We discuss a well-known puzzle about the lexicalization of logical operators in natural language, in particular connectives and quantifiers. Of the many logically possible operators, only few appear in the lexicon of natural languages: the connectives in English, for example, are conjunction _and_, disjunction _or_, and negated disjunction _nor_; the lexical quantifiers are _all, some_ and _no_. The logically possible nand (negated conjunction) and Nall (negated universal) are not expressed by lexical entries in English, nor in any natural language. Moreover, (...) the lexicalized operators are all upward or downward monotone, an observation known as the Monotonicity Universal. We propose a logical explanation of lexical gaps and of the Monotonicity Universal, based on the dynamic behaviour of connectives and quantifiers. We define update potentials for logical operators as procedures to modify the context, under the assumption that an update by \( \phi \) depends on the logical form of \( \phi \) and on the speech act performed: assertion or rejection. We conjecture that the adequacy of update potentials determines the limits of lexicalizability for logical operators in natural language. Finally, we show that on this framework the Monotonicity Universal follows from the logical properties of the updates that correspond to each operator. (shrink)

Some arguments against the assumption that ordinary people may share common knowledge are sound. The apparent cost of such arguments is the rejection of scientific theories that appeal to common knowledge. My proposal is to accept the arguments without rejecting the theories. On my proposal, common knowledge is shared by ideally rational people, who are not just mathematically simple versions of ordinary people. They are qualitatively different from us, and theorizing about them does not lead to predictions about our behavior. (...) Nevertheless, models of action that assume common knowledge have a role to play in our understanding of collective rationality. (shrink)

Given current data, only a few binary Boolean operators are expressed in lexically simple fashion in the world's languages: and, or, nor. These do not occur in every combination, for example, nor is not observed by itself. To explain these cross‐linguistic patterns, we propose an encoding of Boolean operators as update procedures to accept or reject information in a context. We define a measure of conceptual simplicity for such updates, on which attested operators are conceptually simpler than the remaining Booleans. (...) Moreover, we show that language evolution selects for the attested lexical inventories by minimizing the complexity of using a lexical inventory compositionally to convey precise information. (shrink)

We introduce the rejection game, designed to formalize the interaction between interlocutors in a Stalnakerian conversation: a speaker who asserts something and a listener who may accept or reject. The rejection game is similar to other signalling games known to the literature in economics and biology. We point out similarities and differences, and propose an application in linguistics. We uncover basic conditions under which the Gricean maxim of quality emerges from incentives among the players, providing evidence for a functionalist understanding (...) of the Gricean program. (shrink)

Natural language does not express all connectives definable in classical logic as simple lexical items. Coordination in English is expressed by conjunction and, disjunction or, and negated disjunction nor. Other languages pattern similarly. Non-lexicalized connectives are typically expressed compositionally: in English, negated conjunction is typically expressed by combining negation and conjunction (not both). This is surprising: if $$\wedge $$ ∧ and $$\vee $$ ∨ are duals, and the negation of the latter can be expressed lexically (nor), why not the negation (...) of the former? I present a two-tiered model of the semantics of the binary connectives. The first tier captures the expressive power of the lexicon: it is a bilateral state-based semantics that, under a restriction, can express all and only the distinctions that can be expressed by the lexicon of natural language (and, or, nor). This first tier is characterized by rejection as non-assertion and a Neglect Zero assumption. The second tier is obtained by dropping the Neglect Zero assumption and enforcing a stronger notion of rejection, thereby recovering classical logic and thus definitions for all Boolean connectives. On the two-tiered model, we distinguish the limited expressive resources of the lexicon and the greater combinatorial expressive power of the language as a whole. This gives us a logic-based account of compositionality for the Boolean fragment of the language. (shrink)

According to the Maxim of Quality, rational agents tend to speak honestly. Due to the influence of Grice, a connection between linguistic rationality and honesty is often taken for granted. However, the connection is not obvious: structural rationality in language use does not require honesty, any more than it requires dishonesty. In particular, Quality does not follow from the Cooperative Principle and structural rationality. But then what is honest rational speech? I propose to move the discussion in the context of (...) Stalnaker's theory of assertion. From this perspective, although there is no most rational way to behave, Quality follows from the structure of Stalnakerian conversations if interlocutors are sensitive to credibility. In this case, honesty is built on the expectation of reciprocity, and cooperativity is an outcome and not a precondition of rational communication. A benefit of my discussion is that the account of linguistic rationality falls under the more general view of interactive rationality familiar from theoretical economics. (shrink)

The present work outlines a logical and philosophical conception of propositions in relation to a group of puzzles that arise by quantifying over them: the Russell-Myhill paradox, the Prior-Kaplan paradox, and Prior's Theorem. I begin by motivating an interpretation of Russell-Myhill as depending on aboutness, which constrains the notion of propositional identity. I discuss two formalizations of of the paradox, showing that it does not depend on the syntax of propositional variables. I then extend to propositions a modal predicative response (...) to the paradoxes articulated by an abstraction principle for propositions. On this conception, propositions are “shadows” of the sentences that express them. Modal operators are used to uncover the implicit relation of dependence that characterizes propositions that are about propositions. The benefits of this approach are shown by application to other intensional puzzles. The resulting view is an alternative to the plenitudinous metaphysics of impredicative comprehension principles. (shrink)

Natural language contains simple lexical items for some but not all Boolean operators. English, for example, contains conjunction and, disjunction or, negated disjunction nor, but no word to express negated conjunction *nand nor any other Boolean connective. Natural language grammar can be described by a logic that expresses what the lexicon can express by its primitives, and the rest compositionally. Such logic for propositional connectives is described here as a bilateral extension of update semantics. The basic intuition is that a (...) context can be updated by assertion or by rejection, and by one or multiple propositions at once. These distinctions suffice to characterize the logic of the lexicon. (shrink)

ABSTRACTTwo-dimensional accounts of speech and thought make use of so-called ‘diagonal’ propositions. If diagonals are indeed propositions, they can be negated: an ‘anti-diagonal’ is the negation o...

The ability to express negation in language may have been the result of an adaptive process. However, there are different accounts of adaptation in linguistics, and more than one of them may describe the case of negation. In this paper, I distinguish different versions of the claim that negation is adaptive and defend a proposal, based on recent work by Steinert-Threlkeld (2016) and Incurvati and Sbardolini (2021), on which negation is an indirect adaptation.

Communication facilitates coordination, but coordination might fail if there's too much uncertainty. I discuss a scenario in which vagueness-driven uncertainty undermines the possibility of publicly sharing a belief. I then show that asserting an epistemic modal sentence, 'Might p', can reveal the speaker's uncertainty, and that this may improve the chances of coordination despite the lack of a common epistemic ground. This provides a game-theoretic rationale for epistemic modality. The account draws on a standard relational semantics for epistemic modality, Stalnaker's (...) theory of assertion as informative update, and a Bayesian framework for reasoning under uncertainty. (shrink)

Why do we use epistemic modals like 'might'? According to Factualism, the function of 'might' is to exchange information about state-of-affairs in the modal universe. As an alternative to Factualism, this paper offers a game-theoretic rationale for epistemic possibility operators in a Bayesian setting. The background picture is one whereby communication facilitates coordination, but coordination could fail if there's too much uncertainty, since the players' ability to share a belief is undermined. However, 'might' and related expressions can be used to (...) reveal one's uncertainty, and exploit this to coordinate despite the lack of a common epistemic ground. The final result is a way to articulate a non-Factualist view of epistemic possibility modals that builds on their standard semantics. (shrink)

Reference may be fixed by stipulation through a speech act, just like bets and marriages. An utterance of _Let n refer to an/the F_ is a speech act by means of which, if successful, a speaker institutes a practice of referring, and a hearer coordinates by choosing a referent from the domain of discourse. We articulate a metasemantics for this view. On our view, the interlocutors can select a referent randomly, if necessary, motivated by the incentive to coordinate on the (...) use of a name. Moreover, we argue that reference fixed by a performative speech act is ‘thin’, or ‘undemanding’. Finally, we defend the thesis that co-reference might not determinately obtain despite reference being fixed. Performative reference makes sense of ordinary speakers’ practices, who appear to be very liberal and unimpressed by skepticism toward causally inert or epistemically indiscernible objects. (shrink)

There is an apparent dilemma for hierarchical accounts of propositions, raised by Bruno Whittle : either such accounts do not offer adequate treatment of connectives and quantifiers, or they eviscerate the logic. I discuss what a plausible hierarchical conception of propositions might amount to, and show that on that conception, Whittle’s dilemma is not compelling. Thus, there are good reasons why proponents of hierarchical accounts of propositions did not see the difficulty Whittle raises.

The three-yearly conference of Italian Society for Logic and Philosophy of Science (SILFS) has taken place in Bergamo, the 15th, 16th and 17th December 2010. The charming venue has been the former convent of Sant’Agostino, nowadays University of Bergamo. The conference program has been structured distinguishing plenary and parallel sessions: the first ones were 40 minutes long and designed for international guests: S. Abramsky from the Wolfson College of Oxford, A. Hagar from Indiana University, P. Janich from Philipps Universitaet of (...) Marburg and S. Okasha from University of Bristol. The complete program of the conference can be downloaded here: . We followed all the plenary sessions, and the first part of our report concerns them. There is just the exception of professor S. Psillos’ talk, which was indeed programmed, but didn’t take place due to greek unrest of the last December. The second part of our report concers the parallel sessions, that were 20 minutes long and designed for concurrent talks split between subject areas. We will keep this division into areas in our report and we chose four talks per area. However, it must be said that we had not watch the parallel sessions completely, since their being simoultaneous. This means that our review of the conference will be perspective, both because of subjective standpoint and because of the mentioned limitation. Still we hope we can offer a quite complete picture of the three-days conference, as we hope this overview may be considered as a general review of it. Just a few words must be still said to introduce to our review. The structure of each review will consists in a presentation of the talk’s author(s) (which we faithfully copy hereinafter) followed by a brief remark by us. Since many compliments could be surely done to the SILFS’ organization and to the University of Bergamo, an overall effect seems hard to be drawn, because of some arising perplexities. Although these are just our shared impressions about the conference, we think they must be remembered. One could note outward that the conference have had three official languages: English, French and Italian. Apparently, this is something that has not been justified since French has been useless and Italian has often prevented the comprehension by foreigner attendance. Many defections have taken place, something that could be said about the conformity with the program (in spite of the high number of speeches). Of course these defections have been caused by different reasons, but they become an indication of lack of professionalism as the number grows. Coming to an estimation of the inner issues, first we are seriously puzzled about the selection criterion (if any) which the SILFS has chosen the invited speakers with. One can notice that excellent talks have been put together to shallow speech without substantial scientific commitment. One has to keep in mind that who is just worthless, much lowers the general level. The topics have been various, although many were historical reconstruction and the "historiographic" approach in the study of Philosophy of Science seems therefore prevailing. Those talks whose subject was Logic and its applications, have been the highest-quality ones, by the fact that they were close to contemporary researches. More specifically, we would like to quote those concerning Quantum Computation and Logic of Quantum Mechanics. Talks of Philosophy of Biology and Cognitive Science were first-rate works, too, having showed high proficiency, though even specialistic topics were often technically handled, to the detriment of laymen (as us). (shrink)