Abstract
Skyrms, building on the work of Dretske, has recently developed a novel information-theoretic account of propositional content in simple signalling systems. Information-theoretic accounts of content traditionally struggle to accommodate the possibility of misrepresentation, and I show that Skyrms’s account is no exception. I proceed to argue, however, that a modified version of Skyrms’s account can overcome this problem. On my proposed account, the propositional content of a signal is determined not by the information that it actually carries, but by the information that it would carry at the nearest separating equilibrium of the underlying evolutionary dynamics. I show that this amended account yields reasonable ascriptions of false propositional content in a well-known formal model of the evolution of communication (the ‘Philip Sidney’ game), and close with a discussion of the serious but perhaps not insuperable difficulties we face in applying the account to examples of signalling in the real world.
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Notes
See Adams and Beighley (2013) for a particularly clear statement of this sceptical view.
In a sense, the ‘problem of error’ and the ‘disjunction problem’ are two sides of the same coin: information theory struggles to explain misrepresentation because, in cases where a signal can be caused by any of a number of factors, it appears to imply that the signal must truthfully represent the disjunction of these factors. But a number of authors have argued that the disjunction problem is more pervasive than the problem of error, and I need not take sides on this issue here (though see footnote 22). For further discussion of the relationship between the two problems, see Fodor (1990), Neander (1995, 2012), Crane (2003), Adams and Aizawa (2010).
A coordination equilibrium is a special kind of Nash equilibrium. At a Nash equilibrium, no agent gains by unilaterally switching from one strategy to another. At a coordination equilibrium, no agent gains if anyone unilaterally switches.
Of course, individuating ‘relevant states’ can be a significant challenge outside the world of simple formal models. I return to this problem in Sect. 6.
Skyrms here assumes that \( \log \left( 0 \right) = - \infty \). Strictly speaking, we should say that −∞ is the limit of \( \log \left( x \right) \) as \( x \to 0 \), since \( \log \left( 0 \right) \) is undefined. But Skyrms’s assumption seems innocuous enough in the present context.
Godfrey-Smith (2013) briefly notes this problem. Here I aim to spell it out in more detail.
Plainly, the problem here stems from the fact that Skyrms’s account (like Dretske’s before it) implies that a signal must shift the probability of ~p to 0 in order to carry the propositional content that p. Given this, one might naturally suspect that a ‘quick fix’ is available, whereby we simply relax this requirement and attribute propositional content whenever the probability of ~p is downshifted to, say, 0.01. As Dretske realized from the outset, the problem of error would not arise for such an account—at least not in this acute form. However, Dretske (1981, Chaps. 2–4) offers two main arguments against relaxing this requirement. First, he argues that it is needed in order to preserve a transitivity (or ‘Xerox’) principle, such that if A carries the information that B, and B carries the information that C, then A carries the information that C; he proceeds to argue that preserving this principle is crucial if we want information to ‘flow’ through a series of structures. Second, he argues that probabilities of 0 or 1 are needed if we want to preserve a conjunction principle, such that if A carries the information that B, and it also carries the information that C, then it carries the information that B & C. I agree with Dretske that the transitivity and conjunction principles are worth preserving, and that rejecting them in order to make room for error is a high price to pay. The account I develop in subsequent sections is intended to allow for misrepresentation while preserving both principles.
‘H. Paul Grice distinguished between natural and non-natural meaning. Natural meaning depends on associations arising from natural processes. I say that all meaning is natural meaning’ (Skyrms 2010a, p. 1).
Of course, the ‘teleosemantics’ programme is also closely associated with Millikan (1984) and Papineau (1984). But Millikan and Papineau see the notion of biological function as providing as an alternative to information-theoretic semantics, rather than as providing a means of augmenting the information-theoretic approach to accommodate error. I do not discuss these ‘consumer-based’ variants of teleosemantics in this paper.
This would constitute malfunctioning only on the assumption that the alarm call was selected specifically for indicating leopards, and not for indicating (say) large predators. The functional indeterminacy problem (see footnote 14) threatens to raise its head here, but let’s assume for now that the alarm call was specifically selected for indicating leopards. The example is only for illustrative purposes, after all.
See Neander (2012) for a survey. These debates have tended to focus on problems that are shared by all variants of teleosemantics, viz. problems of functional indeterminacy (e.g., Dretske 1986; Sterelny 1990; Griffiths and Goode 1995; Neander 1995) and clashes with intuition in ‘swampman’-type scenarios (e.g. Dretske 1995; Neander 1996; Millikan 1996; Papineau 2001). Millikan (1989) poses a further problem that is specific to accounts that combine the notion of function with information theory. Her concern, in a nutshell, is that the proper function of a representation must be an effect (specifically, a selected effect) that the representation has on a consumer system, and the effect of a representation on a consumer system will be independent of any information it carries about features of the environment. This is a longstanding point of disagreement between Millikan and Neander (see Neander 2013, and Millikan’s reply).
Stampe goes on to characterize these fidelity conditions in functional terms. I want to explore a different possibility here.
Like many other game-theoretic notions, this notion has been imported to biological game theory from economics, where the one-to-one mapping in question is usually that between the price of a product and its quality (e.g. Rothschild and Stiglitz 1976; Milgrom and Roberts 1982; Wolinsky 1983; Easley and O’Hara 1987; Allen and Faulhaber 1989).
This still leaves room for ambiguity. Is the ‘nearest’ equilibrium the one that would require the smallest change in population frequencies to produce, or the one that would take the least time to arrive at by the shortest route, or the one that has a basin of attraction closest to the population’s actual state? There are no doubt further possible measures of dynamical ‘distance’. Hopefully, there will be many cases in which all reasonable measures agree on the nearest separating equilibrium, in which case we need not choose between them. When they disagree, we can choose an arbitrary stipulation of the concept of ‘nearest’ if we want to, but perhaps the more principled response is to say that there is no determinate answer to the question of which separating equilibrium is the ‘nearest’ in these cases.
Philip Sidney was an Elizabethan aristocrat and poet who was mortally wounded at the Battle of Zuphen. The legend goes that, as he lay dying, he handed his water to another wounded soldier, remarking ‘thy necessity is yet greater than mine’. Following Johnstone and Grafen (1992), the game is sometimes known as the ‘Sir Philip Sidney’ game, though this was not Maynard Smith’s original title. The original title is more apt, since a knighthood is a living honour which lapses upon death.
For the particular version of the game studied in Huttegger and Zollman (2010).
In this scenario, unlike in the case of alarm calls, the sender is not necessarily ‘observing’ a state of the world, since it may have non-observational sensitivity to its own health. But we can say that the sender ‘observes’ its own health if we want to, since the mechanism by which a sender comes to detect the relevant state of the world makes no difference to the formalism.
The partition problem is clearly reminiscent of the ‘disjunction problem’, and might be regarded as the way in which one aspect of that problem resurfaces for the NSE account. But note that the problem here is purely one of finding a principled partition of states of the world. Relative to any given partition, the NSE account is able to distinguish between true and false tokenings of a signal; so this aspect of the traditional ‘disjunction problem’ does not resurface.
One option is to individuate states by their payoffs: if two putative states yield identical payoffs under all conditions, then they are identical for the purposes of content ascription. One drawback to this move is that, in real ecological scenarios, payoffs are likely to depend in an extremely fine-grained way on environmental differences, suggesting that few natural populations would even approximate a separating equilibrium by this criterion. But this remains an avenue worthy of further exploration.
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Acknowledgments
Versions of this article were presented between March and June 2013 at the University of Cambridge, the University of Bristol and Duke University. I thank the audiences at these events for their helpful questions and comments, and I thank Peter Godfrey-Smith, Françoise Longy, Manolo Martínez, Nick Shea and Ulrich Stegmann for their detailed and insightful comments on the manuscript.
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Birch, J. Propositional content in signalling systems. Philos Stud 171, 493–512 (2014). https://doi.org/10.1007/s11098-014-0280-5
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DOI: https://doi.org/10.1007/s11098-014-0280-5