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The Brain as an Input–Output Model of the World

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Abstract

An underlying assumption in computational approaches in cognitive and brain sciences is that the nervous system is an input–output model of the world: Its input–output functions mirror certain relations in the target domains. I argue that the input–output modelling assumption plays distinct methodological and explanatory roles. Methodologically, input–output modelling serves to discover the computed function from environmental cues. Explanatorily, input–output modelling serves to account for the appropriateness of the computed function to the explanandum information-processing task. I compare very briefly the modelling explanation to mechanistic and optimality explanations, noting that in both cases the explanations can be seen as complementary rather than contrastive or competing.

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Fig. 1

From Ramsey (2007: 81; Fig. 3c); with permission from Cambridge University Press

Fig. 2
Fig. 3

Adapted from Cannon and Robinson (1987: 1384; Fig. 1); reprinted by permission of the American Physiological Society (APS)

Fig. 4
Fig. 5

Reprinted by permission of Macmillan Publishers Ltd: Zipser and Andersen (1988: 679–684; Fig. 4)

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Notes

  1. See, e.g., Frigg and Hartmann (2017), Weisberg (2013).

  2. See Swoyer (1991) for a general discussion about the relation between modelling and surrogative reasoning. See Grush (2004) for a discussion about modelling and surrogative reasoning in the brain.

  3. Less-than-isomorphism characterizations are in terms of partial isomorphism (French and Ladyman 1999; Da Costa and French 2003), homomorphism (Bartels 2006), and similarity (Giere 2004).

  4. The inputs and outputs need not be peripheral to the brain. In some examples discussed below we talk about sub-systems whose inputs are received and/or their outputs are projected to other parts of the nervous system. The inputs and outputs are very often (magnitude) values of certain properties such as voltages.

  5. The term input–output representation is coined by Ramsey (2007: 68–77), who associates it with task analysis.

  6. See also Gallistel and King: "Representations are functioning homomorphisms. They require structure-preserving mappings (homomorphisms) from states of the world (the represented system) to symbols in the brain (the representing system). These mappings preserve aspects of the formal structure of the world" (2009: x).

  7. See, e.g., Suárez (2010).

  8. Thus Griffiths et al. (2008) say that the big computational question that underlies the Bayesian approach is "How does the mind build rich, abstract, veridical models of the world given only the sparse and noisy data that we observe through our senses?". See also Clark (2015), who further emphasizes the central role of generative models in the hypothesis that the brain is a prediction machine.

  9. We can say that truth-preserving is just a special case of the morphism relation.

  10. See the reviews by Robinson (1968, 1989) and the one by Leigh and Zee (2006).

  11. See also Goldman et al. (2002).

  12. To keep things simpler, I will use here the terms distance and position interchangeably. New (horizontal) position is evaluated on the basis of the distance from the previous position.

  13. Note that in Fig. 3 the term E stands for both the representing (output) neural activity and the represented eye position. Similarly the term Ė stands for both the representing (input) neural activity and the represented eye velocity. This presentation is customary in neuroscience. This sort of presentation underscores (again) the modelling assumption, as it is apparent that the integration relation holds in both representing and represented domains.

  14. This ability is achieved by different animals. A well-known example is the desert ant (Cataglyphis fortis) that returns home after an outward travel of hundreds of meters.

  15. See Mittelstaedt and Mittelstaedt (1982), Collett and Collett (2000), Etienne and Jeffery (2004), Conklin and Eliasmith (2005), McNaughton et al. (2006) and Gallistel and King (2009).

  16. It has been more recently suggested that path integration in rats is computed by the grid cells located in the dorsolateral medial entorhinal cortex (dMEC) (Hafting et al. 2005).

  17. See also Kaplan and Craver (2011), Piccinini and Craver (2011), Miłkowski (2013) and Boone and Piccinini (2016).

  18. They also point out that a "full-blown" mechanistic explanation need not specify the entire properties of the mechanism. It should specify the entire properties that are relevant to the explanandum phenomenon; in some cases (e.g., computational explanations) these properties might all be abstract (e.g., medium-independent) properties (Boone and Piccinini 2016).

  19. There is tension, however, about what counts as a computational explanation. Kaplan seems to claim that computational explanations in neuroscience are adequate to the extent that they describe relevant mechanisms (see also Piccinini 2015; Miłkowski 2013). We suggest that computational explanations of information-processing phenomena also involve a modelling, non-mechanistic, component (Bechtel and Shagrir 2015; Shagrir and Bechtel 2017).

  20. Chirimuuta argues that this minimality conflicts with the more chauvinistic statements about the dominance of mechanistic explanations. Talking about the normalization model, she says that “my key claim is that the use of the term ‘normalization’ in neuroscience retains much of its original mathematical-engineering sense. It indicates a mathematical operation—a computation—not a biological mechanism”, and that this model “departs fully from the model-to-mechanism mapping framework that has been proposed as the criterion for explanatory success” (Chirimuuta 2014); she refers here to Kaplan’s model-to-mechanism mapping (3M) requirement (Kaplan 2011; Kaplan and Craver 2011). For a reply see Kaplan (2017) who argues that the implementation of the normalization equation (in different species) is an essential part of the explanation.

  21. Colin Klein suggested that we might be dealing here with different why questions.

  22. A similar question arises for the different algorithms that support the same function, which is why using one algorithm rather than another.

  23. Marr writes:

    Up to now I have studiously avoided using the word edge, preferring instead to discuss the detection of intensity changes and their representation by using oriented zero-crossing segments. The reason is that the term edge has a partly physical meaning—it makes us think of a real physical boundary, for example—and all we have discussed so far are the zero values of a set of roughly band-pass second-derivative filters. We have no right to call these edges, or, if we do have a right, then we must say so and why (1982: 68).

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Acknowledgements

I am grateful to Lotem Elber-Dorozko, Jens Harbecke, Shahar Hechtlinger, David Kaplan, Colin Klein, Arnon Levy, Gal Patel and two anonymous referees for their comments. Early versions of the paper were presented at seminars in Macquarie University, Tel-Aviv University, University of Canterbury, University of Otago and at the following conferences: The Aims of Brain Research: Scientific and Philosophical Perspectives (Jerusalem), Conference of the International Association for Computing and Philosophy (Thessaloniki), and the 7th AISB Symposium on Computing and Philosophy (London). I thank the participants for stimulating discussion. This research was supported by a grant from GIF, the German-Israeli Foundation for Scientific Research and Development.

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  1. Departments of Philosophy and Cognitive Science, The Hebrew University of Jerusalem, Mt. Scopus, 91905, Jerusalem, Israel

    Oron Shagrir

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Shagrir, O. The Brain as an Input–Output Model of the World. Minds & Machines 28, 53–75 (2018). https://doi.org/10.1007/s11023-017-9443-4

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