Gilead et al. wisely avoid assuming that abstraction and mental time-travel are exclusively confined to human cognition (contra Penn et al. Reference Penn, Holyoak and Povinelli2008; Suddendorf and Corballis Reference Suddendorf and Corballis2007; Reference Suddendorf and Corballis2010), because ample evidence exists for such abilities in animals (e.g., Emery and Clayton Reference Emery and Clayton2004). However, the propensity to perceive hierarchical structure in sequences unfolding through time or space, in multiple modalities, does seem unusually well-developed in our species. This propensity to generate tree-like structures has been dubbed “dendrophilia” (Fitch Reference Fitch2014).
We share the authors' conviction that prediction is fundamental to cognition, and applaud their pluralistic perspective regarding the many abstraction types that support prediction. However, their ontology of abstraction overlooks the importance of the dynamically constructed hierarchies fundamental to music and language. What enables these domains to make “infinite use of finite means” is precisely their hierarchical combinatoriality. Despite pervasive evidence for hierarchical structures in human cognition, evidence for hierarchical representations in nonhuman animals remains sparse (e.g., Jiang et al. Reference Jiang, Long, Cao, Li, Dehaene and Wang2018; Wang et al. Reference Wang, Uhrig, Jarraya and Dehaene2015).
Music and language obviously involve hierarchical structures, whereby, following Gilead et al., abstracta at one level of abstraction act as the concreta for another. Thus, music's concreta include individual notes at certain pitches, whereas speech builds on individual phones. At the first level, the abstracta are pitch classes (the set of pitches that share the same chroma across different octaves, e.g., C3, C4, etc.) and phonemes (incorporating different allophones). Further hierarchical structures compose musical abstracta into melodies (sequences of notes of different pitch classes with a particular rhythmic structure) and musical keys (subsets of certain note classes) whereas language composes phonemes into syllables, morphemes, phrases, sentences, and narratives.
Importantly, the “terminals” in both music and language are themselves abstracta. For instance, a phoneme is not a concrete entity that exists in nature, but is already processed by categorical perception, thus is already an abstraction. Similarly, the “same” melody can be produced with any arbitrary starting note (and thus encompasses an infinite set of surface frequency sequences).
These static structures are consistent with the kind of static (taxonomic) hierarchical structures that Gilead and colleagues consider (e.g., dogs are mammals are vertebrates). But, these do not account for the type of flexible generativity needed to create or understand new sentences or melodies, which requires smaller stored subunits (words, idioms, or short chord sequences) that can flexibly combine into larger wholes. Such compositional subunits go by many names (“subtrees,” “treelets,” and “curried functions”) and are a generalisation of the notion of “predicate,” whose importance the authors rightly emphasise.
Extending Frege's terminology, such “partially saturated entities” are the crucial building blocks of the larger hierarchical structures underlying music and language. But in music, these subunits lack compositional semantics: unlike predicates they do not imply truth values. They are purely combinatoric entities, subunits with open “slots” that allow them to flexibly combine with other subunits in constrained ways. Thus, just as a transitive verb has “slots” demanding an animate subject and an object, a tonic-subdominant-dominant chord sequence allows a constrained set of continuations (canonically a return to the tonic, but unlimited variants are possible). Such compositional chord sub-sequences are not predicates: they make no semantic reference to the world, and entail no truth values.
Crucially, the hierarchical subunits of music and language are learned, and must be stored in a mental lexicon, but are deployed automatically and habitually. Thus, during ontogeny, such learned subunits must be automatised. This blurs the line between the traditional category of habitual or “model-free” abstracta and (conscious) model-based prediction. That some predictions are more habitual or unconscious than others does not mean they are “model-free”: only that the abstracta involved have been automatised.
Consider how we perceive music, where the crucial first level of abstraction is constituted by traversing temporal distance. Musical abstraction applies to the relatively short time-spans of unfolding chords or melodic phrases. These units nest into larger ones, that can be described at increasing levels of abstraction, in terms of for instance Schenkerian time-span reduction, whereby each phrase can be conceived of as an elaboration of a basic underlying tonic-dominant-tonic progression (Schenker Reference Schenker1935). Such dynamic hierarchical abstractions are reflected in electrophysiological evidence for the ability to recognise long-distance harmonic dependencies in music (Koelsch et al. Reference Koelsch, Rohrmeier, Torrecuso and Jentschke2013). Our unconscious knowledge of music is essentially a generative model for an infinite set of melodies (Lerdahl & Jackendoff Reference Lerdahl and Jackendoff1983), built upon a finite set of hierarchical building blocks that combine to form more complex hierarchical structures.
This parallels language, where the learned structures stored in the lexicon (including both morphemes and more complex subunits like idioms; cf. Jackendoff Reference Jackendoff2002), are used online to build up the more complex and variable structures involved in language use. Available data from psycholinguistics indicate that complex structures are built up “on the fly,” in parallel, and unconsciously (Cutler Reference Cutler2017). These processes are not easily available to introspection because they have been automatised. Both cases illustrate the centrality of dynamically created hierarchical structures in human cognition, and the musical case demonstrates that semantics (and thus predicates) need not be involved.
Consider finally the aesthetic dimension of music or poetry. The temporal pattern in which tension unfolds over time, where expectations are unconsciously generated, then challenged, and finally resolved and integrated into a satisfying whole, can be termed an “aesthetic trajectory” (Fitch et al. Reference Fitch, Von Graevenitz and Nicolas2009). In music, the ebb and flow of the aesthetic trajectory operates at the “top” level of this hierarchy, that is, on melodies and keys, not on individual notes. Such dynamic aesthetic trajectories are fundamental to aesthetic experience (including, we argue, to static arts like painting or sculpture; cf. Fitch et al. Reference Fitch, Von Graevenitz and Nicolas2009), but also far beyond, for example, in following narratives, getting jokes, or understanding pragmatics (Hurley et al. Reference Hurley, Dennett and Adams2011).
We conclude that a dendrophilic process of dynamic hierarchical structure building is crucial in music and language, and deserves a prominent place in Gilead's pluralistic ontology of abstracta. This process is based upon combinations of automatised subunits, analogous to but more general than Fregean predicates.
Gilead et al. wisely avoid assuming that abstraction and mental time-travel are exclusively confined to human cognition (contra Penn et al. Reference Penn, Holyoak and Povinelli2008; Suddendorf and Corballis Reference Suddendorf and Corballis2007; Reference Suddendorf and Corballis2010), because ample evidence exists for such abilities in animals (e.g., Emery and Clayton Reference Emery and Clayton2004). However, the propensity to perceive hierarchical structure in sequences unfolding through time or space, in multiple modalities, does seem unusually well-developed in our species. This propensity to generate tree-like structures has been dubbed “dendrophilia” (Fitch Reference Fitch2014).
We share the authors' conviction that prediction is fundamental to cognition, and applaud their pluralistic perspective regarding the many abstraction types that support prediction. However, their ontology of abstraction overlooks the importance of the dynamically constructed hierarchies fundamental to music and language. What enables these domains to make “infinite use of finite means” is precisely their hierarchical combinatoriality. Despite pervasive evidence for hierarchical structures in human cognition, evidence for hierarchical representations in nonhuman animals remains sparse (e.g., Jiang et al. Reference Jiang, Long, Cao, Li, Dehaene and Wang2018; Wang et al. Reference Wang, Uhrig, Jarraya and Dehaene2015).
Music and language obviously involve hierarchical structures, whereby, following Gilead et al., abstracta at one level of abstraction act as the concreta for another. Thus, music's concreta include individual notes at certain pitches, whereas speech builds on individual phones. At the first level, the abstracta are pitch classes (the set of pitches that share the same chroma across different octaves, e.g., C3, C4, etc.) and phonemes (incorporating different allophones). Further hierarchical structures compose musical abstracta into melodies (sequences of notes of different pitch classes with a particular rhythmic structure) and musical keys (subsets of certain note classes) whereas language composes phonemes into syllables, morphemes, phrases, sentences, and narratives.
Importantly, the “terminals” in both music and language are themselves abstracta. For instance, a phoneme is not a concrete entity that exists in nature, but is already processed by categorical perception, thus is already an abstraction. Similarly, the “same” melody can be produced with any arbitrary starting note (and thus encompasses an infinite set of surface frequency sequences).
These static structures are consistent with the kind of static (taxonomic) hierarchical structures that Gilead and colleagues consider (e.g., dogs are mammals are vertebrates). But, these do not account for the type of flexible generativity needed to create or understand new sentences or melodies, which requires smaller stored subunits (words, idioms, or short chord sequences) that can flexibly combine into larger wholes. Such compositional subunits go by many names (“subtrees,” “treelets,” and “curried functions”) and are a generalisation of the notion of “predicate,” whose importance the authors rightly emphasise.
Extending Frege's terminology, such “partially saturated entities” are the crucial building blocks of the larger hierarchical structures underlying music and language. But in music, these subunits lack compositional semantics: unlike predicates they do not imply truth values. They are purely combinatoric entities, subunits with open “slots” that allow them to flexibly combine with other subunits in constrained ways. Thus, just as a transitive verb has “slots” demanding an animate subject and an object, a tonic-subdominant-dominant chord sequence allows a constrained set of continuations (canonically a return to the tonic, but unlimited variants are possible). Such compositional chord sub-sequences are not predicates: they make no semantic reference to the world, and entail no truth values.
Crucially, the hierarchical subunits of music and language are learned, and must be stored in a mental lexicon, but are deployed automatically and habitually. Thus, during ontogeny, such learned subunits must be automatised. This blurs the line between the traditional category of habitual or “model-free” abstracta and (conscious) model-based prediction. That some predictions are more habitual or unconscious than others does not mean they are “model-free”: only that the abstracta involved have been automatised.
Consider how we perceive music, where the crucial first level of abstraction is constituted by traversing temporal distance. Musical abstraction applies to the relatively short time-spans of unfolding chords or melodic phrases. These units nest into larger ones, that can be described at increasing levels of abstraction, in terms of for instance Schenkerian time-span reduction, whereby each phrase can be conceived of as an elaboration of a basic underlying tonic-dominant-tonic progression (Schenker Reference Schenker1935). Such dynamic hierarchical abstractions are reflected in electrophysiological evidence for the ability to recognise long-distance harmonic dependencies in music (Koelsch et al. Reference Koelsch, Rohrmeier, Torrecuso and Jentschke2013). Our unconscious knowledge of music is essentially a generative model for an infinite set of melodies (Lerdahl & Jackendoff Reference Lerdahl and Jackendoff1983), built upon a finite set of hierarchical building blocks that combine to form more complex hierarchical structures.
This parallels language, where the learned structures stored in the lexicon (including both morphemes and more complex subunits like idioms; cf. Jackendoff Reference Jackendoff2002), are used online to build up the more complex and variable structures involved in language use. Available data from psycholinguistics indicate that complex structures are built up “on the fly,” in parallel, and unconsciously (Cutler Reference Cutler2017). These processes are not easily available to introspection because they have been automatised. Both cases illustrate the centrality of dynamically created hierarchical structures in human cognition, and the musical case demonstrates that semantics (and thus predicates) need not be involved.
Consider finally the aesthetic dimension of music or poetry. The temporal pattern in which tension unfolds over time, where expectations are unconsciously generated, then challenged, and finally resolved and integrated into a satisfying whole, can be termed an “aesthetic trajectory” (Fitch et al. Reference Fitch, Von Graevenitz and Nicolas2009). In music, the ebb and flow of the aesthetic trajectory operates at the “top” level of this hierarchy, that is, on melodies and keys, not on individual notes. Such dynamic aesthetic trajectories are fundamental to aesthetic experience (including, we argue, to static arts like painting or sculpture; cf. Fitch et al. Reference Fitch, Von Graevenitz and Nicolas2009), but also far beyond, for example, in following narratives, getting jokes, or understanding pragmatics (Hurley et al. Reference Hurley, Dennett and Adams2011).
We conclude that a dendrophilic process of dynamic hierarchical structure building is crucial in music and language, and deserves a prominent place in Gilead's pluralistic ontology of abstracta. This process is based upon combinations of automatised subunits, analogous to but more general than Fregean predicates.