Behavioral and Brain Sciences (forthcoming)

um. (iv) Because cognition allows the outputs of abstraction to serve as concreta for additional acts of abstraction (Berwick, Friederici, Chomsky, & Bolhuis, 2013), we can speak of mental representations as forming a continuum of abstractness. We define abstractness as a relative term that refers to the relation between two abstracta. Whenever we can say that abstractum X is part of the concreta of abstractum Y, we will say that abstractum Y is more abstract than abstractum X.um Y, we will say that abstractum Y is more abstract than abstractum X. In our definition, if two objects are not distinguishable in any sense by the observer, then there is only a single object in mind, hence there is no abstraction. The requirement of distinguishability means that abstraction involves having at least two dimensions13 in mind: one dimension on which the stimuli differ, and another dimension on which they will be considered identical. Thus, when performing an act of abstraction, one makes a (conscious or non-conscious) decision14 on which dimension is central, and by doing so, one designates other dimensions as secondary or irrelevant in the current context (see Shapira, Liberman, Trope, & Rim, 2012, for a related definition of abstraction). 12 It is important to distinguish between internal criteria of substitutability, which are the rules as they are represented in the mind that performed the act of abstraction (i.e., things that are made of chocolate are tasty); and external criteria of substitutability, which are the actual rules that determine the criterion of substitutability (e.g., unbeknownst to the agent, the reason objects A and B are considered by her as tasty is that they are sugary). 13 In the terminology of Medin et al., (1993), respects for similarity. 14 According to our definition, abstraction is fundamentally a situated, context-dependent process (e.g., Smith & Semin, 2007; Barsalou, 1983; Hintzman, 1986). There is no “correct” hierarchy of abstracta, or some pre-defined criterion for selecting the set of possible objects that will satisfy a belief or desire. For example, in a specific context, “cake” may be deemed substitutable with “ice cream” and both would form the concreta of “dessert”; in another context, “cake” may be deemed substitutable with “bread”, and both will form the concreta of “things that you bake”. In other words, the abstractum is, in principle, a unit that is defined by an ad-hoc use. This, however, does not preclude the emergence of regularly-used abstracta between individuals or between different points in time, nor does it preclude the emergence of abstracta that are more central than others (see later the discussion on the emergence of complex representational structures). https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0140525X19002000 Downloaded from https://www.cambridge.org/core. IP address: 207.241.231.108, on 10 Mar 2020 at 04:00:10, subject to the Cambridge Core terms of use, available at 10 Because abstraction entails selecting/attending to one dimension and disregarding other dimensions that might be salient, many acts of abstraction likely rely on cognitive operations often referred to as “cognitive control” and “selective attention” (e.g., Macleod, 1991; Botvinick et al., 2001). The degree to which cognitive control is needed for an act of abstraction depends on the relative salience of the (attended) dimension of substitutability versus the (ignored) dimension on which the concreta subjectively differ (see Deacon, 1997, for a related idea). Consider a psychology experiment wherein a child sees a picture of a person who has a mustache and wears a dress. The child can form the belief that the person is substitutable with other males (because of the mustache) or with other females (because of the dress). What made “clothing type” a relevant and salient dimension for the child? (see Goodman, 1972; Fodor, 1998)15. Clearly, the dimensions used for generating new criteria of substitutability come from our prior network of beliefs (Murphy & Medin, 1985). However, explaining the formation of new beliefs merely based on prior beliefs leads to an infinite regress. The dimensions that form our criteria of substitutability must have been originally introduced into our mind at some point. The question of where these dimensions come from is a major topic of investigation in the field of developmental psychology and concept formation. Broadly speaking, these dimensions can be acquired in three ways: they can be innate (e.g., infants have an innate biological mechanisms that determine that the velocity and direction of an object is an important dimension to attend to in the newly-discovered world), shaped by personal experience and the gradual discovery of statistical regularities (e.g., a rat may discover that a specific auditory cue is a useful dimension along which to group outcomes), or transferred from other people (e.g., a child may learn from society that gender is a meaningful dimension along which to categorize people). 2. The diverse representational ontology that cognitive science should not ignore 15 Whereas influential models (e.g., Tversky, 1977) have been long able to address the problem of similarity-based categorization, attempts to precisely model theory-based categorization (Murphy & Medin, 1985) have been notoriously challenging (see Pothos & Chater, 2002). Approaches that highlight the need to provide the simplest theory (i.e., “the simplicity principle”; Chater & Vitanyi, 2003) provide a promising avenue for research on this problem (Pothos & Chater, 2002). Future application of the PP framework to higher-order cognition may be able to provide formal accounts of theory-selection processes during theory-based categorization. https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0140525X19002000 Downloaded from https://www.cambridge.org/core. IP address: 207.241.231.108, on 10 Mar 2020 at 04:00:10, subject to the Cambridge Core terms of use, available at 11 As noted earlier, the ability to use abstracta as inputs for further acts of abstraction generates a continuum of abstractness. However, we argue (and in Part 5, review evidence) that there are qualitative distinctions along this continuum. Performing the act of abstraction by relying on different types of inputs and different types of dimensions gives rise to qualitatively different types of abstracta. 2.1.1. Modality-specific features, objects, and relations16. The first steps in moving beyond a concrete representation can be traced to the discovery of identity between different perceptual features (e.g., color, loudness, a nose), and the formation of representational permanence of objects on the basis of perceptual pattern similarity (or “object permanence”; Piaget, 1954). Object permanence relies on the formation of a belief that different sensory impressions that appear across different spatial and temporal contexts are equivalent, in the sense that they all pertain to the same object (e.g., “the image of my dog”). Likewise, perceptual patterns which are best described as relations (e.g., sound A is louder than sound B; objects A and B are similar in color; e.g., Martinho & Kacelnik, 2016) can perhaps be represented in a modality-specific manner, and be deemed equivalent across different instantiations. Such modality-specific abstracta probably often rely on different innate, hard-wired dimensions such as pitch and color (Baillargeon, Spelke, & Wasserman, 1985; Carey, 2009). 2.1.2. Multimodal features, objects, and relations17. Once individuals generate some set of modality-specific abstracta, they may use them in further acts of abstraction. This is because percepts that cannot be grouped together based on perceptual pattern similarity may also be deemed as substitutable—whenever they are bound together by spatiotemporal contiguity. For example, when a toddler experiences the (modality-specific) sound of a dog and the (modality-specific) sight of the dog at the same time, it generates the multimodal abstractum of the dog. As another example, an animal that repeatedly hears a bell before it gets food can bind these two patterns together. Whereas the discovery of modality-specific abstracta often relies on innate substitutability criteria, multimodal abstracta are often acquired via personal experience. 16 In the terminology of Deacon (1997), which follows in the footsteps of semiotic theory (Peirce, 1931/1974), such abstracta exhibit Iconic reference. The ability to perform such an act of abstraction is also referred to as the “Hoffding step” (1891). 17 In the semiotic terminology such abstracta exhibit Indexical reference. https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0140525X19002000 Downloaded from https://www.cambridge.org/core. IP address: 207.241.231.108, on 10 Mar 2020 at 04:00:10, subject to the Cambridge Core terms of use, available at 12 Two types of multimodal representations warrant special consideration. First, a person might group together various different objects that share a temporal context (e.g., “the dog chasing the Frisbee in the park”). The resulting abstractum can be called a mental episode18 (Tulving, 1984). A second important class of multimodal representations are lemmas, which are the entities of our mental lexicon (Roelofs, 1992). These are the abstracta whose concreta include modality-specific representations of a feature/object/relation as well as the linguistic sign (written, spoken) that co-occurs with it. For example, the lemma of a banana will group images of bananas, taste experiences associated with bananas, alongside with the visual symbol “banana”, and the auditory pattern “ba-na-na”. 2.1.3. Categories. Multimodal abstracta can be used as building blocks for further acts of abstraction—even in situations where they cannot be grouped together based on spatiotemporal cooccurrence (Murphy & Medin, 1985). This results in a category