All the Mental Must be Classical?
Systematic Deviations Challenge LOT's Systematicity
This essay will consider whether Fodor’s Language of Thought (hereafter LOT) can capture the systematicity constraint. It will argue that LOT fails when faced with language use that deviates from Fodor’s view of compositionality and must dismiss such evidence to remain coherent.
In “Connectionism and Cognitive Architecture: A Critical Analysis,” Fodor and Pylyshyn argue for the concept of systematicity, which they define as the idea that the ability to produce or understand certain thoughts is intrinsically connected to the ability to produce or understand other related thoughts (Fodor and Pylyshyn 1988, 27). The example that they employ to lay this idea out is one of linguistic systematicity. They argue that if a person has a full grasp of the grammar of English, by being able to understand the sentence “John loves Mary,” they are also able to understand the sentence “Mary loves John” (Fodor and Pylyshyn 1988, 26).
For Fodor and Pylyshyn, systematicity is ensured by compositionality. Compositionality is the principle that sentences or thoughts are built from constituent parts, and that each part contributes roughly the same semantic content wherever it appears. In other words, the meaning of a complex expression (be it sentence or thought) is determined by the meanings of its parts and how they are combined (Fodor and Pylyshyn 1988, 28). Compositionality is necessary because systematically related sentences are not arbitrarily related, but semantically related. Thus, for “John loves Mary” to be systematically related to “Mary loves John,” in both instances, the individuals must preserve their meaning across different combinations. That is, they must be largely context-independent (Fodor and Pylyshyn 1988, 28).
Fodor and Pylyshyn argue that systematicity would be mysterious if sentences were atomic (Fodor and Pylyshyn 1988, 26) and that compositionality “follows from the postulation of constituent structure” (Fodor and Pylyshyn 1988, 26). That is, if sentences were not divisible into constituent parts, our ability to understand one sentence through understanding another would be hard to explain. This claim rests on the idea that shared constituents provide a structural explanation for systematic relations. Therefore, systematicity requires some form of compositionality.
Since Fodor and Pylyshun have only shown that systematicity depends on compositionality in language, they must show how this principle extends to thought. This “bridging argument” takes a psycholinguistic form. They argue that “one uses language to express ones thoughts” (Fodor and Pylyshyn 1988, 30). If we can use some sentences because we can use other semantically related sentences, then we should also be able to think certain thoughts through our ability to think other semantically related thoughts. Since people can only think the thoughts that their mental representations can express, “the ability to be in some representational state must imply the ability to be in certain other, semantically related representational states.” (Fodor and Pylyshyn 1988, 30) The final step is to argue that the only way to explain this is to hold that mental representations must have internal structure corresponding to the internal structure of sentences. Following this reasoning, they conclude that “evidence for the compositionality of sentences is evidence for the compositionality of the representational states of speaker/hearers” (Fodor and Pylyshyn 1988, 30).
What we might call constituent-based, predictable, systematic compositionality follows from Fodor and Pylyshyn’s assumptions that the semantic values of constituents are largely context-independent and that systematically related thoughts share constituents. These assumptions are grounded in what they refer to as their Classicist framework (Fodor and Pylyshyn 1988, 31). This paper will therefore refer to this view as classical compositionality: a compositional system in which complex thoughts are built from shared constituents in a way that, in principle, allows systematic relations to be predicted from the structure. By contrast, non-classical compositionality refers to systems that are not largely predictable, constituent-based, or systematic. Classical compositionality requires only that the underlying structure support systematic manipulation. While the constituents must generally contribute consistently, that each constituent’s role be explicitly recoverable in every instance is not necessary, so long as the combinatorial rules are in place (Fodor and Pylyshyn 1988, 23).
We thus have a situation where systematicity in LOT depends on classical compositionality. If human thought systematically departs from classical compositionality, this poses a challenge for LOT’s ability to fully account for systematicity. We will now turn to a case study in which human concept combination appears non-classical, exhibiting behavior that cannot be straightforwardly predicted from constituent structure. It should be noted that since the following evidence is a case study, the points discussed below would apply to any observed diverging systematic behavior that, according to Fodor, must be both compositional and a mental representation.
James Hampton (1988) performed a study in which he asked participants to rate how well individual items belonged to specific categories using a numerical scale. Each item was rated for its membership in the given categories separately, and then in the conjunction of the two categories. This enabled him to quantify cases where the conjunctive rating exceeded or fell below classical expectations; overextension and underextension, respectively. For example, in Hampton’s fourth experiment in the study, participants rated garlic as being either food or plant, and then conjunctively as food and plant (Hampton 1988, 13–20). Based on participants’ ratings of typicality, garlic had an average membership of 95% for food, 70% for plant, and 79% for food and plant (Hampton 1988, 31), illustrating overextension.
Aerts et al. argue that these overextended results “cannot be modeled in a classical probability space” (Aerts, Sozzo, and Veloz 2015, 4). This is because, if A (food) and B (plant) are treated as classical sets, the membership of an item in the intersection A∩B cannot exceed its membership in either individual set. Specifically, the conjunctive membership should never exceed the lower of the two individual memberships, which in this case is 70%. Note that we must not reduce Hampton’s findings to simple percentage arithmetic. It might seem numerically consistent that 79% of participants could rate garlic as both food and plant, while 95% rate it as food and 70% as a plant. The misunderstanding here is that classical compositionality treats concepts as sets (Fodor and Pylyshyn 1988, 14). The conjunctive concept ”food AND plant” is the intersection of the two sets food and plant. By way of example, imagine we have 100 participants. Of those, 70 classify garlic as a plant. Even if all of these 70 also classify it as a food, no more than 70 could have classified it as both food and plant. This means that overextension cannot be explained by classical compositional rules.
While Aerts et al. use this data to support a quantum-theoretic hypothesis of human reasoning, it is relevant to this paper for a different reason: it challenges the assumption of classical compositionality in human thought. Hampton’s findings do not provide exhaustive evidence, but show that human thought might systematically violate the conditions LOT assumes.
Before examining the implications of such data for LOT, we must be careful not to conflate thoughts with concepts, and clarify why evidence from concept combination is relevant. For Fodor, concepts and thoughts are both mental representations serving different structural roles: concepts function as the constituents of thoughts, and thoughts express propositional contents. Importantly, both are governed by classical compositionality (Fodor 1998, 25). Empirical findings on concept combination therefore speak directly to how far classical compositionality can explain the systematicity of mental representations. If the basic constituents (concepts) combine in ways that systematically deviate from classical predictions, then the mental representations built from them may exhibit corresponding limits. Evidence of non-classical concept combination suggest that compositionality alone may be insufficient to account for the patterns of systematicity in human cognition.
Given systematic deviations from classical compositionality, a key question arises: if classical compositionality assumes that complex representations inherit their semantic properties from their constituents in a rule-governed way, how can it accommodate cases where conjunctive concepts depart from what classical inheritance rules predict? The point becomes clearer by analogy with composition of sentences. If we understand the simple sentences “Garlic is food” and “Garlic is a plant,” then classical compositionality would predict that the meaning of “Garlic is food and a plant” follows straightforwardly from the meanings of its constituents. The conjunctive sentence should not introduce a pattern that departs from the simple ones. Hampton’s findings illustrate that concept conjunction can introduce such departures: the status of “Garlic is food and plant” does not follow from the statuses of the constituents in the way classical compositionality predicts.
Importantly, these patterns are not isolated to garlic, but appear across a range of categories, hinting at it being a systematic deviation rather than a one-off (Hampton 1988, 28–32). These systematic deviations indicate that human concept combination does not always follow classical compositional rules, and that, specifically, concept combination does not track with the assumptions of stable semantic contributions. The semantic contribution and combinatorial potential of concepts like food and plant depend on whether they are conjuncted. That is not to say that the combination patterns observed in Hampton’s data lack a rule-governed structure, but it does imply that the function generating these outcomes is not captured by classical compositionality. To assess whether such systematic deviations would challenge LOT’s ability to capture systematicity, it is important first to consider some potential objections.
One possible objection to concluding from this evidence that classical compositionality fails to capture systematic patterns in human concept combination is Fodor’s distinction between competence and performance. We can think of competence as the internal representation, which follows classical compositionality. Performance, on the other hand, is the actual output of the competency, which has restraints and limitations imposed upon it, such as time, attention, working memory, etc, causing performance to deviate from competence (Fodor and Pylyshyn 1988, 23). This distinction is later defended more fully by Fodor as the separation of atomic mental concepts from fluid, prototype-based stereotypes, with each being the respective building blocks of competence and performance (Fodor 1998, 94). Fodor holds that stereotypes cannot compose, and would therefore likely regard Hampton’s findings as performance data, rather than competence. In that case, the observed conjunctions, even if they appear to reflect some form of non-classical compositionality, would not reflect actual compositional processes (Fodor 1998, 94).
A rebuttal to this line of argumentation is that the deviations observed in Hampton’s data are systematic, not just random noise. It is not that some people confuse the categories or concepts, because it occurs across a spectrum of categories and conjunctions ranging from birds/pets to vehicles/machines and weapons/tools (Hampton 1988, 31–32). Dismissing the conjunctions as not reflecting actual compositional processes seems to discount the consistency of the occurrence. In a sense, it risks begging the question to claim that these observed conjunctions are not compositional simply because they do not conform to a preconceived notion of what compositional processes should look like. Classical compositionality must be demonstrated to hold in the face of counter-evidence, not theorized away.
We cannot, and should not, discount the possibility of a performance-based explanation of Hampton’s data. Indeed, his findings do not rule out such an explanation at all. But, if the cause is indeed performance, we should in principle be able to characterize the function producing these systematic outputs. So, while a performance-based explanation cannot be fully ruled out, the burden of proof must lie with anyone claiming that these patterns arise solely from performance limitations.
A second consideration is that the objection treating Hampton’s findings as performance-data is difficult to hold because it conflicts with Fodor and Pylyshyn’s psycholinguistic bridging argument. As established earlier, their argument relies on the idea that patterns of systematicity in language use provide evidence for patterns of systematicity in thought: because language expresses thought, systematicity in language is taken as reflecting systematicity in the underlying mental representations (Fodor and Pylyshyn 1988, 30). This is compelling, but it has implications for the competence/performance distinction. If language performance is fallible and subject to contextual limitations, then it is unclear how systematic features of thought competence can be reliably inferred from language performance without risking circular reasoning. In other words, if the systematicity we observe in language could be influenced by performance factors, we cannot straightforwardly claim that it reveals the systematicity of underlying mental representations. If we argue against this that it is the systematic appearance of systematicity that grounds it as competence, it is difficult to see how this would not also support that Hampton’s findings reflect competence. To argue that this data reflects performance without tracing how this is so, one must assume that language reliably tracks thought even when performance deviates, which risks circularity (and, in a stronger sense, begs the question against LOT’s classical assumptions).
Moreover, Fodor and Pylyshyn implicitly assume that systematicity is the sole property of mental representations that must be accounted for. This is shown by Michael V. Antony’s critique of Fodor and Pylyshyn’s argument that the human cognitive architecture is Classical. Antony argues that Fodor and Pylyshyn are grounding the need for the cognitive architecture to be Classical in an invalid application of inference to the best explanation (Antony 1991, 327). Antony points out that this inference only holds if systematicity is the only phenomenon a theory of cognitive architecture must explain. If there are “many phenomena other than systematicity that must be explained by the cognitive architecture,” (Antony 1991, 329) and some non-Classical architecture better accounts for these phenomena, then a Classical cognitive architecture is no longer the best explanation. Therefore, further premises are required to show that a Classical cognitive architecture is the best explanation (Antony 1991, 330).
Building on this critique, the problem with treating systematicity as the sole property is that it underpins Fodor and Pylyshyn’s bridging argument. LOT explains systematicity via classical compositionality, so assuming systematicity alone effectively presumes that all relevant systematic patterns are classical. To preserve classical compositionality as a guarantor of systematicity, Fodor must treat evidence that violates classical compositionality as irrelevant or attributable to performance factors. However, evidence such as Hampton’s suggests that systematic patterns can exhibit non-classical compositionality in language use. By the bridging argument, this extends to human thought, indicating that LOT’s explanation of systematicity is incomplete. As such, LOT’s ability to capture systematicity is limited when confronted with non-classical patterns in cognition.
To gather up the threads, all of the above considerations converge on a single point: LOT’s reliance on classical compositionality as the mechanism guaranteeing systematicity cannot fully account for systematic deviations. In the face of systematic deviations from classical expectations in elements that Fodor holds must be compositional and mental representations, LOT is pushed to either ignore such evidence, trace the performance function producing these outputs, or acknowledge that its concept of systematicity is incomplete. The competence/performance distinction cannot rescue LOT here without a principled account, because the bridging argument depends on inferring the systematicity of mental representations from language use. Denying that systematic deviations influence systematicity risks begging the question against the very evidence that challenges LOT’s classical assumptions.
The implications of this discussion are that a purely classical LOT-style architecture cannot fully account for systematic deviations in phenomena that, for Fodor, are compositional and must be represented mentally. Given systematic deviations from classical compositionality, alternative frameworks may better account for how mental representations combine in practice. Connectionist models conceive mental representations as patterns of activation distributed across many units rather than discrete symbols with fixed constituents (Rumelhart and McClelland 1986). Such distributed representations can account for phenomena like over- and underextension by allowing the meaning of a complex concept to emerge from the interaction of overlapping features rather than from strict constituent intersections, and provide a natural explanation. However, since LOT does capture most of how systematicity seems to operate in human cognition, it might seem more apt to consider a hybrid approach, such as Smolensky’s tensor product representation (Smolensky 1990). In this way, LOT’s symbolic architecture is embedded within, yet constrained by, a connectionist system, allowing it to accommodate both the systematicity captured by LOT and systematic deviations. This essay abstains from endorsing a particular theory as best able to account for such systematic deviations without further discussion. It suffices to say that if such evidence holds, LOT alone cannot account for the full range of systematic patterns in human thought, highlighting a gap that hybrid or connectionist frameworks are positioned to fill.
As mentioned, Hampton’s findings function as a case study to consider whether LOT would be able to handle empirical evidence of systematic deviations from classical expectations. His findings are not unassailable, and it is worth considering the methodology and procedure used to obtain these results, before relying on them as the death knell for LOT’s ability to capture systematicity. However, Hampton is far from alone in demonstrating systematic deviations in what should be classically compositional. Other results include McCready and Ogata’s review of Japanese adjectives as encoding degrees of similarity rather than set-membership (McCready and Ogata 2007), or Tabossi et al.’s evidence that idioms do not always exhibit predictable, constituent-based meaning (Tabossi, Fanari, and Wolf 2008). Following the above discussion, LOT’s systematicity would be vulnerable given all such cases.
The final point thus becomes that, in the face of systematic empirical evidence of non-classical compositionality in what, for Fodor, must be compositional and a mental representation, LOT is unable to capture the systematicity constraint. The only way for LOT to capture it is if the evidence is false, or if the evidence can be shown to have no bearing on what systematicity is in human thought. LOT provides a mechanistic explanation of systematicity in principle, but it relies on the non-existence of systematic deviations from classical expectations. If systematic deviations from classical compositionality, as illustrated by Hampton, are representative, then LOT captures only a subset of systematic relations, suggesting that an expanded notion of compositionality or an alternative account of the cognitive architecture would be needed to fully account for systematicity.