The game of life is an excellent framework for metaphysical modeling. It can be used to study ontological categories like space, time, causality, persistence, substance, emergence, and supervenience. It is often said that there are many levels of existence in the game of life. Objects like the glider are said to exist on higher levels. Our goal here is to work out a precise formalization of the thesis that there are various levels of existence in the game of life. To (...) formalize this thesis, we develop a set-theoretic construction of the glider. The method of this construction generalizes to other patterns in the game of life. And it can be extended to more realistic physical systems. The result is a highly general method for the set-theoretical construction of substances. (shrink)

Among many properties distinguishing emergence, such as novelty, irreducibility and unpredictability, computational accounts of emergence in terms of computational incompressibility aim first at making sense of such unpredictability. Those accounts prove to be more objective than usual accounts in terms of levels of mereology, which often face objections of being too epistemic. The present paper defends computational accounts against some objections, and develops what such notions bring to the usual idea of unpredictability. I distinguish the objective unpredictability, compatible with determinism (...) and entailed by emergence, and various possibilities of predictability at emergent levels. This makes sense of practices common in complex systems studies that forge qualitative predictions on the basis of comparisons of simulations with multiple values of parameters. I consider robustness analysis as a way to ensure the ontological character of computational emergence. Finally, I focus on the property of novelty, as it is displayed by biological evolution, and ask whether computer simulations of evolution can produce the same kind of emergence as the open-ended evolution attested in Phanerozoic records. (shrink)

Weak emergence is the view that a system’s macro properties can be explained by its micro properties but only in an especially complicated way. This paper explains a version of weak emergence based on the notion of explanatory incompressibility and “crawling the causal web.” Then it examines three reasons why weak emergence might be thought to be just in the mind. The first reason is based on contrasting mere epistemological emergence with a form of ontological emergence that involves irreducible downward (...) causation. The second reason is based on the idea that attributions of emergence are always a reflection of our ignorance of non-emergent explanations. The third reason is based on the charge that complex explanations are anthropocentric. Rather than being just in the mind, weak emergence is seen to involve a distinctive kind of complex, macro-pattern in the mind-independent objective micro-causal structure that exists in nature. The paper ends by addressing two further questions. One concerns whether weak emergence applies only or mainly to computer simulations and computational systems. The other concerns the respect in which weak emergence is dynamic rather than static. (shrink)

Bedau's influential (1997) account analyzes weak emergence in terms of the non-derivability of a system’s macrostates from its microstates except by simulation. I offer an improved version of Bedau’s account of weak emergence in light of insights from information theory. Non-derivability alone does not guarantee that a system’s macrostates are weakly emergent. Rather, it is non-derivability plus the algorithmic compressibility of the system’s macrostates that makes them weakly emergent. I argue that the resulting information-theoretic picture provides a metaphysical account of (...) weak emergence rather than a merely epistemic one. (shrink)

At the end of the 19th century, Josiah Royce participated in what has come to be called the great debate (Royce, 1897; Armour, 2005).1 The great debate concerned issues in metaphysical theology, and, since metaphysics was primarily idealistic, it dealt considerably with the relations between the divine Self and lesser selves. After the great debate, Royce developed his idealism in his Gifford Lectures (1898-1900). These were published as The World and the Individual. At the end of the first volume, Royce (...) added a Supplementary Essay. The Essay, continuing themes from the great debate, developed an intriguing mathematical model of the relations between the divine Self and lesser selves. The second volume went on to.. (shrink)

A phenomenon resulting from a computationally irreducible (or computationally incompressible) process is supposedly unpredictable except via simulation. This notion of unpredictability has been deployed to formulate recent accounts of computational emergence. Via a technical analysis, I show that computational irreducibility can establish the impossibility of prediction only with respect to maximum standards of precision. By articulating the graded nature of prediction, I show that unpredictability to maximum standards is not equivalent to being unpredictable in general. I conclude that computational irreducibility (...) fails to fulfill its assigned philosophical roles in theories of computational emergence. (shrink)