Pragmatic Norms Are All You Need – Why The Symbol Grounding Problem Does Not Apply to LLM s (2024)

Abstract: Do LLMs fall prey to Harnad’s symbol grounding problem (SGP), as it has recently been claimed? We argue that this is not the case. Starting out with countering the arguments of Bender and Koller (2020), we trace the origins of the SGP to the computational theory of mind (CTM), and we show that it only arises with natural language when questionable theories of meaning are presupposed. We conclude by showing that it would apply to LLMs only if they were interpreted in the manner of how the CTM conceives the mind, i.e., by postulating that LLMs rely on a version of a language of thought, or by adopting said questionable theories of meaning; since neither option is rational, we conclude that the SGP does not apply to LLMs.

## the (philosophical) symbol grounding problem in stark contrast to the engineering sense of the grounding problem, where there is an observable problem in the performance or capacity of aisystems to be solved, there is another sense of the symbol grounding problem that is not about a specific shortcoming in performance; rather, it has been raised explicitly in spite of flawless performance. this philosophical sense is the original sense of the sgp, and it is this sense which still exercises many practitioners in nlp. we first sketch the origin of the symbol grounding problem in the philosophy of mind, then we show how it expanded to linguistics. ## why the sgp does not apply to natural language the basic argument that we will present in this section is that the sgp -both with regard to natural language as well as regarding its systematic abstraction in formal semantics -dissolves if we consider the pragmatic context in which any natural language is at home. we begin by sketching a somewhat generic notion of correspondence theory of meaning @xcite ), which will be called following @xcite the augustinian picture. in the augustinian picture, (1) the primary view of natural language is one of a complex symbol system encompassing syntax and semantics that is at root abstracted from its material, historical, pragmatic, social, etc., context, (2) its meaning-constituting relation is the mapping of linguistic expressions to non-linguistic objects to which they correspond, e.g., the famous so-called middle-sized dry goods such as sticks and stones. this then invites the principle (3) that the typical fundamental unit of linguistic meaning is the concept. bender and koller (2020) develop a correspondence conception of meaning that involves both conventional meaning and the communicative in-tention that a speaker pursues with a specific utterance. in both variants, meaning requires mapping words to the real-world entities to which they refer. the precise relationship that this said to be needed between words and the real world for the words to be meaningful is conceived differently. 8 the underlying notion, however, is the same in all of these different uses, namely the need for linguistic symbols to, as it were, hook up to their non-symbolic referents. given such a correspondence theory of meaning, it follows that one has to be able to map the words onto the objects to which they refer or correspond to. without this meaningconstituting correspondence connection, the words of any natural language are literally meaningless. furthermore, any being, such as the octopus in in section 2 or an llm, that is unable to, as it were, reach beyond language and connect language to these non-linguistic entities, is categorically unable to understand linguistic meaning. correspondence theories of meaning, however, are by no means the only, and arguably not the most convincing, kind of theories of meaning of natural language. 9 therefore, we suggest to take a step back and get a more comprehensive view of the phenomenon of language by taking its social and contextual institution and constitution seriously. this is what so-called pragmatists have advocated for decades @xcite ; we here follow the version of pragmatism developed by @xcite @xcite , which is further detailed in the appendix, section d.1. briefly, compared to the three principles of the augustinian picture, pragmatism replaces (1) with conceiving natural language primarily as a norm8 as the grounding of a linguistic element in the real world @xcite , as connecting to the real world (ibid., p. 5188, 5188, 5190), as mapping between words and real-world entities (ibid., 5189), or as being about things in the real world (ibid, p. 5190). this is just a rough sketch of pragmatism, which is admittedly strongly influenced by brandom. however, the three principles do justice to the main tenets of pragmatism broadly conceived, as pioneered by @xcite . furthermore, it also aligns with the influential speech act theorists @xcite and @xcite , who have emphasized that the primary locus of language is its use in speech acts rather than as a system standing in splendid isolation. with regard to (3), our position aligns with @xcite @xcite ) and frege (1892). in the 20th century, important proponent is @xcite , and more recently @xcite . emphasizing the fact that natural language -unlike mentalese -is constantly used, and pointing out that this use determines the meaning of utterances and the reference of concepts, allows us to resolve the puzzle that initiated this section by pointing to a rather mundane source of meaning for sentences, and hence for words: the users of language. whether "this is a dog" or "tkr br drkg" has any meaning at all and, correspondingly, is able to refer to any non-linguistic entity, depends on the existing practices of a community of speakers. these practices are governed by norms that determine that "this is a dog" can be used in a speech act -to claim that the relevant object pointed out is a dog -, while "tkr br drkg" cannot. so, echoing the sgp represented in figure 2 , we can easily resolve the mystery in the case of natural language by pointing to conventional norms, see figure 3 . this in turn allows us to embed the phenomena examined by formal semantics such as mts using its powerful analytic tools back into the actual use of language in human societies, as described by pragmatist perspectives on language. in short, while mts serves as a highly successful tool to analyze relationships between meaningful statements and referring concepts, it is the conventional norms that govern the use of both that ensure that these statements, including the abstractions and analyses of them by mts, have meaning or refer respectively. note that it is precisely this context of norm-governed use that is missing with mentalese symbols: being unconscious, non-linguistic elements of the mental computer, it is obvious that they are not used in a norm-governed way by humans and hence cannot receive their meaning and reference from there. in sum, in this section, we have suggested that whether the sgp gains any traction with regard to natural language is a question of the theory of linguistic meaning that one embraces. on the augustinian picture, and in general on correspondence theories of meaning as such, the sgp does indeed come up. however, on the pragmatic conception of linguistic meaning that we have sketched and recommended here, it is conventional norms, defined by and defining speaking communities that establish reference between certain symbols and the non-symbolic entities which they signify and thereby prevent any sgp in the first place. ## why the sgp does not apply to llms after having discussed the origins of the sgp in the ctm, and after having shown how it has expanded into formal semantics and natural language, and also how the sgp can be dissolved there by reconsidering language in the everyday context of norm-governed use, we are now finally ready to consider the central question of this article: does the sgp apply on llms? as we have seen above (section 2 and section 5), @xcite worry that llms, being trained solely on strings of text, cannot get the meaning, that is, on their notion of meaning, the world-items corresponding to the strings that they process. however, as we have argued, this theory of meaning is questionable. if we take into view that it is conventional norms, constituting and constituted by the social practice of speaking a language, that give meaning to claims and concepts, then we can see that llms might pick up linguistic meaning: the norms observed by language users will leave recognizable patterns in the training data which the llms can represent and with them infer the norms governing the use of expressions, that is, the meanings of these same expressions. so, while the correspondence theory of meaning would predict, as bender and koller did, that there are linguistic tasks for which llms are not qualified because they lack the relevant exposure to the non-linguistic meaning of words, the pragmatic conception of meaning developed here would predict the contrary, namely that there is no principled limit to the linguistic performance of llms. we submit that (albeit with the gift of hindsight compared to bender and koller 2020) empirical evidence clearly favors the pragmatic side here: time and again, and even more so after the publication of chatgpt on november 30, 2022, llms have managed to shine in one linguistic challenge after another that was previously thought be beyond them. hence, for the theoretical and empirical reasons sketched, we should abandon the correspondence theory of meaning in favor of a pragmatic one; and with the correspondence theory, bender and koller's reason for applying the sgp to llms also goes by the board. this verdict contrasts with mollo and millière (2023), who insist that there is a symbol grounding problem that needs a solution. @xcite justify the existence of such a problem with reference to the octopus test introduced and critically assessed above (section 2), emphasizing that "[t]he vectors they [the llms, rg] receive and manipulate during internal processing are merely meaningless arrays of numbers, ungrounded in anything outside statistical patterns in language, just like the outputs they generate" (ibid, p. 8). this shows that, unlike bender and koller (2020), mollo and millière (2023) want to anchor the sgp not in a specific theory of linguistic meaning, but rather in the inner workings of llms, which puts them closer to the origins of the sgp in the ctm than to its location in linguistic theories. specifically, @xcite argue that the vectors that represent the input tokens face the sgp and require some specific sort of grounding, namely referential grounding. so, does the sgp apply to the inner workings of llms, including their vectors? to begin answering this question, note that the ctm as well as the chinese room thought experiment that gives traction to the sgp are both firmly situated in the good old-fashioned, rule-based world of ai (compare quilty-dunn et al. 2023, 5). llms, in contrast, are connectionist, statistical devices that have no intrinsic symbolic structure. it is, however, this symbolic structure that is presupposed in the ctm, the chinese room thought experiment, and hence also in the symbol grounding problem. see figure 4 for an illustration of why the sgp fails to get traction with statistical methods such as transformers: there are no symbols that would need grounding. this implies that to make plausible that llms are subject to the sgp, one would have to find reasons interpret their inner going-ons in a way that is analogous to how the ctm interprets the human mind, namely by postulating non-linguistic symbols -a kind of llm-mentalese -that are being manipulated by an llm to perform its functions. in other words, one would have to credit the llms with a version of fodor's language of thought. what reasons could there be to postulate a language of thought in llms? to answer this question, it is helpful to return to fodor's original argument for his language of thought in human minds: fodor introduced the language of thought hypothesis to account for the productivity and the systematicity of thought and thinking @xcite . the productivity of thought consists in the fact that we as competent language users can potentially produce an infinite number of well-formed sentences; often, recursive phenomena are used to make this point (a simple example for this would be to add "'s daughter": to the end of the output of the last recursion: "sarah is mary's daughter" -> "sarah is mary's daughter's daughter", etc.). the systematicity of thought consists in systematic in-terrelations between thoughts that we can entertain; one of the prime examples is the transitivity of deductive inference. fodor explicitly motivates his language of thought hypothesis with recourse to these properties of human language and thought. however, there does not seem to be any solid, reliable evidence that llms actually are truly productive in fodor's sense. while it is rather simple to create a gofai-algorithm that uses recursion to create as many different sentences as the computing architecture used allows, it seems less obvious that this is also possible with purely associative, implicit systems such as llms, and there is, to the best of the knowledge of the author, no study available that would provide positive evidence for it. the situation seems even worse regarding systematicity. as the empirically established problem of generalization in nli shows (see the appendix, section d.2), and as @xcite argue on a theoretical level, llms are not particularly good at such systematic thinking, such as drawing and labelling deductively valid inferences. in sum, then, this presents the following picture. first, as llms are not instances of symbolic ai, it requires a positive reason to postulate that their inner workings proceed by processing of some kind of symbols that would then have to be grounded. in the case of the human mind, fodor has argued for this by referring to the systematicity and the productivity of thought. hence, if mollo and millière (2023) want to read the token embedding vectors of llms as symbols requiring some sort of grounding, they should, as fodor did, make explicit the explanatory need that exists for positing such symbols (that could then be seen as in the need of grounding). mollo and millière (2023) might respond to that with the emphatic insistence that, regardless of any explanatory benefits, the embedding vectors certainly need to mapped onto the real-world entities to which they refer, or, as they put it (ibid, p. 28): "hook onto the world". this moves the discussion on the level of theories of meaning, where my response would be to point to the sketch of the two different paradigms of theories of meaning displayed in ## conclusion in this article, following @xcite , we have focused on conceptualphilosophical considerations of nlp research. specifically, we have considered their claim that llms are vulnerable to the so-called symbol grounding problem (sgp), as introduced by @xcite . after distinguishing the sgp, which is a philosophical problem, from empirical doppelgängers, we have shown how it has emerged from the theoretical background of the computation theory of mind (ctm) and from there expanded to linguistic theories, including model-theoretic semantics (mts). we have then argued that mts, understood properly, does not give rise to the sgp, as the powerful formalism that it furnishes is best understood as systematically analyzing pre-existing meaningful statements, which in turn receive their meaning from norm-governed use. furthermore, with regard to natural language, the sgp arises only if one adopts a correspondence theory of meaning, which is in competition with more comprehensive pragmatic conceptions of meaning that elegantly dissolve the sgp by bringing into view the conventional norms that govern language use. with regard to llms, we have found that, given that they are neural network rather than gofai architectures, there is no reason to assume that the sgp arises, as it would require postulating mentalese-like symbols in the llms, which in turn would require an explanatory need to do so which we are currently lacking. of course, the questions whether llms, being the kind of thing they are, can understand meaning, properly conceived, remains an important conceptual and empirical question. however, by carefully delineating the conceptual landscape surrounding the sgp, we hope to have shown that nlp researchers can safely stop worrying about the sgp and go on about their business, and thus to have provided a case in point where philosophy can foster progress in nlp.