Kant distinguishes between autonomous and heteronomous agents. Because Kant is concerned with the nature of moral action, not its consequences, he isn’t concerned with whether autonomous agents achieve better outcomes than heteronomous agents. And yet, the question about the expected outcomes of the different types of agency is an interesting one to pursue, for it is not obvious up front which type of agent would achieve better outcomes. This paper uses game theory to explore and begin to answer this question. (...) We present a game theoretic examination of five forms of heteronomy and their corresponding forms of autonomy. We show that across a significant range of interactive situations agents who have the autonomy to choose between selfishness and either empathy or altruism achieve expected material payoffs equal to the maximum expected material payoffs of the corresponding heteronomous agents. We also show that across the same range of interactions agents who have the autonomy to choose between a deontological moral law and selfishness, empathy, or altruism achieve higher expected material payoffs than the corresponding heteronomous agents. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)

The traditional problem of free will has reached an impasse; we are unlikely to see progress without rethinking the terms in which the problem had been cast. Our approach offers an alternative to the standard terms of the debate, by developing an authorially parameterized approach articulated within a two-dimensional semantics for temporal predicates.

The use of evolutionary game theory to explain the evolution of human norms and the behavior of humans who act according to those norms is widespread. Both the aims and motivation for its use are clearly articulated by Harms and Skyrms (2008) in the following passage: "A good theory of evolution of norms might start by explaining the evolution of altruism in Prisoner’s Dilemma, of Stag Hunting, and of the equal split in the symmetric bargaining game. These are not well-explained (...) by classical game theory based on rational choice. From a technical point of view, they present different theoretical challenges. In the bargaining game, there are an infinite number of equilibria with no principled (rational choice) way to select the cooperative one. In Stag Hunt there are only two, but the non-cooperative one is selected by risk-dominance. In Prisoner’s Dilemma the state of mutual cooperation is not a Nash equilibrium at all, and cooperation flies in the face of the rational-choice principle that one does not choose less rather than more. In contrast to rational choice theory, the most common tool of evolutionary game theory is the replicator dynamics, in which the propagation rate of each strategy is determined by its current payoffs. These dynamics have a rationale in both biological and cultural evolutionary modeling, and sometimes tell us things that rational choice theory does not." We agree with the first sentence in this quotation: a good theory about the behavior under norms ought to explain altruism in the Prisoner’s Dilemma (PD), playing Stag in Stag Hunt (SH), and offering equal splits in the symmetric Nash bargaining game (NB). We also agree with Harms and Skyrms about the difference in technical challenges each of these games poses. Finding a single mechanism, even one as broadly understood as evolution, that could solve these challenges en masse is no doubt a tall order. Nonetheless, in this paper, we present a single, simple, modification to SH, NB, and a general n-player PD that does just that: we introduce deontological autonomy into the models. (shrink)

In this note, I discuss a very simple time-dependent formula and its relation to the cosmological constant. I first note that the the formula yields an exact match of the cosmological constant on the assumption that the age of the universe is 8.08×10^60 in Planck units. I then suggest a physical interpretation of the formula according to which the cosmological constant is the result of a magnetic field.

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. (shrink)

The idea that a being can be identical to its own essence has a long and venerable history in theological speculation. As with many ideas in theology, however, such an idea has never been given an adequate mathematical formulation. The key to such a formulation, I argue, is introducing an essence axiom into non-well-founded set theory. According to such an axiom, for every set, x, there is a set that contains all and only those sets that contain x. With such (...) an axiom, it becomes possible to introduce an essence function that takes each set to its essence. An object that is identical to its essence, then, is simply a fixed point of the essence function. In this paper, I first discuss a theorem according to which any fixed point of the essence function is universally symmetrical with respect to the set membership relation. After proving the theorem, I discuss its theological implications. I go on to argue that the process of counting the members of a set that is identical to its essence is a Sisyphusian process. Such a fact I suggest shows that the absurdity of human existence is not alleviated by the existence of God but rather is entailed by it. (shrink)

In The Divine Fractal, Studtmann (2021) introduced a novel conception of God, what he calls the symmetry conception, and showed that such a conception not only can be formalized within extensional non-well-founded set theory but also entails the Thomistic view that God is identical to her essence. In this paper, I show that Studtmann’s symmetry conception of God can be integrated into a recent approach to quantum gravity, namely causal set theory. The theory that results has two significant consequences. First, (...) God is the necessarily existing set of spacetime events. Second, the square root of the probability that a spacetime event randomly chosen from N spacetime events is uncaused is given by the following formula: ((Harmonic [N])/N)^(1/2). I conclude the paper by briefly discussing a connection between this formula and the cosmological constant. (shrink)