While the relations between an operation and its residuals play an essential role in substructural logic, a closely related relation between operations is that of conjugation — so closely related that with Boolean negation, the conjugates and residuals of an operation are interdefinable. In this talk extensions of Positive Non-Associative Lambek Calculus including conjugates (and residuals) of fusion are investigated. Some interesting properties of the conjugates are discussed, a proof system is presented, its adequacy questioned, and some further logics with conjugated operations are pondered.
I will be talking about the syntax and semantics of contractual offers. In particular, I will be exploring whether there are any linguistic reasons for modeling contractual offers (as in, “If you do X for me, then I’ll do Y for you.”) as conditional promises, as is often taken to be the case in the legal literature.
Investigations of linguistic meaning crucially rely on truth-value judgments: whether a sentence can truthfully describe a given scenario. On the basis of such judgments, researchers have concluded that young children perform quite differently from adults when it comes to understanding ambiguous utterances with multiple potential meanings. For example, when adults hear “Every horse didn’t jump over the fence,” they entertain two interpretations: either none of the horses jumped or not all of the horses jumped. Children usually only endorse the “none” interpretation, rejecting the utterance in a scenario where only two out of three horses jumped. However, subtle changes to the truth-value judgment task setup make children more adult-like. I summarize key results from the literature on child ambiguity resolution, noting three core variables that affect children’s disambiguation behavior. One of these variables concerns children’s processing ability: how easy it is to access the different grammatical interpretations. The other two variables concern children’s ability to manage the pragmatic context: understanding what the topic of conversation is, and modulating expectations about the world being described. I also highlight the nature of the truth-value judgment task children are being asked to engage in, which I then formally articulate using a cognitive computational model that specifies the role of each of these three variables in providing truth-value judgments. The results suggest that pragmatic factors play a larger role than processing factors in explaining children’s non-adult-like ambiguity resolution behavior, and the computational modeling framework allows us to understand exactly why that’s so. Indeed, by modeling the task itself, we see that the truth-value judgment data typically used to demonstrate children’s difficulty with ambiguity in fact require no disambiguation at all — just the ability to manage the pragmatics of the task.
Claim: Both the directly referential semantics and the more recent anaphoric accounts of 1st and 2nd person indexicals offer a picture of indexicality which is empirically and conceptually inadequate. They fail to capture this fact: Indexicals are essentially perspectival, as reflected in the fact that 1st and 2nd person indexicals are always de se.
Why hasn’t that been evident before?
Here is something important that compositional semantics has taught us: You cannot properly assess the meaning of an expression without considering its use and meaning in embedded contexts. But, as Kaplan drove home, the English 1st and 2nd person pronouns never seem to vary in interpretation in embedded contexts. However, recent work in linguistics has uncovered a wide variety of unrelated languages where the 1st and 2nd person pronouns can be shifted under attitudes. Careful consideration of their shifted meanings offers a new perspective on indexicality. Accordingly, I offer arguments for a de se account of indexicality.
This talk will be an introduction to the ultraproduct construction and the model theoretic notion of saturation, which are two of the themes in Maryanthe Malliaris’s Annual Logic Lecture next week. My goal is to introduce these concepts with some examples and motivation to give anyone interested some familiarity with the key characters in Maryanthe’s story before she arrives. Maryanthe will define these concepts in her talk and will not presuppose any material from my talk.
The framework of strict-tolerant consequence championed by Cobreros, Egré, Ripley and van Rooij provides a novel setting that permits one to have a transparent truth predicate without abandoning classical logic. The semantics for this notion of consequence, due to van Rooij, employs the three-valued strong Kleene matrices. A second framework that has received renewed attention is the collection of weak Kleene matrices, which have frequently appeared in the context of so-called logics of nonsense, making the pairing of these topics a natural avenue for investigation. In this talk, I’ll discuss strict-tolerant consequence on the weak Kleene matrices, its corresponding proof theory, and its interpretation. I’ll also discuss how the resulting notion of consequence bears on several matters in philosophical logic, including the content-theoretic interpretation of bounds consequence, the semantic properties of paradoxical sentences in the Principia Mathematica, and debates concerning the logical analysis of category mistakes.
When speakers utter conflicting moral sentences (“X is wrong”/“X is not wrong”), it seems clear that they disagree. It has often been suggested that the fact that the speakers disagree gives us evidence for a claim about the semantics of the sentences they are uttering. Specifically, it has been suggested that the existence of the disagreement gives us reason to infer that there must be an incompatibility between the contents of these sentences (i.e., that it has to be the case that at least one of them is incorrect). This inference then plays a key role in a now-standard argument against certain theories in moral semantics. In this paper, we introduce new evidence that bears on this debate. We show that there are moral conflict cases in which people are inclined to say both (a) that the two speakers disagree and (b) that it is not the case at least one of them must be saying something incorrect. We then explore how we might understand such disagreements. As a proof of concept, we sketch an account of the concept of disagreement and an independently motivated theory of moral semantics which, together, explain the possibility of such cases.
The recent literature maintains that the behavior of modal expressions motivates a non-truth-conditional account of their meaning, and non-classical account of their underlying logic. The key aspect of interpretation of modal claims is the characteristic dynamic effect they have on the context, and the corresponding dynamic notion of validity captures their seemingly non-classical behavior. While prima facie supported by the puzzling behavior of modals in discourse, I argue that this approach is empirically inadequate. Instead I develop and argue for a dynamic theory of context-change which assigns standard truth-conditional meaning to modal utterances, and a corresponding dynamic notion of validity which preserves classical logic.
Logical pluralism is commonly described as the view that there is more than one correct logic. It has been claimed that, in order for that view to be interesting, there has to be at least a potential for rivalry between the correct logics (e.g., in Field 2009, Priest 2006, Read 2006, Russell 2008). In this talk, I explore how the relevant notions of rivalry and correctness could be combined when relying on a semantic conception of rivalry in terms of disagreement. I first give a brief intuitive characterization of the sort of rivalry in question before reviewing some standard proposals on how to capture it. I argue that none of those proposals aligns well with pluralism. More recent proposals (Shapiro 2014) to adopt the semantic framework used in the debate on context-dependence and disagreement in the philosophy of language seem to do a better job, but ultimately, it remains doubtful whether the semantics of disagreement is able to capture a notion of rivalry suitable for pluralists.
A historical survey of mathematical practice in support of a pragmatic inductive philosophy of mathematics.