Marr’s levels of analysis and the notion of copying

Colleagues in the wider field of cognitive science have commented that understanding language and its acquisition in monolingual speakers is a hard enough problem; dealing with it in the context of bi- or multilingual speakers is simply too daunting. This is a valid point. At the same time, we must acknowledge that from a global perspective, monolingualism is an exotic phenomenon. Thus if our goal is to understand human language and language acquisition, we cannot but frame the problem in the context of what is normal for most humans, namely learning and using two or more languages to various degrees.

Unlike most, Westergaard is undaunted. The model of language acquisition outlined in Westergaard (2021) comprises second language (L2) and third and subsequent language (L3) acquisition – a distinction that, writing this in what could variously be classified as my second, third, fourth or fifth language (depending on what and how we count), I have always found difficult to understand – as well as first language (L1) acquisition. The problem space Westergaard seeks to address is formidable, and I commend and admire her for taking on the challenge. Ultimately, a comprehensive model of human language acquisition of the type she proposes is what we must strive for.

Given the size and complexity of the challenge, it is only natural that some aspects of the proposed model will require further specification and development. To make progress in this regard, it may be helpful to begin by clarifying and separating the three levels of analysis that Marr (1982) famously proposed are needed to understand any complex cognitive system: (1) the computational level, which addresses the goal of the system and specifies the objects that are manipulated and the constraints that must be satisfied: the what and why; (2) the algorithmic level, which addresses how the computations are accomplished to map input to output; and (3) the implementational level, which describes the physical instantiation of the system, such as the hardware of a machine or the wetware of the brain.

Theories about the nature of grammar are unambiguously situated at Marr’s first level of analysis (Johnson, 2017). This was observed by Marr himself: ‘Chomsky’s (1965) theory of transformational grammar is a true computational theory in the sense defined earlier’ (Marr, 1982: 28), and endorsed by Berwick and Chomsky (2016: 132), who conclude an outline of the minimalist view of the Basic Property of language by stating that ‘[a]ll this might be taken as the answer to what David Marr (1982) called the first level of analysis of any information processing system – what problem is being solved.’ Westergaard (2021) explicitly positions her approach within the generative tradition. The Linguistic Proximity Model (LPM) she proposes is effectively a model of the nature and development of grammatical representations in multiple languages. Schwartz and Sprouse’s (1996) Full-Transfer/Full-Access (FT/FA) model – against which Westergaard positions her Full-Transfer-Potential (FTP) approach – is similarly and unambiguously grounded in Chomskyan linguistic theory. Thus it seems clear that the arguments and explanations we are dealing with in the context of Westergaard’s (2021) proposal must be situated at Marr’s first level of analysis, the computational level.

However, there are instances where Westergaard’s argumentation appears to shift to a different level. This is perhaps most apparent in her critique of FT/FA, where she writes that ‘the intention of Schwartz and Sprouse (1996) seems to have been that the brain does make a real copy of the L1’ (p. 387; emphasis added). The brain is relevant, indeed critical, for explanations at Marr’s third level; it has no place, however, in arguments at the first level. As Marr (1982: 27) observed, ‘if the idea that different phenomena need to be explained at different levels is kept clearly in mind, it often helps in the assessment of the validity of the different kinds of objections that are raised.’ From this perspective, the validity of Westergaard’s objections to the notion of copying grammatical representations from an earlier learnt language becomes questionable. Once we understand that we are dealing with explanations at Marr’s first level, there can be little doubt, contrary to Westergaard’s assertion (p. 387), as to ‘whether the idea of a copy [in the FT/FA model] has been intended and interpreted as an abstraction or an actual neurobiological process’. Neurobiological processes simply cannot be explanatory constructs at the computational level. ¹

At the computational level of analysis, a copy has no physical dimension, in the same way that the system of Arabic numerals that is part of a computational level theory of addition has no physical or neurobiological instantiation. In Marr’s terms, we are dealing with symbols in ‘formal schemes’ (Marr 1982: 20). Of note, copying as a property of Internal Merge constitutes an integral part of narrow syntax in the minimalist program (e.g. Berwick and Chomsky, 2016: 129). All this indicates that once we are firmly grounded at Marr’s first level, there is nothing problematic about the notion of creating copies of grammatical representations.

This alone does not entail that copying grammatical representations from earlier learnt languages is necessary at the L2 or L3 initial state. Westergaard (2021: 388) argues strongly that it is not. In particular, in the context of L2 acquisition, she argues that because the L1 grammar always remains active and thus constitutes a potential resource for parsing L2 input, there is no need to make a copy of it. When the current L2 grammar cannot parse the L2 input, recourse is taken to the L1 grammar: ‘When exposed to L2 input, learners will try to parse it, first scanning their L1. If an identical structure (micro-cue) exists in the L1, parsing will be facilitated’ (Westergaard 2021: 389). The concern with this argument is that it invokes the evaluation of an identity function (‘if an identical structure exists’), which requires a comparison between two objects. One is the structure (micro-cue) in the L1 grammar. But what is the other? Westergaard emphasizes that new grammars are built incrementally as a result of learning by parsing. She does not state explicitly what the initial state of a new grammar looks like. (In Westergaard’s (2021) Figure 3, the left-hand image appears to show an early, but not the initial, L2 state. What would the truly initial state look like?) Based on the emphasis on incremental building of new grammars, I can only infer that the initial state of the L2 grammar must be the empty set. If so, this means that there is no structure (or micro-cue) in this initial state L2 grammar that can be compared against the structure from the L1 grammar. In other words, the identity function cannot be evaluated. Full-Transfer-Potential (FTP) as outlined in Westergaard’s example (16) thus appears to run into a chicken-and-egg problem.

FT/FA does not encounter this problem. With a copy of the L1 grammar as the L2 initial state, no comparisons are involved. The copy of the L1 grammar is used to parse the L2 input, and is restructured or consolidated as a result of failure or success. This is learning by parsing. FT/FA presents a logically coherent computational level analysis of the L2 initial state. This does not mean that it must be the right or even the best analysis. In the context of L2 acquisition, empirical support for FT has been substantial. Yet, to the extent that our goal is to seek a theoretical account of language acquisition that encompasses L2 as well as L3 acquisition, FT/FA is insufficient. Once there are multiple earlier learnt grammars, it becomes unclear what is copied at the L3 initial state. FT/FA does not offer a mechanism for resolving this problem. This unresolved issue has been the driving force behind multiple recent models of L3 acquisition, discussed in some detail in Westergaard (2021), and vigorous debate among its proponents. Westergaard’s Linguistic Proximity Model (LPM) is a valuable contribution to this debate, a debate that is necessary if our aim is to arrive at a theory of language and language acquisition that encompasses L1, L2 and L3 acquisition. For this debate to be fruitful and productive, however, we must be clear about the level of analysis at which our arguments and explanations are situated. Ultimately, we will want to seek explanations at all three of Marr’s levels and relate them to each other. Yet given the size and complexity of the problem, it seems prudent to start with the first, and be careful to keep explanations and arguments consistently at the same level. Marr’s approach will not solve all problems, but it may help us see them and argue over them more clearly.