Permutation Games: Playing Cat and Mouse with Language
Jürgen Riedel
Humanising technology to foster more trust-based businesses using modern strategies and a multi-disciplined approach anchored in GenAI solutions| Founder@Baiomics, a DeepTech, ML/AI Tech Consultancy | PhD
The philosophers Ludwig Wittgenstein and Saul Kripke, a prominent American philosopher and logician, challenged the act of rule-following and therefore illuminated the intricate relationship between language, thought, and community practices. Wittgenstein, in "Philosophical Investigations," [1] states that rule-following is not merely a mental activity but is embedded within the broader context of our life and social practices. This standpoint challenges traditional perspectives by asserting that understanding and meaning are constituted within shared human practices, rather than being rooted solely in individual mental states or private experiences.
Kripke, in "Wittgenstein on Rules and Private Language," [2] extends this exploration through his "sceptical challenge." He questions the existence of objective facts underpinning rule-following, leading to a profound scepticism about the nature of meaning. His argument uses examples like 'addition' and 'quaddition' to illustrate that past actions alone do not conclusively determine the rule being followed. This argument introduces uncertainty regarding the consistency of meaning over time. Kripke's "sceptical solution" to his challenge proposes that meaning and understanding arise from a community's collective agreement or acceptance of specific linguistic usages and rules. This shifts the focus from seeking objective, meaning-constituting facts to appreciating the role of communal consensus in language and thought. It implies that meaning is not an intrinsic property of words or mental states but a product of collective human activities and societal practices. Thus, Kripke's approach, while building on Wittgenstein's insights, introduces a more radical scepticism and a community-centric view of meaning.
Wittgenstein and Kripke highlight the complexities and intricacies of linguistic meaning, emphasizing the importance of context, shared practices, and community in the interpretation and understanding of language. This perspective significantly influences philosophical discussion, offering a nuanced view that contrasts with the algorithmic, formal-language approach, thereby challenging conventional ideas about the innate, rule-based nature of language and its role in human cognition and social interaction.
Connecting language with thought
The Language of Thought Hypothesis (LOT) [3], as stated by Jerry Fodor, seeks a conceptual bridge with Saul Kripke's "sceptical solution" in Wittgensteinian philosophy, particularly in the treatment of meaning and mental representation. Kripke “sceptical challenge” aligns with the foundational precepts of LOT, which states that thought processes are structured in a language-like, rule-governed manner. LOT provides a potential resolution to Kripke's scepticism by suggesting that mental representations in a "language of thought" could serve as the internal standards of correctness. In this framework, the systematic, rule-bound structure of LOT offers a way to anchor the meanings of words and concepts, addressing Kripke's concern about the possibility of private rule-following and meaning. Thus, LOT can be seen as offering a cognitive underpinning to Kripke's philosophical exploration, bridging the gap between abstract philosophical concerns about language and meaning, and the psychological mechanisms of thought and understanding.
It is important to note that LOT hypothesis faces critiques from various theoretical perspectives, such as Behaviorism which emphasizes observable behaviour over internal mental representations, and Embodied Cognition which argues that cognition is grounded in bodily interactions. Additionally, Connectionism, Neural Network Models, and theories of Situated and Distributed Cognition challenge LOT by proposing that cognitive processes are emergent from neural patterns and environmental interactions, while Dynamic Systems Theory views cognition as a continually evolving process, countering LOT's static, rule-based approach.
Are language and thought one of the same?
The Identification Hypothesis (IH) [3] is a theoretical proposition in the domain of philosophy of mind and linguistics, particularly concerning the nature and structure of thought. Fundamentally, IH assesses that the language of thought is identical to natural language. This hypothesis suggests that the very structures and forms found in natural languages (such as English, German, etc.) are the same as those utilized in our cognitive processes for thinking. Essentially, having a thought is linked to internally tokening an expression in a natural language, and the characteristics that define these thoughts are inextricably linked to their linguistic properties. The core implication of IH is that the cognitive operations involved in thinking are not distinct from the linguistic processes of generating and understanding natural language.
IH has a close relation to the Language of LOT where thinking occurs in a mental language, often termed "Mentalese." According to LOT, thoughts are composed of complex arrangements of mental symbols and cognitive processes operate on these symbolic structures in a manner analogous to linguistic syntax. While LOT suggests the existence of a language-like structure inherent to thought, IH takes this a step further by specifically identifying this mental language with the natural languages we speak and understand. This identification implies that the structural rules and principles governing natural languages are the same as those that govern our thinking processes. IH thus attends to bridge the gap between the abstract, theoretical structure of thought as proposed by LOT and the concrete, observable properties of natural languages.
Important is to understand that the acceptance of IH depends heavily on empirical findings in linguistics, particularly in understanding the generative nature of language and its cognitive underpinnings. Debates around IH often involve discussions on the universality of linguistic structures, the nature of grammar and syntax in natural languages, and the extent to which language influences or reflects cognitive processes. The hypothesis challenges traditional distinctions between language as a tool for communication and thought as a private, cognitive function. It also raises new questions about the learnability of language, the innateness of linguistic structures, and the potential for thoughts that exceed or deviate from standard linguistic forms. As such, IH remains a subject of considerable debate and ongoing research within the fields of cognitive science, linguistics, and philosophy.
From abstract philosophical discourse to the physiology of the human brain
The "Neurofunctional Segregation Theory of Language Processing" (NSTLP) [4] explores the intricate relationship between language processing and brain function, focusing on how the human brain manages the complexity of hierarchical structures in language, which are a hallmark of human linguistic capability. Central to NSTLP is the distinction between two key aspects of language processing: the syntactic computation of hierarchical structures and the demands these structures place on working memory. The study employs functional magnetic resonance imaging (fMRI) and diffusion tensor imaging (DTI) to dissect the roles of two specific brain regions (Figure 1): the left pars opercularis (LPO) (which is a part of the articulatory network involved in motor syllable) and the left inferior frontal sulcus (LIFS) (which acts as a phonologic working memory that buffers the phonemes in an upcoming utterance organized by their location within the syllable). The LPO is identified as playing a pivotal role in processing the hierarchical structures inherent in language, which is a cognitive faculty arguably distinct to humans. In contrast, the LIFS is associated with managing the working memory load that such complex structures entail. This segregation of functions within the brain underlines the specialized nature of language processing, attributing the handling of structural complexity and memory demands to distinct but interconnected neural regions.
NSTLP looks further into the brain's linguistic architecture and highlights functional and anatomical interconnectivity between the LPO and LIFS, especially in contexts involving complex sentence structures. This connectivity suggests a cooperative interaction between syntactic processing and memory management, essential for comprehending sentences with embedded clauses. Such an interplay underscores the brain's remarkable capacity to simultaneously process and store linguistic information, facilitating the understanding of complex syntactic constructions. This neural underpinning of language reveals a sophisticated network within the brain that is finely tuned to the unique demands of human language processing. It not only advances our understanding of the cognitive and neurological foundations of language but also holds implications for studying language disorders and the evolution of linguistic capabilities in humans.
Syntactic “permutation game” to probe language understanding
The English language is not a word order-free language, contrary to languages like German which offer more flexibility in word order due to their rich inflectional morphology. In English, the word order is relatively fixed and plays a critical role in conveying the syntactic structure and meaning of a sentence. Deviations from the standard Subject-Verb-Object (SVO) order can lead to sentences that are grammatically incorrect or semantically ambiguous.
One can define the concept of a “permutation game” that serves as a tool to explore the limits and flexibility of syntactic structures in each language and to examine how variations in word order affect meaning and interpretability. The “permutation game” involves creating all possible permutations of the words in a given sentence and analysing the grammaticality and meaning of each permutation. This exercise aims to understand the interplay between syntax (word order) and semantics (meaning) in language processing. It provides insights into the cognitive processes involved in language comprehension and the mental representations underlying language use. By examining how meaning changes or is preserved across different permutations, we can glean insights into the rules and constraints of the language's syntax and the flexibility of its semantic interpretation.
The “permutation game” not only highlights the structural characteristics of different languages but also provides a window into the cognitive mechanisms of language processing. It underscores how humans navigate and interpret linguistic structures, adapting to the constraints and affordances of their native language, and reveals the extent to which thought processes in language are shaped by these linguistic features.
Let’s consider a concrete example. The permutation exercise with the sentence "The cat caught the mouse," treating "The cat" and "The mouse" as single entities, the six possible permutations of the three elements (Subject "The cat," Verb "caught," Object "The mouse") (Table 1) reveal varying degrees of grammatical correctness and clarity in meaning. While some permutations retain grammatical structure but sound unnatural or shift the sentence's focus, others render the sentence grammatically incorrect or semantically ambiguous. This outcome highlights the rigidity of the Subject-Verb-Object format in English and underscores the cognitive effort required in language processing when standard syntactic structures are altered. Such an analysis aligns with the Language of Thought hypothesis, which posits a rule-governed, structured format for mental representations, suggesting that deviations from linguistic norms can pose challenges in cognitive processing. The “permutation game” thus serves as a valuable tool for exploring the constraints of syntax and the dynamics of language comprehension within the framework of cognitive linguistics.
The “permutation game”, when applied to these word-order free languages, becomes a more complex and nuanced tool. It still can reveal how different permutations, while still retaining grammatical correctness, might convey varied nuances, focus, or emphases in meaning, showcasing the intricate relationship between inflectional morphology and syntactic flexibility in shaping language comprehension and cognitive processing.
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How the “permutation game” challenges our brain
Within NSTLP the LPO is identified as a crucial region for processing hierarchical structures in language. The “permutation game” directly challenges these structures by altering the conventional word order, thus engaging the LPO in determining the grammaticality of these new formations. The LPO is tasked with discerning whether these new arrangements still adhere to syntactic norms. This aspect of the game highlights the LPO's role in distinguishing grammatically coherent sentences from those that are structurally flawed, regardless of how unconventional or non-standard these permutations might be.
The “permutation game” also impacts the LIFS, which is responsible for managing working memory in language processing. As the game introduces sentences with varying levels of syntactic complexity and semantic ambiguity, the LIFS becomes critical in maintaining the elements of each sentence (subject, verb, object) in memory while the brain interprets their meaning. In cases where the typical SVO structure is disrupted, the LIFS is likely to show increased activity. This is reflective of the additional working memory load needed to process structures that deviate from the normative syntactic pattern of English.
The Exploration of how changes in the word order of the “permutation game” affect meaning is particularly relevant to the study’s findings on the functional coupling between the LPO and LIFS. This interplay is vital when processing sentences with complex or altered structures, where understanding both the hierarchical order (syntax) and the relational meaning (semantics) of the elements is necessary. For instance, in a permutation like “The mouse caught the cat,” the cognitive processes for interpreting such an unexpected reversal of roles would involve both syntactic analysis (facilitated by the LPO) and working memory (managed by the LIFS).
The deviations from typical linguistic patterns necessitate more complex neural processing, as demonstrated by the distinct yet interactive roles of the LPO and LIFS. This increased cognitive effort in processing non-standard structures, as evident in some permutations, highlights the brain’s adaptation to standard language structures and reveals how deviations from these norms can pose significant challenges in cognitive processing.
The “permutation game” on language and thought
The concept of the “permutation game”, as described, offers a fascinating avenue for exploring the interplay between syntax and semantics in language, and its relevance to the Language of Thought Hypothesis (LOT) and the Identification Hypothesis (IH). This exercise essentially probes the structural limits of a language's syntax and the extent to which its semantic content is malleable or fixed.
In the context of LOT, the “permutation game” highlights the structured nature of mental representations since processes involve the manipulation of mental representations that have a language-like, rule-governed structure. The permutations generated in this game reveal the extent to which a deviation from syntactic norms affects comprehensibility and coherence. When the standard word order (Subject-Verb-Object in the case of English) is altered, the resulting sentences range from slightly unnatural to completely nonsensical or semantically ambiguous. This variability in comprehensibility and naturalness of the permutations can be seen as reflecting the mental effort required to process and interpret these sentences. It aligns with the LOT notion that our thoughts are organized in a structured format, and deviations from this structure can lead to cognitive challenges. The “permutation game” thereby may provide empirical support for LOT by demonstrating how alterations in linguistic structure impact our cognitive processing of language.
Regarding IH, the “permutation game” serves as a practical tool to examine how closely thoughts (as structured mental representations) align with the structure of natural language. IH argues that the language of thought is essentially the same as natural language. This hypothesis suggests that the cognitive processes underlying language comprehension and thought are not merely similar but are fundamentally identical. By analysing the permutations, one can assess how shifts in word order influence meaning and interpretability. If thoughts were truly identical to natural language expressions, as IH suggests, then any permutation that generates a syntactically coherent and semantically interpretable sentence should be as easily processable as the original sentence. However, the varying degrees of difficulty in understanding the permutations challenge this notion. Some permutations, while grammatically possible, are harder to process and understand, indicating a possible divergence between the flexibility of thought and the rigidity of syntactic structures in natural language.
For instance, in the given example "The cat caught the mouse," permutations like "Caught the mouse the cat" or "The mouse the cat caught" retain the core semantic content but alter the focus or feel unnatural due to their deviation from the standard SVO order. This outcome suggests that while our cognitive processes are adept at handling standard linguistic structures, they may require additional effort to parse and interpret sentences that deviate from these norms. This observation can be seen as a challenge to IH, as it implies that the structure of thought (as manifested in language comprehension) may not be entirely congruent with the fixed syntactic structures of natural language.
Evaluating LLMs with the “permutation game”
The paper "What Artificial Neural Networks Can Tell Us About Human Language Acquisition" by Warstadt and Bowman [5] scrutinizes the role of Artificial Neural Networks (ANNs) and neural language models (LMs) in understanding human language acquisition. They highlight the ambiguity in defining language-specific biases, noting the presence of hierarchical structures in both linguistic and non-linguistic contexts, which blurs the line between language-specific and general cognitive biases. Challenging the notion that greater model expressiveness equates to better language learning, they argue that models can be more effective when less expressive, provided they focus on relevant hypotheses, mirroring human language acquisition processes.
The paper also addresses the limitations of current neural network architectures like RNNs and Transformers, which do not fully capture human inductive bias despite their success in NLP tasks. It shows that ANNs often lack essential traits like strong compositionality and hierarchical biases, key in human language processing. Nonetheless, ANNs are valuable in language acquisition studies due to their scalability and ability to emulate diverse linguistic environments. The paper also advocates for more ecologically valid models and learning environments to better align with human learning processes and also proposes that insights from model learners, despite their limitations, can contribute significantly to our understanding of language acquisition, emphasizing the need for computational models that more closely replicate human linguistic capabilities.
In examining Large Language Models (LLMs) like GPT-4 through the lens of the “permutation game”, we can gain a nuanced understanding of their capabilities and limitations in processing language, as highlighted [13]. By analysing GPT-4's responses to the six permutations of "The cat caught the mouse"(Table 1) we observe the model's varied interpretative abilities. For instance, standard sentences like "The cat caught the mouse" are clearly understood and contextualized by the model, reflecting its proficiency in standard syntactic structures. However, permutations such as "The cat the mouse caught" and "Caught the cat the mouse," which involve role reversals or unusual word orders, elicit responses from GPT-4 that range from recognizing grammatical oddities to interpreting these structures as imaginative or poetic expressions. This showcases the model's ability to process non-standard linguistic constructs, yet also reveals its reliance on learned patterns, lacking the deeper contextual understanding inherent in human language comprehension.
Even showing some promising capabilities of LLMs in understanding linguistic competence there are remaining concerns regarding their contribution to our understanding of linguistic competence, since these models are primarily trained to simulate human performance, their insights into the deeper, rule-governed aspects of linguistic competence may be limited. There is still a distinction between mimicking language performance and truly grasping the underlying principles of language competence. Despite limitations, LLMs can offer valuable insights into human language acquisition and processing. This is particularly evident in experimental settings where LLMs can simulate various aspects of language learning. The “permutation game” aligns with this perspective, serving as a potential evaluation metric for LLMs' language understanding. By assessing how LLMs like GPT-4 interpret and respond to permutations that challenge standard syntactic and semantic conventions, one can gauge the models' linguistic flexibility, creativity, and their approximation to human-like language processing. Such evaluations, while recognizing the metaphorical comparison to human brain processes like those in Broca's and Wernicke's areas, can provide a comprehensive understanding of LLMs' capabilities in linguistic interpretation, going beyond mere pattern recognition and venturing into the domain of semantic and syntactic analysis.
In this article, I explored the connections between the Wittgensteinian views on language with the idea that language and thought are the same. I also investigated the connection between neuroscience and the processing of language and thought in the human brain. All leads to a better understanding of how one can interpret the emergent properties of LLMs. Perhaps LLMs are more than just statistical functions on fixed language output of us humans and perhaps a real manifestation of reality through thoughts.
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