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Epistemology and the Structure of Language

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Abstract

We are concerned here with how structural properties of language may come to reflect features of the world in which it evolves. As a concrete example, we will consider how a simple term language might evolve to support the principle of indifference over state descriptions in that language. The point is not that one is justified in applying the principle of indifference to state descriptions in natural language. Instead, it is that one should expect a language that has evolved in the context of facilitating successful action to reflect probabilistic features of the world in which it evolved.

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Notes

  1. There is a tradition of such explanations in the field. Skyrms (2010a) shows how communication may evolve without natural salience, but not that it actually did so; Barrett (2007) and Purves (2018) show that it is possible for partitioning into linguistic kinds to evolve and to be ideally successful without latching onto natural kinds, but not that linguistic kinds in fact fail to track natural kinds; and Roth and Erev (1995), Erev and Roth (1998), and Barrett and Zollman (2009) show that dynamics like forgetting and experimenting may promote the evolution of language, but not that they actually have been causal factors in the evolution of language.

  2. Though, see the discussion in Huemer (2009), Bradley (2019), and Neth (2019).

  3. See Argiento et al. (2009) for details.

  4. See Barrett (2014b) for a discussion of such games more generally.

  5. See Barrett (2014a) for a detailed description of this particular sender-predictor game, its behavior, a discussion of the problem of priors, and a proposed dissolution of the problem.

  6. See Barrett (2007) and Purves (2018) for explanations of this sort of failure.

  7. See also Bertrand (1889).

  8. Another well-known problem with the principle of indifference is that it leads to complications and inconsistencies on infinite domains (Keynes 1921). This will not concern us here, given that all of our examples are finite.

  9. See also O’Connor (2017), who discusses interactions between structures in the world and structures in language in signaling games, and Purves (2018).

  10. This is sometimes referred to as the maximum entropy principle. It is closely tied to the principle of indifference, but for reasons discussed in the last section and later in the paper, we do not take maximum entropy to provide any justification whatsoever for adopting the principle of indifference. See Jaynes (1957), and Williamson (2010) for contrary views on this issue.

  11. See Shannon (1948), and Shannon and Weaver (1949). For a careful analysis of information in the context of signaling games, see Skyrms (2010a), and Skyrms (2010b).

  12. For empirical work on reinforcement learning in nature, see Rescorla and Wagner (1972), Roth and Erev (1995), Schultz et al. (1997), Erev and Roth (1998), and Schultz (2004). For an introduction to reinforcement learning in a computational framework, see Sutton and Barto (1998).

  13. Every partition that takes advantage of both signals, that is, every partition except (0, 10) and (10, 0)—which are dynamically unstable—has the same expected payoff as long as the sender and receiver coordinate upon the partition and regardless of what weight the receiver puts on each action conditional upon the relevant signal. See LaCroix (2019) for details.

  14. The average expected payoff is calculated from the evolved dispositions of the agents (that is, from their actual urn contents) at the end of the run given the unbiased (or biased as in the next section) states of nature.

  15. The fastest run achieves this payoff within 1801 plays and the slowest after 25995 plays. 0.90 runs are within 5% of their final expected payoff prior to the first 7500 plays.

  16. The cumulative success rate is a measure of success that takes account of the history of the game. It is calculated by dividing the number of plays that led to a success by the total number of plays in that run. When the players are successful, early failures are washed out as the number of plays increases.

  17. To provide a bit more detail, the null hypothesis is that the combinatorial distribution and the empirical distribution are identical for the \(10\times 2\times 10\) signaling game. The K–S test gives the statistic \(D=0.0843\), which is the supremum of the set of distances between the empirical distribution function we observe and the expected distribution function from the combinatorial measure. This corresponds to a p value of 0.0017; hence one might reject the null hypothesis with high confidence.

  18. 0.90 runs are within 5% of their final expected payoff prior to the first 9500 plays.

  19. A K–S test of the empirical distribution against a distribution sampled from the combinatorial expectation yields the statistic \(D = 0.1912\), with a p value \(p < 0.0001\), suggesting again that the combinatorial expectations do not by themselves explain the empirical results.

  20. 0.90 runs are within 5% of their final expected payoff prior to the first 2200 plays.

  21. 0.90 runs are within 5% of their final expected payoff prior to the first 10000 plays.

  22. A (5, 3, 1) partition occurs 0.073, a (4, 4, 1) partition occurs 0.019, a (5, 2, 2) partition occurs 0.066, a (4, 3, 2) partition occurs 0.030, and a (3, 3, 3) partition occurs 0.005. In each case, the distinct permutations of these partitions occur with roughly equal frequency.

  23. For example, the data presented in the original studies of Seyfarth et al. (1980a, b) on vervet monkey alarm-call systems indicated substantial variation in responses and that the responses are probabilistic rather than deterministic. Furthermore, vervets do not just vocalize for alarm calls. They also call when they find food, in aggressive confrontations, and during sexual activity, among others. Vervets additionally vocalize via grunting in a variety of circumstances: (a) when a submissive meets a dominant individual, (b) when a dominant meets a submissive individual, (c) when one vervet goes out into an open area, and (d) when a vervet comes across an out-group conspecific (Cheney and Seyfarth 1982, 1990). Schlenker et al. (2016) provide a linguistic analysis of approximately 40 years of data from experimental primatology, which displays several complexities of monkey communication systems. This highlights but some of the myriad ways in which the world is significantly more complex than the model which we use to represent it.

  24. See Barrett and Zollman (2009) for several learning dynamics that typically behave very differently than simple reinforcement learning. As a quick and very simple example, the learning dynamics win-stay/lose-shift would not even evolve a stable language in the present games, let alone one that supported the principle of indifference.

  25. There is an extensive literature in cognitive science that seeks to quantify how language might reflect the structure of the world. See Lupyan and Dale (2016) for an overview and discussion of the linguistic niche hypothesis.

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Acknowledgements

Both authors would like to thank the reviewers for comments on an earlier draft of the paper. They would also like to thank Brian Skyrms for insightful conversations on the nature of information in signaling games. LaCroix would like to thank Charles Reiss and the audience at CRSP (Winter 2020) in Montréal. LaCroix would additionally like to thank Mila - Québec Artificial Intelligence Institute and, in particular, Yoshua Bengio for providing generous space and resources.

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  1. Department of Logic and Philosophy of Science, University of California, Irvine, CA, USA

    Jeffrey A. Barrett & Travis LaCroix

  2. Mila - Québec Artificial Intelligence Institute, Montréal, Canada

    Travis LaCroix

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  1. Jeffrey A. Barrett
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Correspondence to Travis LaCroix.

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Barrett, J.A., LaCroix, T. Epistemology and the Structure of Language. Erkenn 87, 953–967 (2022). https://doi.org/10.1007/s10670-020-00225-4

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