several longstanding cosmological problems—namely, the problem of infinite initial density, the coincidence problem, and the flatness problem—all with the introduction of a single temporal parameter.

Kant distinguishes between autonomous and heteronomous agents. Because Kant is concerned with the nature of moral action, not its consequences, he is not concerned with whether autonomous agents achieve better outcomes than heteronomous agents. But the question of the expected outcomes of the different types of agency is an interesting one to pursue since it is not obvious up front which type of agent would achieve better outcomes. In this paper, we present a game-theoretic examination of four forms of heteronomy and their corresponding forms of autonomy. We show that in one case autonomy achieves the same payoffs as heteronomy and that in three cases autonomy outperforms heteronomy. In the course of our discussion, we find a type of moral agency that comes close to achieving the maximum possible total payoff across all possible dyadic symmetric interactions. Intriguingly, the type of agency involves a synthesis of utilitarianism and deontology.

According to Augustine, abstract objects are ideas in the Mind of God. Because numbers are a type of abstract object, it would follow that numbers are ideas in the Mind of God. Let us call such a view the Augustinian View of Numbers (AVN). In this paper, I present a formal theory for AVN. The theory stems from the symmetry conception of God as it appears in Studtmann (2021). I show that Robinson’s Arithmetic is a conservative extension of the axioms in Studtmann’s original paper. The extension is made possible by identifying the set of natural numbers with God, 0 with Being, and the successor function with the essence function. The resulting theory can then be augmented to include Peano Arithmetic by adding a set-theoretic version of induction and a comprehension schema restricted to arithmetically definable properties. In addition to these formal matters, the paper provides a characterization of the mind of God. According to the characterization, the Being essences that constitute God’s mind act as both numbers and representations – each (except for Being itself) has all the properties of some number and encodes all the properties of that number’s predecessor. The conception of God that emerges by the end of the discussion is a conception of an infinite, ineffable, axiologically and metaphysically ultimate entity that contains objects that not only serve as numbers but also encode information about each other.

In this paper, I present what I call the symmetry conception of God within 1st order, extensional, non-well-founded set theory. The symmetry conception comes in two versions. According to the first, God is that unique being that is universally symmetrical with respect to set membership. According to the second, God is the universally symmetrical set of all sets that are universally symmetrical with respect to set membership. I present a number of theorems, most importantly that any universally symmetrical set is identical to its essence, that show that the two symmetry conceptions intersect with some dominant theological conceptions of God. The theorems also show that both of the symmetry conceptions of God entail that God has a fractal like structure.

According to Augustine, abstract objects are ideas in the mind of God. Because numbers are a type of abstract object, it would follow that numbers are ideas in the mind of God. Call such a view the “Augustinian View of Numbers” (AVN). In this paper, I present a formal theory for AVN. The theory stems from the symmetry conception of God as it appears in Studtmann (2021). I show that the theory in Studtmann’s paper can interpret the axioms of Peano Arithmetic minus the induction schema. This fact allows for the development of arithmetic in a natural way. The development eventuates in a theory that can interpret second-order arithmetic. The conception of God that emerges by the end of the discussion is a conception of an infinite, ineffable, self-cause that contains objects that not only serve as numbers but also encode information about each other.

We present a game-theoretic analysis of the evolution of moral agency via deontological autonomy. Unlike traditional models that rely on kin selection, reciprocity, punishment, group selection, or assortative matching, our parameter-free approach demonstrates that a “moral conception” of human behavior can emerge endogenously from the strategic dynamics of interactions. We show that deontologically autonomous agents can successfully invade a monomorphic Nashian society and eventually comprise approximately 60% of the population under random matching. We further show that with high enough assortment, deontologically autonomous agents can invade a monomorphic society of Nashians completely. Our unified framework accounts for diverse phenomena including public goods provision, coordination in stag-hunt scenarios, fair splits in Nash bargaining, and reduced aggression in hawk-dove conflicts.

The Nash counterfactual considers the question: what would happen were I to change my behaviour assuming no one else does. By contrast, the Kantian counterfactual considers the question: what would happen were everyone to deviate from some behaviour. We present a model that endogenizes the decision to engage in this type of Kantian reasoning. Autonomous agents using this moral framework receive psychic payoffs equivalent to the cooperate-cooperate payoff in Prisoner’s Dilemma regardless of the other player’s action. Moreover, if both interacting agents play Prisoner’s Dilemma using this moral framework, their material outcomes are a Pareto improvement over the Nash equilibrium.

Aristotle's categorial scheme presents two seemingly unrelated difficulties. First, nowhere does Aristotle articulate any procedure for the construction of his scheme. Although some scholars have proposed methods by which Aristotle might have constructed his scheme, these methods are philosophically suspect, and hence, they are incapable of providing support for Aristotle's scheme. As a result, Aristotle's scheme has faced the charge of arbitrariness; and it is unclear that Aristotle has the resources to defend it against other categorial schemes such as those presented by Kant, Hegel, Whitehead, and more recently Chisholm. Second, nowhere does Aristotle make explicit the relationship between his categorial scheme and the other main ontological theory he developed, hylemorphism. As a result scholars have proposed alternative theories about the relationship between Aristotle's two systems. The three main interpretations are as follows. First, some argue that the categorial scheme and hylemorphism contradict each other; second, some argue that the two systems are about distinct domains and hence are in some sense incommensurable; and third, some think that hylemorphism is a development of the categorial scheme, and hence that the categorial scheme undergirds hylemorphism. ;Although the above three interpretations about the relationship between hylemorphism and Aristotle's categorial scheme are the only ones discussed in recent literature, there is another interpretation, one that allows for a single, comprehensive solution to both of the above problems. In my dissertation, I argue that Aristotle's categorial scheme is entailed by his hylemorphism and metaphysical truths about the nature of predication. Thus, the relationship between Aristotle's categorial scheme and his hylemorphism is entirely perspicuous: hylemorphism entails the categorial scheme. Furthermore, because Aristotle provides extensive argumentation for his hylemorphic ontology, and because the additional axioms needed to entail the categorial scheme are knowable a priori, the construction of the categorial scheme can proceed in an entirely systematic manner. As a result, Aristotle's categorial scheme can escape the charge of arbitrariness. ;Although my interpretation is not discussed in recent literature, it in fact has a rich historical lineage. Rudolphus Brito, Albert the Great, Thomas Aquinas, and Franz Brentano all attempted to prove that Aristotle's categorial scheme is derivable from hylemorphism and certain logical/semantic axioms. Although extremely suggestive and insightful, their derivations are not given with the sort of detail needed in order to adequately assess them. The bulk of my dissertation is thus devoted to examining carefully and clarifying the fundamental concepts and presuppositions in a derivation of the categorial scheme from hylemorphism. In the first chapter, I discuss the general interpretive issues involved in my thesis. In the second, third and fourth chapters, I discuss form, matter and the relations between the two. And in the fifth chapter, I provide a detailed derivation of the categorial scheme from hylemorphism

In this paper, I address both the interpretive and philosophical issues concerning prime matter. My aim is to show that a philosophically interesting account of prime matter can be articulated that strongly coheres with, even if it is not necessitated by, Aristotle’s texts. In articulating the interpretation, I first examine a view defended by both Richard Sorabji and Robert Sokolowski according to which prime matter is extension. Such a view, I argue, is problematic for a number of reasons. Nonetheless, it provides a convenient starting point for the view I defend according to which prime matter is intimately linked to, though not identical with, extension.

There is a very deep tension that exists at the heart of Aristotle’s metaphysical system in virtue of the fact that his works seem to contain two distinct and not obviously commensurate ontologies: an early ontology that Aristotle outlines in the Categories and a later ontology that he develops in his physical–metaphysical treatises. In this paper I briefly describe the two ontologies, discuss the sources of conflict and outline different scholarly speculations about the relationship between the two.

In 'Subjunctive Conditionals: Two Parameters vs. Three' Pavel Tichy articulates and defends a three-parameter account of counterfactuals. In the paper, he responds to a well known objection against the validity of various forms of inference, in particular strengthening of the antecedent, contraposition, and hypothetical syllogism. In this paper, I argue that his response to the objection is inadequate. I then propose an alternative form of the three-parameter account of counterfactuals that avoids the objection in question.

Aristotle's categorial scheme had an unparalleled effect not only on his own philosophical system, but also on the systems of many of the greatest philosophers in the Western tradition. The set of doctrines in the Categories, known as categorialism, play, for instance, a central role in Aristotle's discussion of change in the Physics, in the science of being qua being in the Metaphysics, and in the rejection of Platonic ethics in the Nicomachean Ethics. Plainly, the enterprise of categorialism inaugurated by Aristotle runs deep in the philosophical psyche. Even so, despite its wide-reaching influence—and, indeed owing to that influence—any attempt to describe categorialism faces a significant difficulty: experts disagree on many of its most important and fundamental aspects. This article argues that Aristotle's categorial scheme, as is the case with many works in the history of philosophy, is best illuminated by opposing beams of interpretive light. It examines how Aristotle arrived at his list of categories and considers the connection between Aristotle's categories and his hylomorphism.