Abstract
According to the contemporary consensus, when reaching in the lexicon grammar looks for items like nouns, verbs, and prepositions while logic sees items like predicates, connectives, and quantifiers. In fact, there doesn’t seem to be a single lexical category contemporary grammar and logic both make use of. I hope to show that while a perfect match between the lexical categories of grammar and logic is impossible there can be a substantial overlap. I propose semantic definitions for all the major parts of speech (noun, verb, adjective, and adverb). I argue that the differences among these categories can be captured in terms of distinctions recognized in logic (referring expression vs. predicate, constant vs. variable).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
I do not want to make the stronger claims that well-formed sentences are well-formed in virtue of their grammatical form and valid inferences are valid in virtue of their logical form. To provide a full explanation of well-formedness or validity we have to appeal to facts beyond form. For arguments that no validity is purely a matter of form, see Szabó (2012).
Montague (1970): 398.
This is called quantifier rising. It was first proposed in May (1985) and it remains one of the many popular options for treating quantifiers in natural languages.
These are called generalized quantifiers, introduced first by Lindström (1966). Natural language quantifiers are typically interpreted by semanticists as generalized quantifiers of some sort.
The remaining differences can be eliminated if we modify the syntax of the language of first-order logic along the lines suggested in section 7.4 of Heim and Kratzer (1998) and assume an analogous syntax for English.
Cf. Bar-Hillel (1953).
Some might find it convenient to call certain inferences valid even if they contain ill-formed sentences; e.g. ‘All men are mortal, Socrates is a man; therefore Socrates are mortal’. I am not opposed to call such arguments loosely valid, but then I would also insist that their premises and conclusions are loosely well-formed. By contrast, I would resist the idea that a string like ‘Man Socrates a is; therefore man Socrates a is’ is a valid inference. If valid inferences preserve truth then their premises and conclusions must be capable of truth.
One may object that ‘I know that snow is white and you know that snow is white and grass is green too’ is ungrammatical even though it is the result of substituting ‘Snow is white and grass is green’ for the second occurrence of ‘Snow is white’ within the perfectly well-formed ‘I know that snow is white and you know that snow is white too’. But I am not convinced that ‘I know that snow is white and you know that snow is white and grass is green too’ is ill-formed. Suppose it is common ground that the speaker knows that grass is green but it is very much up in the air whether he knows that snow is white. In this (admittedly slightly contrived) case the sentence does not seem out of place.
The lexicon is often characterized as a finite list of all the words of a language, but lexical items can also be non-compositional phrases—such as compounds (e.g. ‘dog run’), phrasal verbs (e.g. ‘run off’), or idioms (e.g. ‘on the run’). The traditional individuation of lexical items is sensitive to derivational morphology (thus ‘run’ and ‘running’ count as distinct lexical items) but not to inflectional morphology (thus ‘run’ and ‘ran’ count as the same lexical item).
Of course, the English adjective ‘legal’ comes presumably from the Latin adjective ‘legalis’, which in turn was derived from the noun ‘lex’.
Of course, (4) is well-formed if ‘there’ is a demonstrative; I am focusing on ‘there’ as an expletive as it is most naturally taken in (3).
While the question whether the major categories of speech are truly universal remains open, there are very few plausible examples of languages without them. For a detailed argument of their universality, see Baker (2003). The role of the major parts of speech in language acquisition in uncontested; the focus of research is on whether there are major differences in the way words belonging to different categories are learned. For a survey, see Gleitmen and Wanner (1982).
For example, Baker (2003) argues that to be a verb is to be a lexical category that has a specifier and to be a noun is to carry a referential index consisting of a pair of integers. These bring hefty assumptions about what universal grammar must look like.
There is a contrast here with minor parts of speech (the closed lexical categories of grammar). On the traditional picture, these are fully characterizable in syntactic terms. They do not signify parts of reality and they contribute to the form, rather than the content of sentences.
Formal semanticists these days usually adopt the standard mathematical reduction of functions to relations and of relations to sets. (This would have been anathema to Frege, who thought that functions are unsaturated entities while sets are just special sorts of objects.) If we take these reductions seriously, the fundamental ontological categories underlying lexical divisions are those between objects and sets.
Compare ‘Recklessly, Hugo opened the door’ and ‘Hugo opened the door recklessly’.
In the Language Blog of Lingua Franca, June 20, 2012. Thanks to Justin Khoo for the pointer.
Many of these context-sensitive words have homonyms that are adverbs; e.g. the first word is a noun in ‘Tomorrow is a Friday’ but an adverb in ‘Tomorrow we go swimming’. In Stanley and Szabó (2000) we argued that all nouns are variables in this broad sense—their lexical meaning includes an element which designates the domain for quantificational determiners the nouns combine with. Stanley (2002) has amended this view by claiming that these elements occupy their own leaf in the syntactic form of quantified sentences. Whether the details of the latter proposal are exactly right is a matter of debate; that it is an improvement over the earlier one is not. Domain-sensitivity is not a good reason to abandon the view that nouns are constants.
Relational nouns—such as ‘mother’, ‘enemy’, ‘speed’, ‘temperature’—are sometimes interpreted as variables. The idea is that to be a brother is to be a brother of x, where the value of x is supplied by context. My view is that to be a brother is simply to be someone’s brother—which is fully compatible with ‘brother’ being a constant. It is undeniable that relational nouns form a subcategory of nouns distinguishable both by grammatical and logical features: ‘Some Labradors are Bill’s dogs’ is well-formed, ‘Some Bulgarians are Bill’s friends’ is not, ‘Bill’s dogs are Labradors; therefore Bill has dogs’ is valid, ‘Bill’s friends are Bulgarians; therefore Bill has Bulgarians’ is not. But these differences can be captured in the compositional semantics without treating ‘brother’ as a variable.
I do think it is interesting that definite descriptions can be used to say what something is called but complex demonstratives and specific indefinites are marginal at best.
This captures obstinate rigidity; the clause can be adjusted if ‘Socrates’ is deemed to be persistently rigid.
Note that if this is supposed to be the criterion, English mass nouns all turn out to be referring expressions.
This is the clause neo-Davidsonean would assign to proper names; cf. Larson and Segal (1995), ch.5 and Sainsbury (2005), ch.3. It is customary to write the right hand side of (14) as ‘x = Socrates’. I think it is best to state our semantic clauses without appealing to resources from different languages: ‘=’ is not a word of English, ‘if” is not a word of the standard formal languages of logic. This might sound nit-picky but it isn’t. When we mix languages we smuggle in assumptions about the grammar of these languages—in this case, the assumption that the noun ‘Socrates’ is grammatically like an individual constant. I think this false, but even if it were true it would need to be established rather than simply taken for granted.
Larson and Segal (1995) argue that semantics theory is hardwired and its sole function is to deliver interpretative T-sentences using extremely weak logical resources. If this is so, there is no reason why the axioms of the theory couldn’t be false—as long as the T-sentences it derives are all true the theory does exactly what it is supposed to.
Sainsbury (2005) argues that the right logic employed in the meta-language of a semantic theory of English is a negative free logic. Since he thinks the semantics should ideally be homophonic, this amounts to a commitment that the logic of English is non-classical.
Of course, if the argument places are filled by quantifying expressions then verbs say something relative to an assignment about the things referred to relative to the same assignment by expressions filling their argument places.
Parsons (1990): 98 argues that inferences of this sort aren’t valid at all. Jill can dream that she is stabbed but nobody stabbed her, which suggests that stabbings without stabbers aren’t logical impossibilities.
Davidson (1967).
Parsons (1990) and Schein (1993). Note that the argument I presented above targets the assumption that verbs are predicates of their arguments alone. Davidson could say that run is a two-place predicate of runnings and runners. Then the logical form of ‘Jack ran’ could be ‘∃x run(x, j)’ and of ‘Jack ran the Boston Marathon’ could be something like ‘∃x (run (x, j) ∧ Theme (x, b))’. Then we do predict that ‘Jack ran the Boston Marathon’ logically entails ‘Jack ran’ but the latter does not logically entail ‘Jack ran something or other’, as desired. Note however, that the proposal lacks independent support. While there are proposals on the market that recommend thematic separation of only the external argument of verbs, to my knowledge there is no precedent for separating only an internal argument. Thanks to Jonathan Schaffer for discussion.
Note that I am not saying that this is the logical form of these sentences. The project is to keep grammatical and logical form in natural languages as close as possible and the grammatical form of (26) and (27) is nothing like the grammatical form of any English sentence.
The strings marked by ‘??’ are not ungrammatical, but they require a special interpretative effort. ‘Jill crossed the Atlantic for days’ is fine if read as saying that Jill kept going back and forth between the two sides of the Atlantic for four days and ‘Jill walked in four days’ is fine if understood as saying that four days after the reference time Jill walked.
Couldn’t we say that the semantic essence of verbs is that they assign thematic roles? No: some nouns assign thematic roles as well (e.g. relational nouns, like ‘mother’ or ‘friend’ have Themes) and some verbs assign no thematic role (e.g. weather verbs, like ‘rain’ and raising verbs, like ‘seem’) to their subjects.
Once you have predicates inflected for tense and aspect, they are all full VP’s and can be freely coordinated; cf. ‘Jack cheats, is dishonest, and is a liar’.
pr is sometimes optionally voiced in English as ‘as’; cf. ‘I regard you (as) a friend.’ Overt pr is present in many languages throughout the world; cf. Baker (2003): 40.
The argument is from Baker (2003): 78.
I suspect ‘[VP greet]’ and ‘[PREDP [PR∅][NP a greeting]’ are synonyms. This explains the near-perfect synonymy of ‘Socrates greeted Plato’ and ‘A past greeting of Plato was by Socrates’.
Of course, there are artificial languages with such predicates. In a language of first-order logic we can introduce a non-logical constant liar and we can stipulate that it is a predicate satisfied by x if and only if x is a liar. But this word has no proper translation to English. The noun ‘liar’ comes close, but it differs from liar in being a referring expression, rather than a predicate.
Kennedy (2007).
Given the heterogeneity of the traditional category my decision to include only open category items in major parts of speech may be significantly more revisionary in the case of adverbs than elsewhere.
Chapter 4.5 of Baker (2003) takes the opposite view.
Whether these sentences mean the exact same thing is a tricky issue: it depends, among other things, on whether the possessive construction (usually regarded as a definite description) carries a semantic uniqueness implication that is missing from the first sentence. My own view is that the uniqueness implications of definite descriptions are pragmatic; cf. Szabó (2000, 2005).
The observation that there is this ambiguity is due to Larson (1998).
‘Play’ does not occur on the surface in (34) but is presumably part of the semantic contribution of the derived noun ‘player’.
See Szabó (2003) for an attempt to provide a semantic analysis for such subject-centered occurrences of adverbs.
Baker (2003): 292.
He could have added ‘Chris exists hungrily’ which, on its literal interpretation, means roughly what any of (37)–(39) do.
I thank audiences at Oxford University, at Rutgers University, and at Universität Erfurt for questions, comments, and discussion. Special thanks to Cian Dorr, Tamar Szabó Gendler, David Liebesman, Paul Pietroski, Jonathan Schaffer, and Anna Szabolcsi.
References
Baker, M. (2003). Lexical categories: Verbs, nouns, and adjectives. Cambridge: Cambridge University Press.
Bar-Hillel, Y. (1953). A quasi-arithmetical notation for syntactic description. Language, 29, 47–58.
Bowers, J. (1993). The syntax of predication. Linguistic Inquiry, 24, 591–656.
Bowers, J. (2001). Predication. In M. Baltin & C. Collins (Eds.), The handbook of contemporary syntactic theory. Oxford: Blackwell.
Burge, T. (2007). Predication and truth. Journal of Philosophy, 104, 580–608.
Chomsky, N. (1981). Lectures on government and binding. Dordrecht: Foris.
Croft, W. (1991). Syntactic categories and grammatical relations. Chicago: Chicago Univresity Press.
Davidson, D. (1967). The logical form of action sentences. Reprinted in essays on actions and events (pp. 105–121). Oxford: Oxford University Press. (2001).
Frege, G. (1892). On concept and object. Vierteljahrschrift für wissenschaftliche Philosophie, 16. Reprinted in B. McGuinness (ed.), Collected papers on mathematics, logic, and philosophy (pp. 182–194). Oxford: Basil Blackwell, 1984.
Furth, M. (1968). Two types of denotation. In Studies in Logical Theory. Cambridge: Blackwell.
Gleitmen, L., & Wanner, E. (1982). Language acquisitions: The state of the state of the art. In E. Wanner & L. Gleitman (Eds.), Language acquisition: The state of the art. Cambridge: Cambridge University Press.
Grimshaw, J. (1990). Argument structure. Cambridge, MA: MIT Press.
Gruber, J. (1965). Studies in lexical relations. Ph.D. Dissertation, MIT.
Heim, I., & Kratzer, A. (1998). Semantics in generative grammar. Oxford: Blackwell.
Kennedy, C. (2007). Vagueness and grammar: The semantics of relative and absolute gradable predicates. Linguistics and Philosophy, 30, 1–45.
Larson, R. (1998). Events and modification in nominals. In D. Strolovitch & A. Lawson (Eds.), Proceedings from SALT (Vol. VIII, pp. 145–168). Ithaca, NY: CLC.
Larson, R., & Segal, G. (1995). Knowledge of meaning: An introduction to semantic theory. Cambridge, MA: MIT Press.
Lindström, P. (1966). First-order predicate logic with generalized quantifiers. Theoria, 32, 186–195.
MacFarlane, J. (Fall 2009 Edition). Logical constants. In E. N. Zalta (ed.), The stanford encyclopedia of philosophy. http://plato.stanford.edu/archives/fall2009/entries/logical-constants/.
May, R. (1985). Logical form: Its structure and derivation. Cambridge, MA: MIT Press.
Montague, R. (1970). Universal grammar. Theoria, 36. Reprinted in R. H. Thomason (ed.), Formal philosophy (pp. 222–246). New Haven: Yale University Press, 1974.
Murphy, L. (2010). Lexical meaning. Cambridge: Cambridge University Press.
Parsons, T. (1990). Events in the semantics of english. Cambridge, MA: MIT Press.
Rothschild, D., & Segal, G. (2009). Indexical predicates. Mind and Language, 24, 467–493.
Russell, B. (1918). The philosophy of logical atomism. Monist 28, 29. Reprinted in Logic and knowledge (pp. 177–281). London: Allen and Unwin, 1956.
Sainsbury, M. (2005). Reference without referents. Oxford: Oxford University Press.
Schein, B. (1993). Plurals and events. Cambridge, MA: MIT Press.
Stanley, J. (2002). Nominal restriction. In G. Peters & G. Preyer (Eds.), Logical form and language (pp. 321–344). Oxford: Oxford University Press.
Stanley, J., & Szabó, Z. (2000). On quantifier domain restriction. Mind and Language, 15, 219–261.
Strawson, P. (1950). On referring. Mind, 59. Reprinted in Logico-linguistic papers (pp. 1–27). London: Methuen, 1971.
Szabó, Z. G. (2000). Descriptions and uniqueness. Philosophical Studies, 101, 29–57.
Szabó, Z. (2001). Adjectives in context. In I. Kenesei & R. M. Harnish (Eds.), Perspectives on semantics, pragmatics, and discourse (pp. 119–146). Amsterdam: John Benjamins.
Szabó, Z. (2003). On qualification. Philosophical Perspectives, 17, 385–414.
Szabó, Z. (2005). The loss of uniqueness. Mind, 114, 1185–1222.
Szabó, Z. (2012). Against logical form. In G. Preyer (Ed.), Donald Davidson on truth meaning, and the mental (pp. 105–126). Oxford: Oxford University Press.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Szabó, Z.G. Major Parts of Speech. Erkenn 80 (Suppl 1), 3–29 (2015). https://doi.org/10.1007/s10670-014-9658-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10670-014-9658-1