Abstract
In this essay, we propose that Peirce’s Existential Graphs can derive the desired uniqueness implication (or in a weaker claim, the definite description readings) of donkey pronouns in conjunctive discourse (A man walks in the park. He whistles), without postulating a separate category of E-type pronouns.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
The arguments for interpreting donkey pronouns as definite descriptions (and therefore involving uniqueness if definite descriptions carry this feature) are standard in the literature, particularly for donkey anaphora involving conjunctive discourse (Evans 1977; Sells 1985; Kadmon 1990; Dorrepaal 1993, among others). Few people argue against the uniqueness implication in intersentential donkey anaphora, and for those who argue against uniqueness in classical donkey anaphora (relatives and conditionals), the uniqueness in intersentential anaphora is also admitted. For example, Chierchia (1995, p. 19) states that there appear to be no systematic uniqueness presuppositions in donkey sentences, perhaps the only case in which such uniqueness presupposition seems to be systematically present are coordinated narrative sequences. Moltmann (2006) admits that the possibility of uniqueness not being satisfied is obvious in the case of relative clauses and conditionals, but less obvious in the case of conjunctions.
The only exception seems to be Heim (1982). Nevertheless, it should be pointed out that Heim did not question the assumption that certain anaphoric pronouns mean the same thing as certain definite descriptions; she only questions the assumption that definite descriptions are to be analyzed as involving uniqueness implication. My paper is aimed at deriving the definite description readings of some anaphoric pronouns, and whether definite descriptions have uniqueness implication (either entailed or presupposed) is actually a different matter. In this paper I adopt the Russellian view. And if definite descriptions are shown to have no uniqueness implication at all but some conversational implicature or familiarity (like Szabó 2000), our thesis shall not be affected fundamentally.
This problem in a different guise is also faced by E-type theory (Evans 1977). Though in this theory donkey pronouns are interpreted as definite descriptions, the question of why they get interpreted as such has never been answered completely. One of the aims of this work is to answer this question.
EG represents the whole edifice of Peirce’s philosophical and logical thoughts, invariably its complexity and profoundness are far more than what this paper can do justice to. For a comprehensive understanding of EG and its philosophical significance, interested readers can consult Peirce’s own writings on Existential Graphs (CP 4.372–584 in Collected Papers Vol 4; Peirce’s tutorial on existential graphs MS 514 with commentary by John Sowa; the 1906 Monist paper, also in CP 4.530–572), monographs on EG (Zeman 1964; Roberts 1973; Shin 2002; Pietarinen 2006b; among others).
Citations to Peirce’s writings follow the usual practice in Peircean scholarship: CP 4.394 means Collected Papers Volume 4 paragraph 394, and MS 514 means manuscript number 514.
We use squares to represent SAs and rounded squares to represent cuts. If unnecessary, we may drop the square for SA, but remember it is always the SA on which the graph-instances are scribed.
Of course, we need an algorithm to map syntactic structures to EGs, much like Kamp and Reyle ’s (1993) construction rules mapping syntactic structures into DRSs. In this algorithm, some top–down and left–right conventions have to be posited.
In his 1905 MS 430, Peirce proposed that Graph 9 entails Graph 8 by means of some transformation rules. We will return to these rules later in this section.
This condition of scope may shed light on the restricted scope of universal quantifier like every and the relatively free scope of existential quantifier like a/some (Fodor and Sag 1982). According to this definition of scope, the scope of universal quantifiers is always limited because they must be represented as a LI within a scroll. Consequently, their scope is confined to that scroll. On the other hand, nothing prevents the line for existential quantifier from occurring at any location on a SA. This is because existential quantifiers in natural language are represented as lines of identities which may be either enclosed or unenclosed (CP 4.567). Then, in an ambiguous sentence like A man loves every woman, it is the existential quantifier that ‘moves’, not the universal quantifier. This is an important issue that cannot be pursued in this article.
This condition looks much looser than the classical c-command condition for quantificational binding. It should be properly restricted to exclude some wild overgeneration (like crossover effects). However, for the present article, this condition is adequate.
We will use shading for the oddly-enclosed areas.
The Line Linking Condition can join two lines into one, regardless whether they are in positive or negative areas. This application is different from the rule of insertion, which only applies in a negative area.
Peirce has another rule, called The Rule of Assertion. “Any graph well-understood to be true may be scribed unenclosed...This rule is to be understood as permitting the explicit assertion of three classes of propositions; first, those that are involved in the conventions of this system of existential graphs; secondly, any propositions known to be true but which may not have been thought of as pertinent when the graph was first scribed or as pertinent in the way in which it is now seen to be pertinent (that is to say, premisses may be added if they are acknowledged to be true); thirdly, any propositions which the scription of the graph renders true or shows to be true.” (CP 4.507) In our case, it scribes the second class of propositions.
Though Peirce did not discuss donkey sentences in his writings, he did discuss some more complex donkey-like sentences, possibly may be called as benefactress sentences (in MS 430, A-V. Pietarinen, personal communication). These sentences are rather complex.
(i) There is a benefactress of everybody whom anybody she has not rejected must love.
(ii) Everybody has some benefactress who rejects everybody that does not love her.
(iii) Anybody has either been rejected by somebody or loves some benefactress of himself.
(iv) Somebody rejects everybody that does not love some benefactress of him.
Peirce (1906, CP 4.546) also discussed some other sentences of the following type, which is dubbed as ‘Peirce’s Puzzle’ and which has caused some discussions in formal semantics, see Dekker (2001) and references cited there.
(v) There is some married woman who will commit suicide in case her husband fails in business.
(vi) There is some married woman who will commit suicide if every married man fails in business.
The assumptions made in EG-account are quite standard, without any radical departures from classical semantics: there is nothing peculiar with the indefinite (DRT), it is just an existential quantifier; there is nothing peculiar with the pronoun (E-type), it is just a variable; and there is nothing peculiar with conjunction (DPL), it is just a truth conditional operator. Then something must be peculiar. In Existential Graphs, the peculiar thing is the importing and exporting of information into and out of the contexts in the form of five transformation rules, which are standard natural deductive system.
We suggest that the, like he, also introduces a line of identity in EG with a loose end to be linked to another fully-attached line. Different from he, the line for the needs a branch to be predicated of a noun (such as man). Informally, the can be translated as \(\lambda P\lambda Q \exists x[x{=}? \wedge Px \wedge Qx]\). Then “A man walks in the park. The man whistles” will have the following standard logical analysis: \(\exists x[\textit{man}\ x \wedge \textit{walks} \ \textit{in} \ \textit{the} \ \textit{park} \ x] \wedge \exists y[\textit{man}\ y \wedge \forall x[\textit{man}\ x \wedge \ \textit{walks} \ \textit{in} \ \textit{the} \ \textit{park} \ x \rightarrow x{=}y] \wedge \ \textit{whistles} \ y].\) So, the Russellian semantics of the is also derived. Pronouns and definite articles are closely related in interpretation, with one syntactic difference. This conclusion is independently arrived with that of Elbourne ’s (2005) NP deletion account, but we are uncertain on whether pronouns are assimilated into definite articles or definite articles are assimilated into pronouns or there is no such assimilation.
References
Barker, C. & Shan, C.-C. (2008). Donkey anaphora is in-scope binding. Semantics & Pragmatics, 1, 1–46.
Barwise, J., & Cooper, R. (1981). Generalized quantifiers and natural language. Linguistics and Philosophy, 4, 159–219.
Burch, R. W. (1994). Game-theoretical semantics for Peirce’s existential graphs, Synthese, 99(3), 361–375.
Burch, R. W. (1997). A Tarski-style semantics for Peirce’s beta graphs. In J. Brunning & P. Forster (Eds.), The Rule of Reason: The Philosophy of Charles Sanders Peirce (pp. 81–95). Toronto: University of Toronto Press.
Burch, R. W. (2011). The fine structure of Peircean ligatures and lines of identity. Semiotica, 186(1/4), 21–68.
Chierchia, G. (1995). Dynamics of meaning: Anaphora, presupposition, and the theory of grammar. Chicago: University of Chicago Press.
Cooper, R. (1979). The interpretation of pronouns. In F. Heny & H. Schnelle (Eds.), Syntax and semantics 10. New York: Academic Press.
Dau, F. (2011). Ligatures in Peirce’s existential graphs. Semiotica, 186, 89–109.
Dekker, P. (1994). Predicate logic with anaphora. In L. Santelmann & M. Harvey (Eds.), Proceedings of the 4th Semantics and Linguistic Theory Conference. DMLL Publications, Cornell University.
Dekker, P. (2001). Dynamics and pragmatics of ‘Peirce’s Puzzle’. Journal of Semantics, 18(3), 211–241.
Dorrepaal, J. (1993). On the notion of uniqueness. In Proceedings of the 6th Conference on European Chapter of the Association for, Computational Linguistics (pp. 106–112).
Elbourne, P. (2005). Situations and individuals. Cambridge, MA: MIT Press.
Evans, G. (1977). Pronouns, quantifiers, and relative clauses (l). Canadian Journal of Philosophy, 7, 467–536.
Fodor, J. D., & Sag, I. (1982). Referential and quantificational indefinites. Linguistics and Philosophy, 5, 355–398.
Geach, P. (1962). Reference and generality. Ithaca, NY: Cornell University Press.
Groenendijk, J., & Stokhof, M. (1991). Dynamic predicate logic. Linguistics and Philosophy, 14, 39–100.
Hammer, E. (1998). Semantics for existential graphs. Journal of Philosophical Logic, 27, 489–503.
Heim, I. (1982). The semantics of definite and indefinite noun phrases. (Doctoral dissertation: University of Massachusetts, Amherst).
Heim, I. (1990). E-type pronouns and donkey anaphora. Linguistics and Philosophy, 13, 137–177.
Hilpinen, R. (1982). On C.S. Peirce’s theory of the proposition: Peirce as a precursor of game-theoretical semantics. The Monist, 65(2), 182–188.
Hintikka, J. (1973). Logic, language-games and information. Oxford: Oxford University Press.
Hintikka, J., & Kulas, J. (1985). Anaphora and definite descriptions. Dordrecht: Reidel.
Johnson-Laird, P. N. (2002). Peirce, logic diagrams, and the elementary operations of reasoning. Thinking and Reasoning, 8(1), 69–95.
Kadmon, N. (1990). Uniqueness. Linguistics and Philosophy, 13, 273–324.
Kamp, H. (1981). A theory of truth and semantic representation. Formal methods in the study of language, Groenendijk. Amsterdam: Mathematical Centre.
Kamp, H., & Reyle, U. (1993). From discourse to logic. Dordrecht: Kluwer.
Karttunen, L. (1976). Discourse referents. In J. McCawley (Ed.), Syntax and semantics 7 (pp. 363–385). New York: Academic Press.
Krahmer, E., & Muskens, R. (1995). Negation and disjunction in Discourse Representation Theory. Journal of Semantics, 12, 357–376.
McKinsey, M. (1986). Mental anaphora. Synthese, 66(1), 159–175.
Moltmann, F. (2006). Unbound anaphoric pronouns: e-Type, dynamic, and structured-propositions approaches. Synthese, 153, 199–260.
Neale, S. (1990). Descriptions. Cambridge, MA: MIT Press.
Pagin, P., & Westerståhl, D. (1993). Predicate logic with flexibly binding operators and natural language semantics. Journal of Logic, Language and Information, 2, 89–128.
Partee, B. (1978). Bound variables and other anaphors. In D. Waltz (Ed.), Proceedings of TINLAP-2 (pp. 79–85). Champaign, IL: University of Illinois. (Also in Compositionality in formal semantics. Blackwell Publishing).
Peirce, C. (1906). Prolegomena to an apology for pragmaticism. The Monist, 16(4), 492–546.
Peirce, C. (1933). In C. Hartshorne & P. Weiss (Eds.), The Collected Papers of C. S. Peirce, (Vol. 4, 5). Cambridge, MA: Harvard University Press.
Peirce, C. (1967). Manuscripts in the Houghton Library of Harvard University. In R. Robin (Ed.), Annotated Catalogue of the Papers of Charles S. Peirce. Amherst: University of Massachusetts Press.
Pietarinen, A-V. (2004). Peirce’s game-theoretic ideas in logic. Semiotica, 144(4), 33–47.
Pietarinen, A-V. (2006a). Peirce’s contributions to possible-worlds semantics. Studia Logica, 82(3), 345–369.
Pietarinen, A.-V. (2006b). Signs of logic: Peircean Themes on the philosophy of language, games, and communication. Synthese library 329. Dordrecht: Springer.
Roberts, C. (1989). Modal subordination and pronominal anaphora in discourse. Linguistics and Philosophy, 12, 683–721.
Roberts, D. (1973). The Existential Graphs of Charles S. Peirce. The Hauge: Mouton and Co.
Russell, B. (1905). On denoting. Mind, 14, 479–493.
Sánchez, V. (1991). Studies on Natural Logic and Categorial Grammar. (Doctoral Dissertation, University of Amsterdam).
Saurer, W. (1993). A natural deduction system for discourse representation theory. Journal of Philosophical Logic, 22(3), 249–302.
Sells, P. (1985). Restrictive and non-restrictive modification, CSLI report 85–28.
Shin, S.-J. (2002). The iconic logic of Peirce’ s Graphs. Cambridge, MA: The MIT Press.
Simons, M. (2000). Issues in the semantics and pragmatics of disjunction. New York: Garland.
Soames, S. (1989). Review of Gareth Evans’ The Collected Papers. Journal of Philosophy, 86(1), 141–156.
Sowa, J. (2000). Knowledge representation: Logical, philosophical and computational foundations. Pacific Grove: Brooks/Cole.
Strawson, P. F. (1952). Introduction to logical theory. London: Methuen.
Szabó, Z. G. (2000). Descriptions and uniqueness. Philosophical Studies, 101(1), 29–57.
van den Berg, H. (1995). Existential graphs and dynamic predicate logic. In G. Ellis et al. (Eds.), Conceptual structures: Structure-based knowledge representation (pp. 338–352). Berlin: Springer.
Van Rooy, R. (2001). Exhaustivity in dynamic semantics; referential and descriptive pronouns. Linguistics and Philosophy, 24, 621–657.
Zeman, J. (1964). The graphical logic of C. S. Peirce. (Doctoral dissertation, University of Chicago).
Acknowledgments
An earlier version of this paper was presented at the student session of 2010 Sino-European Winter School in Logic, Language and Computation (SELLC-2010, Guangzhou of China). I thank the guest editor A-V. Pietarinen and two Synthese anonymous reviewers for very valuable comments and suggestions. This paper also benefited from consultations with and teachings of Robin Cooper, Jaakko Hintikka, Jianhua Hu, Yan Jiang, Thomas Lee, Bing Li, Chunyan Ning, Haihua Pan, and Dag Westerståhl at different occasions. This work receives the financial support from China Ministry of Education Humanities and Social Sciences Research Fund Project No. 12YJA740021, which is appreciated. All errors are mine.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
He, C. E-type interpretation without E-type pronoun: how Peirce’s Graphs capture the uniqueness implication of donkey pronouns in discourse anaphora. Synthese 192, 971–990 (2015). https://doi.org/10.1007/s11229-013-0325-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-013-0325-x