# Your search: "author:"Barrett, Jeffrey""

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## Scholarly Works (20 results)

David Lewis (1969) introduced sender-receiver games as a way of investigating how meaningful language might evolve from initially random signals. In this report I investigate the conditions under which Lewis signaling games evolve to perfect signaling systems under various learning dynamics. While the 2-state/2-term Lewis signaling game with basic urn learning always approaches a signaling system, I will show that with more than two states suboptimal pooling equilibria can evolve. Inhomogeneous state distributions increase the likelihood of pooling equilibria, but learning strategies with negative reinforcement or certain sorts of mutation can decrease the likelihood of, and even eliminate, pooling equilibria. Both Moran and APR learning strategies (Bereby-Meyer and Erev 1998) are shown to promote successful convergence to signaling systems. A model is presented that illustrates how a language that codes state-act pairs in an order-based grammar might evolve in the context of a Lewis signaling game. The terms, grammar, and the corresponding partitions of the state space co-evolve to generate a language whose structure appears to reflect canonical natural kinds. The evolution of these apparent natural kinds, however, is entirely in service of the rewards that accompany successful distinctions between the sender and receiver. Any metaphysics grounded on the structure of a natural language that evolved in this way would track arbitrary, but pragmatically useful distinctions.

This dissertation argues that what drives the emergence of complex communication systems is a process of modular composition, whereby independent communicative dispositions combine to create more complex dispositions. This challenges the dominant view in language-origins research, which attempts to resolve the explanatory gap between (simple) communication and (natural) language by demonstrating how complex syntax evolved. I show that these accounts fail to maintain sensitivity to empirical data: genuinely compositional syntax is extremely rare or non-existent in nature. In contrast, I propose that the reflexive properties of natural language—the ability to use language to talk about language—provide a plausible alternative explanatory target.

Part I provides the philosophical foundation of this novel account using the theoretical framework of Lewis-Skyrms signalling games and drawing upon relevant work in evolutionary biology, linguistics, cognitive systems, and machine learning. Part II provides a concrete set of models, along with analytic and simulation results, that show precisely how (and under what circumstances) this process of modular composition is supposed to work.

Our epistemic limits depend on the nature of the physical world we inhabit and the ways in which we can observe and manipulate it. This dissertation examines these limits in the realm of physical computation. It focuses on quantum computing and particularly computing in GRW quantum mechanics, although it has implications for both quantum computing in particular and physical computation more broadly. By rigorously investigating the conceptual issues that arise when looking at computation in GRW, we see how the conceptual issues in the foundations of quantum mechanics and our solutions to these issues determine what models of quantum computation can be realized and what quantum computing can achieve. More broadly, we see how grounding our discussions of physical computation in precise physical theories informs our understanding of computational and epistemic limits and illustrates the challenges and nuances involved in the work of developing a rigorous understanding of what is physically computable.

David Lewis's 1969 account of convention formation broke ground through its use of game theory to model how these patterns of behavior might emerge without prior explicit agreement. Of particular interest to us are Lewis's ``signaling games'', a how-possible model for the evolution of a primitive language. Recent work by philosophers and economists applies evolutionary game theory techniques to Lewis's signaling games and demonstrates how a range of cognitively diverse species might learn to communicate. The current manuscript is written in the same spirit: we use evolutionary game theory to investigate how players might reach a successful convention in more generalized signaling game structures.

After a brief introduction in the first chapter, chapter 2 gives results for a simple learning rule, probe and adjust, on three natural extensions of Lewis's original model: the chain game, multiple sender game, and multiple receiver game. The chapter concludes by defining signaling network chains as a particularly flexible generalization of signaling games and with a discussion of probe and adjust on this new model. We show that probe and adjust users converge to a signaling system with probability 1 in all of these signaling game variants. Chapter 3 is an empirical investigation into the effects of extra or too few signals on human subjects' success and learning in Lewis signaling games. Finally, chapter 4 investigates Win-Stay/Lose-Shift with Inertia, a new learning dynamic in which players only change strategies after repeated failure and which seems to characterize some subjects' behavior in chapter 3. We show that this dynamic converges to a signaling system in the limit with probability 1 for all inertia levels and game sizes, with one exception. Our simulations also suggest that a moderate dose of inertia helps agents' speed to convergence in the short and medium run.

The general aim of this thesis is to explore applications of transfinite computation within the philosophy of mathematics|particularly the foundations and philosophy of set theory and to contribute to the young but rapidly growing literature on the technical capabilities and limits of transfinite computation. The material is divided into two main parts. The first concerns transfinite recursion, an essential component of the practice of set theory. Here we seek intrinsically justified reasons for believing in transfinite recursion and the notions of higher computation that surround it. In doing so, we consider several kinds of recursion principle and prove results concerning their relation to one another. Next, philosophical motivations are considered for these formal principles, coming from the idea that computational notions lie at the core of our conception of set. This is significant because, while the iterative conception of set has been widely recognized as insufficient to establish Replacement and recursion, its supplementation by considerations pertaining to algorithms suggests a new and philosophically well-motivated reason to believe in such principles.

The second part addresses technical questions on the mathematical capabilities and limits of a family of models of transfinite computation. These models resemble the infinite-time Turing machine (ITTM) model of Hamkins and Lewis, except with α-length tape (for some ordinal α < ω). Let T_{α<\sub> denote the machine model of tape length α (so Tω<\sub> is equivalent to the ITTM model). Define that Tα<\sub> is computationally stronger<\italic> than Tβ<\sub> (abbreviated Tα<\sub> > Tβ<\sub> ) precisely when Tα<\sub> can compute all Tβ<\sub>-computable functions on binary input strings of size min(α,β), plus more. The following results are found: (1) Tω1<\sub> > Tω<\sub>. (2) There are countable ordinals α such that Tα<\sub> > Tω<\sub>, the smallest of which is the supremum of ordinals clockable by Tω<\sub>. In fact, there is a hierarchy of countable Tα<\sub>s of increasing strength corresponding to the transfinite (weak) Turing-jump operator. (3) There is a countable ordinal μ such that neither Tμ<\sub> ≥ Tω1<\sub> nor Tμ<\sub> ≤ Tω1<\sub> --- that is, the models Tμ<\sub> and Tω1<\sub> are computation-strength incommensurable (and the same holds if countable μ' > μ replaces μ). A similar fact holds for any larger uncountable device replacing Tω1<\sub>. (4) Further observations are made about}

*countable T _{α<\sub>s, including the existence of incommensurabilities between them.}*