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Summary Paul Grice coined the term 'implicature' and the two sub-categories of it: conventional implicature and conversational implicature. Speakers convey their conventional implicatures by means of linguistic conventions. Consider the example of a speaker saying, "He is an Englishman; he is, therefore, brave." According to Grice, the speaker has only literally said that he [the person referred to] is an Englishman and that he is brave. The speaker has conventionally implicated that his bravery is a consequence of his Englishness by means of the conventional meaning of 'therefore'. 
Key works The first, and most important key work is Grice's "Logic and Conversation" in Grice 1989, in which Grice lays out the initial account of implicature, including conventional implicature. Bach 1999 presents one of the most significant challenges to that Grice's account of conversational implicature. 
Introductions Grice 1989; Bach 1999
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  1. Patricia Amaral, Craige Roberts & E. Allyn Smith (2007). Review of the Logic of Conventional Implicatures by Chris Potts. [REVIEW] Linguistics and Philosophy 30 (6):707-749.
    We review Potts’ influential book on the semantics of conventional implicature (CI), offering an explication of his technical apparatus and drawing out the proposal’s implications, focusing on the class of CIs he calls supplements. While we applaud many facets of this work, we argue that careful considerations of the pragmatics of CIs will be required in order to yield an empirically and explanatorily adequate account.
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  2. Kent Bach (1999). The Myth of Conventional Implicature. Linguistics and Philosophy 22 (4):327-366.
    Grice’s distinction between what is said and what is implicated has greatly clarified our understanding of the boundary between semantics and pragmatics. Although border disputes still arise and there are certain difficulties with the distinction itself (see the end of §1), it is generally understood that what is said falls on the semantic side and what is implicated on the pragmatic side. But this applies only to what is..
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  3. Stephen Barker (2014). Pure Versus Hybrid Expressivism and the Enigma of Conventional Implicature. In Guy Fletcher & Mike Ridge (eds.), Having it Both Ways: Hybrid Theories and Modern
Metaethics. Oxford.
    Can hybridism about moral claims be made to work? I argue it can if we accept the conventional implicature approach developed in Barker (Analysis 2000). However, this kind of hybrid expressivism is only acceptable if we can make sense of conventional implicature, the kind of meaning carried by operators like ‘even’, ‘but’, etc. Conventional implictures are a form of pragmatic presupposition, which involves an unsaid mode of delivery of content. I argue that we can make sense of conventional implicatures, but (...)
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  4. Stephen Barker (2011). Truth-Bearers and the Unsaid. In Ken Turner (ed.), Making Semantics Pragmatic. CUP.
    I argue that conventional implicatures embed in logical compounds, and are non-truth-conditional contributors to sentence meaning. This, I argue has significant implications for how we understand truth, truth-conditional content, and truth-bearers.
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  5. Stephen Barker (2003). Truth and Conventional Implicature. Mind 112 (445):1-34.
    Are all instances of the T-schema assertable? I argue that they are not. The reason is the presence of conventional implicature in a language. Conventional implicature is meant to be a component of the rule-based content that a sentence can have, but it makes no contribution to the sentence's truth-conditions. One might think that a conventional implicature is like a force operator. But it is not, since it can enter into the scope of logical operators. It follows that the semantic (...)
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  6. Stephen J. Barker (2000). Is Value Content a Component of Conventional Implicature? Analysis 60 (267):268–279.
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  7. Claudia Bianchi (2013). Implicating. In Pragmatics of Speech Actions, Handbooks of Pragmatics (HoPs) Vol. 2.
    Implicating, as it is conceived in recent pragmatics, amounts to conveying a (propositional) content without saying it – a content providing no contribution to the truth-conditions of the proposition expressed by the sentence uttered. In this sense, implicating is a notion closely related to the work of Paul Grice (1913-1988) and of his precursors, followers and critics. Hence, the task of this article is to introduce and critically examine the explicit/implicit distinction, the Gricean notion of implicature (conventional and conversational) and (...)
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  8. Robert Francescotti (1995). Even: The Conventional Implicature Approach Reconsidered. [REVIEW] Linguistics and Philosophy 18 (2):153 - 173.
    Like Bennett's account of ‘even’, my analysis incorporates the following plausible and widespread intuitions. (a) The word ‘even’ does not make a truth-functional difference; it makes a difference only in conventional implicature. In particular, ‘even’ functions neither as a universal quantifier, nor amost ormany quantifier. The only quantified statement that ‘EvenA isF’ implies is the existential claim ‘There is anx (namely,A) that isF’, but this implication is nothing more than what the Equivalence Thesis already demands. (b) ‘Even’ is epistemic in (...)
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  9. Roni Katzir (2007). Structurally-Defined Alternatives. Linguistics and Philosophy 30 (6):669-690.
    Scalar implicatures depend on alternatives in order to avoid the symmetry problem. I argue for a structure-sensitive characterization of these alternatives: the alternatives for a structure are all those structures that are at most as complex as the original one. There have been claims in the literature that complexity is irrelevant for implicatures and that the relevant condition is the semantic notion of monotonicity. I provide new data that pose a challenge to the use of monotonicity and that support the (...)
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  10. Ewa Mioduszewska (1992). Conventional Implicature and Semantic Theory. Wydawnictwa Uniwersytetu Warszawskiego.
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  11. Christopher Potts, 106. Conventional Implicature and Expressive Content.
    This article presents evidence that individual words and phrases can contribute multiple independent pieces of meaning simultaneously. Such multidimensionality is a unifying theme of the literature on conventional implicatures and expressives. I use phenomena from discourse, semantic composition, and morphosyntax to detect and explore various dimensions of meaning. I also argue that, while the meanings involved are semantically independent, they interact pragmatically to reduce underspecification and fuel pragmatic enrichment. In this article, the central case studies are appositives like Falk, the (...)
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  12. Christopher Potts (2007). Into the Conventional-Implicature Dimension. Philosophy Compass 2 (4):665–679.
    Grice coined the term ‘conventional implicature’ in a short passage in ‘Logic and conversation’. The description is intuitive and deeply intriguing. The range of phenomena that have since been assigned this label is large and diverse. I survey the central factual motivation, arguing that it is loosely uni- fied by the idea that conventional implicatures contribute a separate dimen- sion of meaning. I provide tests for distinguishing conventional implicatures from other kinds of meaning, and I briefly explore ways in which (...)
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  13. Steven Rieber (1997). Conventional Implicatures as Tacit Performatives. Linguistics and Philosophy 20 (1):51-72.
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  14. Craige Roberts, Mandy Simons & Judith Tonhauser, Presupposition, Conventional Implicature, and Beyond: A Unified Account of Projection.
    We define a notion of projective meaning which encompasses both classical presuppositions and phenomena which are usually regarded as non-presuppositional but which also display projection behavior—Horn’s assertorically inert entailments, conventional implicatures (both Grice’s and Potts’) and some conversational implicatures. We argue that the central feature of all projective meanings is that they are not-at-issue, defined as a relation to the question under discussion. Other properties differentiate various sub-classes of projective meanings, one of them the class of presuppositions according to Stalnaker. (...)
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  15. Andreas Stokke (2013). Lying and Asserting. Journal of Philosophy 110 (1):33-60.
    The paper argues that the correct definition of lying is that to lie is to assert something one believes to be false, where assertion is understood in terms of the notion of the common ground of a conversation. It is shown that this definition makes the right predictions for a number of cases involving irony, joking, and false implicature. In addition, the proposed account does not assume that intending to deceive is a necessary condition on lying, and hence counts so-called (...)
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  16. Daniel Whiting (2013). It's Not What You Said, It's the Way You Said It: Slurs and Conventional Implicatures. Analytic Philosophy 54 (3):364-377.
    In this paper, I defend against a number of criticisms an account of slurs, according to which the same semantic content is expressed in the use of a slur (e.g. 'chink') as is expressed in the use of its neutral counterpart (e.g. 'Chinese'), while in addition the use of a slur conventionally implicates a negative, derogatory attitude. Along the way, I criticise competing accounts of the semantics and pragmatics of slurs, namely, Hom's 'combinatorial externalism' and Anderson and Lepore's 'prohibitionism'.
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  17. Zsófia Zvolenszky (2012). A Gricean Rearrangement of Epithets. In Ferenc Kiefer & Zoltán Bánréti (eds.), 20 Years of Theoretical Linguistics in Budapest: A selection of papers from the 2010 conference celebrating the twentieth anniversary of the Theoretical Linguistics Programme of Eötvös Loránd University. Tinta Publishing House. 183-218.