Abstract
As the content of propositional attitudes, propositions are usually taken to help explain the behavior of rational agents. However, a closer look at signaling games suggests otherwise: rational agents often acquire partial beliefs, and many of their signals are ambiguous. Signaling games also suggest that it is rational for agents to mix their behavior in response to partial beliefs and ambiguous signals. But as I show in this paper, propositions cannot help explain the mixing behavior of rational agents: to explain mixing behavior, we need a probabilistic notion of content. I also show that a probabilistic notion of content renders propositions explanatorily idle in the case of unambiguous signals and full beliefs as well. My suggestion is thus that we should abandon propositions in explanations of rational behavior and adopt instead a probabilistic notion of content. The notion of probabilistic content ultimately provides a simpler framework for explanations of rational behavior than the notion of propositional content.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Philosophers in the naturalist tradition may be skeptical that content—propositional or otherwise—could explain behavior: no matter what account is given of it, the content of a signal or mental state is an abstract entity that cannot enter causal relations with concrete mental states and linguistic expressions. This objection demands clarification. The notion of content is a high-level description of mental and linguistic phenomena that may or may not have a physical basis. If it turns out that such phenomena do not in fact have a physical underpinning, naturalist philosophers would be justified in jettisoning the notion of content. In this paper, I remain neutral on this issue.
For simplicity, assume that participants in a conversation always share the same context set. This is what Stalnaker (2002) calls a “non-defective” context.
The notation used here makes it easier to state my argument, but note that it is not the notation used by Skyrms.
A general point of contention is about how precise we should take partial beliefs to be. Perhaps beliefs should be represented by a family of probability functions—and not by a single probability function, as I assume throughout. Indeed, some argue that imprecise evidence rationally dictates imprecise beliefs and that imprecise belief are also more realistic on psychological grounds (Joyce 2010). Notice, however, that my argument does not hinge on a model of precise beliefs. Whether or not rational agents use or should use imprecise credences in inference and decision making, it is clear that rational agents must acquire beliefs that are compatible with the available evidence. And if the available evidence supports only (a family of) partial beliefs, the actions of a rational agent must reflect the intermediate (and imprecise) probability values associated with those beliefs. And reasons are given above for thinking that propositions cannot explain the actions of a rational agent when her actions are guided by partial beliefs.
It would be possible to restore the explanatory power of the truth-functional account by abandoning the requirement that truth values be binary. Using the tools of fuzzy set theory, a proposition could be represented as a function from possible worlds to values between 0 and 1. On this proposal, a proposition would thus be a function of the form \(P\,{:}\,W \rightarrow [0,1]\), where P is a membership function mapping the set of possible worlds W onto the unit interval. This approach would also solve the problems raised above. However, I favor the use of probabilities for the following reasons. First, game-theoretical models of signaling are built on the language of probabilities. It is therefore convenient to keep the formal toolkit to a minimum and extend the use of probabilities. Second, Stalnaker—the greatest proponent of the truth-functional account—insists that truth values are binary. To reject this requirement would be too great a departure from the truth-functional account. But notice that the use of probabilities is not uniquely required. Any formal system that allows for a function to map possible worlds onto intermediate values—whether it be the probability calculus or fuzzy set theory—would account equally well for the behavior of rational agents that act on partial beliefs and send ambiguous signals.
Recent theories of content inspired by signaling games tend to overlook the role of ambiguous signals and partial beliefs in guiding rational behavior, presupposing instead that signals and beliefs all have content that is devoid of ambiguity—see, for example, Birch (2014) and Stegmann (2009). Although the question addressed here is orthogonal to debates about what fixes the content of signals and beliefs in signaling games, my argument suggests that any account of content that restricts its scope to ambiguity-free contexts is at best incomplete.
Given that probability values can take any value in the unit interval, a distribution of probability distributions would be better represented as a continuous distribution. For simplicity and ease of exposition, I assume here otherwise. But nothing hinges on this point.
References
Birch, J. (2014). Propositional content in signalling systems. Philosophical Studies, 171(3), 493–512.
Bruner, J., O’Connor, C., Rubin, H., & Huttegger, S. M. (2014). David Lewis in the lab: Experimental results on the emergence of meaning. Synthese. doi:10.1007/s11229-014-0535-x.
Cai, H., & Wang, J. T.-Y. (2006). Overcommunication in strategic information transmission games. Games and Economic Behavior, 56(1), 7–36.
Crawford, V. P., & Sobel, J. (1982). Strategic information transmission. Econometrica: Journal of the Econometric Society, 50, 1431–1451.
Dickhaut, J. W., McCabe, K. A., & Mukherji, A. (1995). An experimental study of strategic information transmission. Economic Theory, 6(3), 389–403.
Dretske, F. (1981). Knowledge and the flow of information. Cambridge: MIT Press.
Franke, M., & Correia, J. P. (2016). Vagueness and imprecise imitation in signaling games. British Journal for the Philosophy of Science. doi:10.1093/bjps/axx002.
Franke, M., Jäger, G., & Van Rooij, R. (2010). Vagueness, signaling and bounded rationality. In JSAI international symposium on artificial intelligence (pp. 45–59). Springer.
Gee, N. R., & Harris, S. L. (2010). Homograph norms: An alternative approach to determining meaning dominance. Behavior research methods, 42(4), 976–986.
Godfrey-Smith, P. (2011). Signals: Evolution, learning, and information, by Brian Skyrms. Mind, 120(480), 1288–1297.
Godfrey-Smith, P., & Martínez, M. (2013). Communication and common interest. PLoS Computational Biology, 9(11), 1–6.
Haro, J., Ferré, P., Boada, R., & Demestre, J. (2016). Semantic ambiguity norms for 530 Spanish words. Applied Psycholinguistics. doi:10.1017/S0142716416000266.
Huttegger, S. M., Skyrms, B., Smead, R., & Zollman, K. J. (2010). Evolutionary dynamics of Lewis signaling games: Signaling systems vs. partial pooling. Synthese, 172(1), 177–191.
Huttegger, S. M., & Zollman, K. J. (2010). Dynamic stability and basins of attraction in the Sir Philip Sidney game. Proceedings of the Royal Society of London B: Biological Sciences, 277(1689), 1915–1922.
Joyce, J. M. (2010). A defense of imprecise credences in inference and decision making. Philosophical Perspectives, 24(1), 281–323.
Lewis, D. (1969). Convention: A philosophical study. Cambridge: Harvard University Press.
Maynard-Smith, J. (1991). Honest signalling: The Philip Sidney game. Animal Behaviour, 42(6), 1034–1035.
Moss, S. (2013). Epistemology formalized. Philosophical Review, 122(1), 1–43.
Navigli, R. (2009). Word sense disambiguation: A survey. ACM Computing Surveys (CSUR), 41(2), 10.
O’Connor, C. (2014). The evolution of vagueness. Erkenntnis, 79(4), 707–727.
O’Connor, C. (2015). Ambiguity is kinda good sometimes. Philosophy of Science, 82(1), 110–121.
Perea, A. (2012). Epistemic game theory: Reasoning and choice. Cambridge: Cambridge University Press.
Quine, W. V. (1934). Ontological remarks on the propositional calculus. Mind, 43(172), 472–476.
Rubin, H., Bruner, J., O’Connor, C., & Huttegger, S. M. (2016). Communication without the cooperative principle: A signaling experiment. Unpublished manuscript.
Santana, C. (2014). Ambiguity in cooperative signaling. Philosophy of Science, 81(3), 398–422.
Scarantino, A. (2015). Information as a probabilistic difference maker. Australasian Journal of Philosophy, 93(3), 419–443.
Serra-Garcia, M., Van Damme, E., & Potters, J. (2011). Hiding an inconvenient truth: Lies and vagueness. Games and Economic Behavior, 73(1), 244–261.
Skyrms, B. (2010). Signals: Evolution, learning, and information. Oxford: Oxford University Press.
Staffel, J. (2013). Can there be reasoning with degrees of belief? Synthese, 190(16), 3535–3551.
Stalnaker, R. (1976). Propositions. In Issues in the philosophy of language (pp. 79–91).
Stalnaker, R. (1978). Assertion. Syntax and Semantics, 9, 315–332.
Stalnaker, R. (1984). Inquiry. Cambridge: MIT Press.
Stalnaker, R. (2002). Common ground. Linguistics and philosophy, 25(5), 701–721.
Stalnaker, R. (2003). Ways a world might be: Metaphysical and anti-metaphysical essays. Oxford: Oxford University Press.
Stegmann, U. E. (2009). A consumer-based teleosemantics for animal signals. Philosophy of Science, 76(5), 864–875.
Wagner, E. O. (2011). Deterministic chaos and the evolution of meaning. The British Journal for the Philosophy of Science, 63(3), 547–575.
Wagner, E. O. (2013). The dynamics of costly signaling. Games, 4(2), 163–181.
Zollman, K. J., Bergstrom, C. T., & Huttegger, S. M. (2012). Between cheap and costly signals: The evolution of partially honest communication. Proceedings of the Royal Society B: Biological Sciences. doi:10.1098/rspb.2012.1878.
Acknowledgements
I thank Alex Rosenberg, Karen Neander, Robert Brandon, and especially Carlotta Pavese for invaluable feedback on previous drafts of this paper, as well as three anonymous referees for their helpful comments. I also thank Hannah Read for her support. Funding was provided by Graduate School, Duke University.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ventura, R. Ambiguous signals, partial beliefs, and propositional content. Synthese 196, 2803–2820 (2019). https://doi.org/10.1007/s11229-017-1580-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-017-1580-z