Brian Skyrms offers a fascinating demonstration of how fundamental signals are to our world. He uses various scientific tools to investigate how meaning and communication develop. Signals operate in networks of senders and receivers at all levels of life, transmitting and processing information. That is how humans and animals think and interact.

Skyrms-Lewis signaling games illustrate how meaningful language may evolve from initially meaningless random signals (Lewis, Convention 1969; Skyrms 2008). Here we will consider how incommensurable languages might evolve in the context of signaling games. We will also consider the types of incommensurability exhibited between evolved languages in such games. We will find that sequentially evolved languages may be strongly incommensurable while still allowing for increasingly faithful descriptions of the world.

We consider the following signaling game. Nature plays first from the set {1, 2}. Player 1 (the Sender) sees this and plays from the set {A, B}. Player 2 (the Receiver) sees only Player 1’s play and plays from the set {1, 2}. Both players win if Player 2’s play equals Nature’s play and lose otherwise. Players are told whether they have won or lost, and the game is repeated. An urn scheme for learning coordination in this game is as (...) follows. Each node of the desicion tree for Players 1 and 2 contains an urn with balls of two colors for the two possible decisions. Players make decisions by drawing from the appropriate urns. After a win, each ball that was drawn is reinforced by adding another of the same color to the urn. A number of equilibria are possible for this game other than the optimal ones. However, we show that the urn scheme achieves asymptotically optimal coordination. (shrink)

This article concerns how rule-following behavior might evolve, how an old evolved rule might come to be appropriated to a new context, and how simple concepts might coevolve with rule-following behavior. In particular, we consider how the transitive inferential rule-following behavior exhibited by pinyon and scrub jays might evolve in the context of a variety of the Skyrms-Lewis signaling game, then how such a rule might come to be appropriated to carry out inferences regarding stimuli different from those involved in (...) the original evolution of the rule, and how this appropriation involves a step toward the evolution of basic ordinal concepts. (shrink)

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. (shrink)

Lewis sender‐receiver games illustrate how a meaningful term language might evolve from initially meaningless random signals (Lewis 1969; Skyrms 2006). Here we consider how a meaningful language with a primitive grammar might evolve in a somewhat more subtle sort of game. The evolution of such a language involves the co‐evolution of partitions of the physical world into what may seem, at least from the perspective of someone using the language, to correspond to canonical natural kinds. While the evolved language may (...) allow for the sort of precise representation that is required for successful coordinated action and prediction, the apparent natural kinds reflected in its structure may be purely conventional. This has both positive and negative implications for the limits of naturalized metaphysics. (shrink)

We are concerned here with explaining how successful rule-following behavior might evolve and how an old evolved rule might come to be successfully used in a new context. Such rule-following behavior is illustrated in the transitive judgments of pinyon and scrub-jays (Bond et al., Anim Behav 65:479–487, 2003). We begin by considering how successful transitive rule-following behavior might evolve in the context of Skyrms–Lewis sender–receiver games (Lewis, Convention. Harvard University Press, Cambridge, 1969; Skyrms, Philos Sci 75:489–500, 2006). We then consider (...) two ways that an agent might come to use an old evolved rule in a new context. The first involves the agent evolving successful dispositions for one concrete type of experience, then associating a new type of experience with the old evolved dispositions. The second involves the agent evolving dispositions that represent a general inferential schema, then composing these dispositions with others in a way that allows the agent to make inferences concerning a new concrete type of experience. (shrink)

Insofar as empirical inquiry involves the coevolution of descriptive language and theoretical commitments, a satisfactory model of empirical knowledge should describe the coordinated evolution of both language and theory. But since we do not know what conceptual resources we might need to express our future theories or to provide our best future faithful descriptions of the world, we do not now know even what the space of future descriptive options might be. One strategy for addressing this shifting-resource problem is to (...) track the predictive and linguistic dispositions of inquirers rather than to track their theories and conceptual resources directly. Sender-predictor games, a variant of Skyrms–Lewis sender-receiver games, provide very simple models for the coordinated coevolution of predictive and linguistic dispositions. Such models explain how it is possible for (1) predictive and descriptive dispositions of inquirers to coevolve, (2) term-wise incommensurable, but nevertheless descriptively faithful languages, to sequentially evolve, and (3) a sort of underdetermination to occur where inquirers might satisfy their descriptive and predictive aims by revising their linguistic dispositions, their theoretical dispositions, or both. Such models also provide an elementary characterization of what it might mean for descriptions of the world to be faithful and hence for empirical inquiry to be successful. In doing so they provide a relatively weak, but perfectly clear, endogenous account of epistemic norms. (shrink)

Amodel for inventing newsignals is introduced in the context of sender–receiver games with reinforcement learning. If the invention parameter is set to zero, it reduces to basic Roth–Erev learning applied to acts rather than strategies, as in Argiento et al. (Stoch. Process. Appl. 119:373–390, 2009). If every act is uniformly reinforced in every state it reduces to the Chinese Restaurant Process—also known as the Hoppe–Pólya urn—applied to each act. The dynamics can move players from one signaling game to another during (...) the learning process. Invention helps agents avoid pooling and partial pooling equilibria. (shrink)

Skyrms-Lewis sender-receiver games with invention allow one to model how a simple mathematical language might be invented and become meaningful as its use coevolves with the basic arithmetic competence of primitive mathematical inquirers. Such models provide sufficient conditions for the invention and evolution of a very basic sort of arithmetic language and practice, and, in doing so, provide insight into the nature of a correspondingly basic sort of mathematical knowledge in an evolutionary context. Given traditional philosophical reflections concerning the nature (...) and preconditions of mathematical knowledge, these conditions are strikingly modest. (shrink)