Abstract
When dealing with ‘meaning’ or related notions, one cannot ignore what for a long time was the dominant paradigm in semantics (call it truth-conditional cognitivism). According to such paradigm, truth-conditional formal semantics for natural language is a theory of semantic competence. In this article, I shall discuss a foundational problem for such semantic program (call it the lexical problem). I shall first be following authors who claim that truth-conditional formal semantics is unable to provide a complete account of lexical competence, and, therefore, it suffers from incompleteness. Moreover, as a few authors observed, a coherent completion of lexical meaning/competence cannot be easily provided in the philosophical framework of truth-conditional semantics. The problem is a consequence of Kripke’s and Putnam’s arguments against the view that semantic values (intension, reference) of words are cognitively determined. I shall argue that these arguments undermine the notion that formal semantics can be, at the same time, a theory of truth-conditions and a theory of semantic competence. I shall outline and critically discuss two general attempts to solve this problem, which I shall refer to as the social/ideal route and the (Fodorian) concepts route. The conclusions of the article are deliberately open. I shall argue that both these attempts are exposed to conceptual troubles and counterintuitive consequences, and so the lexical problem still remains a deep and unresolved issue for (formal) semantics.
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Notes
In his early papers, however, Davidson seems to endorse a more psychological approach. In “Truth and Meaning” (1967), for instance, he writes that the “[e]mpirical power in [a truth] theory depends on success in recovering the structure of a very complicated ability—the ability to speak and understand a language” (p. 25; see also 1966). It is only in his later writings that Davidson moved towards a more resolute anti-cognitivist position, according to which truth theories are part of a theory of radical interpretation, having nothing to say “about the details of the inner workings of some part of the brain” (1986, p. 96).
On the history of cognitivism in formal semantics, see also Partee’s draft papers and presentations in section (d) [“History of the issues of 'Semantics: Mathematics or Psychology?', psychologism vs anti-psychologism, 'internalism', etc.”.] of her website:
As Dowty et al. write in their Introduction to Montague semantics (1981): “[i]n constructing the semantic component of a grammar, we are attempting to account not for speakers’ judgements of grammaticality, grammatical relations, etc., but for their judgments of synonymy, entailment, contradiction, and so on” (p. 2).
A notable exception is Heim and Kratzer’s well-known introduction to formal semantics (1998), where no explicit reference to semantic competence or psychology is provided. However, the two authors locate their view in the generative paradigm, as the textbook’s title suggests (Semantics in Generative Grammar).
For example, this idea is explicit in the Larson and Segal’s introduction to Davidsonian semantics (1999): “[w]e have been pursuing semantics as a theory of the real but unconscious knowledge of speakers. We have argued that what is known by speakers is a set of rules and principles that are finite in number and compositional in form. […] What kind of rules and principles are known? The idea we will adopt and develop in this book derives from the work of Davidson, who proposes that the work of semantic theory can be done by a particular sort of formal theory called a truth-theory, or T-theory for short” (p. 25). By contrast, this idea has been explicitly ruled out by Lepore and Ludwig (2007). They argue that “[a] compositional meaning theory aims to capture the structure of the dispositions of the speaker which constitute her competence in speaking and understanding speech in the language.” (p. 19). However, “there is no suggestion here that it is or must be a theory which speakers of the language know, explicitly or implicitly” (p. 19).
This view has been explicitly endorsed by Emma Borg in her Minimal Semantics (2004): “[i]f, say, we treat grasp of literal linguistic meaning as the canonical derivation of truth-conditions for sentences, for example, along the lines of Larson and Segal (1995), then semantic understanding can form part of a genuine language module, for this is clearly a function which is encapsulated and computational. Knowledge of meaning, on this kind of account, consists of knowledge of a proprietary body of information (the lexicon for the language) and knowledge of a set of rules operating only on that information, rules which consist of formal transformations of the data. Thus modularity and formal semantics, it seems, go very nicely together” (p. 81). […] “A formal semantic theory alone can be part of a (Fodorian) modular language faculty” (p. 75).
Of course, the complete convergence between the representations and processes utilized by a truth-conditional semantic analysis and those posited by a cognitive theory of semantic competence is highly unlikely. Nevertheless, there seems to be nothing wrong with the idea that the recursive apparatus of a truth theory can model structural competence at the level of the ‘computational theory’, in Marr’s sense.
Notice that, differently from Montagovian axioms, axioms in Davidsonian-style do not appear to be ‘incomplete’ but ‘uninformative’. For example, in order to understand [A2] one needs to know what cat means. But this is exactly the information that [A2] is supposed to provide. In other words, unless one already knew what cat means, one wouldn't learn anything from such axiom. Some defenders of TCC have argued that the situation is different for ‘allophonic’ or ‘nonhomophonic’ axioms (and theorems), such as “the predicate gatto is true of x (in Italian) if and only if x is a cat” (Larson and Segal 1995). Nevertheless, this argument is unconvincing (for a discussion on this point, see Dummett 1975 or Marconi 2002).
For instance, in certain lighting conditions, our visual system may tend to mistake porcelain cats for cats, or real cats for porcelain cats. It may also be systematically deceived by unusual animals having the appearance of cats but a different DNA. However, the word cat does not refer to such unusual animals, nor to porcelain cats. Therefore, our theory of (cognitive) meaning does not provide the right information to determine the reference of cat; it would force us to apply cat to entities that do not belong to the extension of the word (i.e. that are not cats), or not to apply cat to entities that do belong to the extension of the word (i.e. that are cats). Note that—if Kripke and Putnam are right—the simple reasoning presented above can be replicated with almost every natural kind word. With this kind of words, referential dispositions are intrinsically defective; they are part of a speaker’s cognitive system and, consequently, they are characterized by its limitations. For instance, ordinary speakers are disposed to apply diamond to transparent zircon, which is visually very similar to diamond, flower to plastic imitation flowers, water to hydrogen peroxide, and so on. In this sense, the referential dispositions of an ordinary speaker do not determine reference. This reasoning, however, cannot be easily generalized to all kinds of word. It is hard to see how it could work with words denoting fictional entities (e.g., unicorn) or words denoting artefacts (e.g., pencil). According to many authors, Putnam included, the direct theory of reference can also be applied to artefacts, but there is an ongoing debate in philosophical semantics on this issue (see, e.g., Marconi 2013, 2019 for discussion).
A similar point was made by Dowty in his introductory text to Montague semantics (1981). Dowty admits that “[c]ontemporary linguists […] almost invariably profess to be concerned with the ‘psychological reality’ of the theoretical concepts they postulate in semantic analysis” (1981, p. 375). According to him, however, such cognitivist position is untenable for the reasons made clear by Kripke and Putnam: “[t]o get to the point right away, let me confess that I believe that the model-theoretic intension of a word has in principle nothing whatsoever to do with what goes on in a person's head when he uses that word” (p. 375).
See Partee’s draft papers/presentations in section (d) [“History of the issues of 'Semantics: Mathematics or Psychology?', psychologism vs anti-psychologism, 'internalism', etc”.] of her website: http://people.umass.edu/partee/Research.htm.
Indeed, reference is not determined by a single expert in isolation. Reference determination is not a straightforward and unique process; there is a continuing discussion among experts about what the reference of a word is to be, e.g., about what metals have to be named gold. Experts may need years or even decades to reach a stable consensus (see Marconi 1997). This does not affect the notion that, according to this line of thought, there is a social element in the determination of reference: “extension is determined socially, not individually, owing to the linguistic division of labour” (Putnam 1975, p. 224). Referential dispositions of a normal speaker do not fix the reference of a term because it is only the “sociolinguistic state of the collective linguistic body to which the speaker belongs that does it” (Putnam 1975, p. 229).
On the alleged incompatibility between the social account of reference determination, endorsed by social externalists, and the direct theory of reference, endorsed by Kripke, Putnam and many others, see Liu 2002.
Of course, such view assumes that: what characterizes a natural kind is “some ‘essential nature’ which the thing shares with other members of the natural kind” (Putnam 1970, p. 188). Our ignorance of reference, both as individual and as community, therefore, is not surprising, since it directly derives from our inevitable lack of complete knowledge of the physical environment.
This is, for instance, the position famously taken by David Lewis: “I distinguish two topics: first, the description of possible languages or grammars as abstract semantic systems whereby symbols are associated with aspects of the world; and, second, the description of the psychological and sociological facts whereby a particular one of these abstract semantic systems is the one used by a person or population. Only confusion comes of mixing these two topics” (Lewis 1970, p. 19).
In Explanation and Partiality in Semantic Theory, Michal Glanzberg proposes that lexical axioms in Davidsonian semantics should be conceived as “pointers to concepts which are indicated by the non-quoted side of a disquotation clause” (2014, p. 28). Glanzberg argues he is not interested in endorsing a particular view of concepts (e.g., Fodorian concepts). But he also argues that “whatever pointers point to must provide extensions for predicative expressions, if they are to fix their contributions to truth conditions” (p. 28).
For instance, according to Fodor (1990), “all that matters for meaning is functional relations between symbols and their denotations. In particular, it doesn’t matter how that covariation is mediated; it doesn’t matter what mechanisms (neurological, intentional, spiritual, psychological, or whatever) sustain the covariation” (p. 83, note 6).
Pietroski et al. (2009) and Lidz et al. (2011) seem to consider their views as complementary to the truth-conditional analysis of meaning, not in opposition to it. Pietroski has recently proposed a more explicit and radical departure of semantics from truth and reference in his recent book, suggestively entitled Conjoining Meanings: Semantics Without Truth Values. In his view, “lexical meanings are instructions for how to fetch concepts that can be combined in certain ways, while phrasal meanings are instructions for how to build concepts that are monadic and conjunctive” (Pietroski 2018, p. 77). In this sense, according to Pietroski, “meanings are not extensions”, and “do not even determine extensions” (p. 9).
The philosophical approach to meaning based on the notion of inference has been recently developed by the philosopher Robert Brandom (1994) and his followers (e.g., Peregrin 2006). Nevertheless, the application of inferentialist semantics, or proof-theoretic semantics (PTS) to natural language is still in its infancy. Francez and colleagues have recently made a first step in this direction by developing a PTS for several fragments of English (Francez and Dyckhoff 2010; Francez et al. 2010).
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Calzavarini, F. Truth-Conditional Cognitivism and the Lexical Problem. Topoi 40, 43–54 (2021). https://doi.org/10.1007/s11245-019-09657-2
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DOI: https://doi.org/10.1007/s11245-019-09657-2