The classical rule of Repetition says that if you take any sentence as a premise, and repeat it as a conclusion, you have a valid argument. It's a very basic rule of logic, and many other rules depend on the guarantee that repeating a sentence, or really, any expression, guarantees sameness of referent, or semantic value. However, Repetition fails for token-reflexive expressions. In this paper, I offer three ways that one might replace Repetition, and still keep an interesting notion of (...) validity. Each is a fine way to go for certain purposes, but I argue that one in particular is to be preferred by the semanticist who thinks that there are token-reflexive expressions in natural languages. (shrink)

This paper defends the thesis that counterfactuals are strict conditionals. Its purpose is to show that there is a coherent view according to which counterfactuals are strict conditionals whose antecedent is stated elliptically. Section 1 introduces the view. Section 2 outlines a response to the main argument against the thesis that counterfactuals are strict conditionals. Section 3 compares the view with a proposal due to Aqvist, which may be regarded as its direct predecessor. Sections 4 and 5 explain how the (...) view di ers from the theories of counterfactuals advocated by Stalnaker and Lewis, and from some contextualist strict conditional accounts of counterfactuals that have emerged recently. Finally, section 6 addresses the thorny issue of disjunctive antecedents. (shrink)

Gillian Russell has recently proposed counterexamples to such elementary argument forms as Conjunction Introduction and Identity. These purported counterexamples involve expressions that are sensitive to linguistic context—for example, a sentence which is true when it appears alone but false when embedded in a larger sentence. If they are genuine counterexamples, it looks as though logical nihilism—the view that there are no valid argument forms—might be true. In this paper, I argue that the purported counterexamples are not genuine, on the grounds (...) that they equivocate. Having defused the threat of logical nihilism, I argue that the kind of linguistic context sensitivity at work in Russell’s purported counterexamples, if taken seriously, far from leading to logical nihilism, reveals new, previously undreamt-of valid forms. By way of proof of concept I present a simple logic, Solo-Only Propositional Logic, designed to capture some of them. Along the way, some interesting subtleties about the fallacy of equivocation are revealed. (shrink)

According to the interpretational theory of logical validity (IR), logical validity is preservation of truth in all interpretations compatible with the intended meaning of logical expressions. IR suffers from a seemingly defeating objection, the so-called cardinality problem: any instance of the statement ‘There are n things’ is true under all interpretations, since it can be written down using only logical expressions that are not to be reinterpreted; yet ‘There are n things’ is not logically true. I argue that the cardinality (...) problem is indeed a serious problem for IR, when understood in terms of ‘asymmetry of information’. I then argue that IR can be rehabilitated by making quantifiers context-sensitive: what we do not reinterpret is the Kaplanian character of a quantifier, rather than its content. ‘There are n things’ is false in a context where fewer than n things are relevant, so it is not logically true in IR. I finally discuss some objections and ramifications of my account: I discuss how to make space for the possibility of an explicitly absolutely general quantifier in my framework, how terms can be logical even though context-sensitive, and how to recapture classical logic within my framework. (shrink)

Semanticists often restrict their theories by imposing constraints on the parameters that can be employed for interpreting the expressions of a language. Such constraints are based on non-logical features of actual contexts of utterance, but they often have important effects on issues that do pertain to logic, like analyticity or entailment. For example, Kaplan’s restriction to so-called “proper contexts” was required in order to count “I am here now” as valid. In this paper I argue that constraints of this kind (...) are often posited in an arbitrary and non-consistent way, and that they yield the intended results only at the price of imposing ad hoc principles whose justification could in turn justify further, often undesirable restrictions into the theory. I also introduce a criterion for telling whether such constraints are imposed in a legitimate manner. (shrink)

1. Complex demonstratives (noun phrases of the form ‘that F’) often behave in devious ways which do not fit well with their traditional understanding as devices of direct reference. Namely, there a...

Token-reflexive theories of indexicals – words like ‘I,’ ‘here,’ and ‘today’ – are widely thought to face a problem in account for intuitively valid arguments involving indexicals. Yet all discussions of the problem with which I am familiar focus on particular examples or on particular rules of inference. In this paper, I first state the problem in its full generality, and then argue that two recent attempts to reject the problem fail. Finally, I consider the proposal by García-Carpintero that demonstratives (...) – ‘this’ and ‘that’ – raise the same problem. I argue that while there are important similarities between the logic problem for token-reflexives and the role of demonstratives in logic, recent work on the logic of demonstratives can offer insights into logic that token-reflexive theories cannot. (shrink)

Theories of propositions as sets of truth-supporting circumstances are committed to the thesis that sentences or other representations true in all and only the same circumstances express the same proposition. Theories of propositions as complex, structured entities are not committed to this thesis. As a result, structured propositions can play a role in our theories of language and thought that sets of truth-supporting circumstances cannot play. To illustrate this difference, I sketch a theory of transparent, non-deflationary truth consistent with some (...) theories of structured propositions, but inconsistent with any theory of propositions as sets of truth-supporting circumstances. (shrink)

Building on recent work by Delia Graff Fara and Ora Matushansky on appellative constructions like ‘Mirka called Roger handsome’, I argue that if Millianism about proper names is true, then the quantifier ‘something’ in ‘Mirka called Roger something’ is best understood as a kind of substitutional quantifier. Any adequate semantics for such quantifiers must explain both the logical behavior of ‘Mirka called Roger something’ and the acceptability of ‘so’-anaphora in ‘Mirka called Roger something, and everyone so called is handsome’. Millianism (...) about proper names is inconsistent with such quantifiers being standard non-substitutional second-order quantifiers. But this is not the only option for Millianism: I provide two different propositional semantics for substitutional quantification, each of which is adequate in the sense above, given Millianism. One of these is based on Tobias Rosefeldt’s work on non-nominal quantification, and I identify in what way Rosefeldt’s semantics is substitutional. (shrink)

Theoria, Volume 87, Issue 1, Page 136-151, February 2021.

The standard truth-conditional semantics for substitutional quantification, due to Saul Kripke, does not specify what proposition is expressed by sentences containing the particular substitutional quantifier. In this paper, I propose an alternative semantics for substitutional quantification that does. The key to this semantics is identifying an appropriate propositional function to serve as the content of a bound occurrence of a formula containing a free substitutional variable. I apply this semantics to traditional philosophical reasons for interest in substitutional quantification, namely, theories (...) of truth and ontological commitment. (shrink)

The past decades have seen remarkable progress in the study of substructural logics, be it mathematically or philosophically oriented. This progress has a somewhat perplexing effect: the more subst...

Logical nihilism is the view that the relation of logical consequence is empty: there are counterexamples to any putative logical law. In this paper, I argue that the nihilist threat is illusory. The nihilistic arguments do not work. Moreover, the entire project is based on a misguided interpretation of the generality of logic.

Montague and Kaplan began a revolution in semantics, which promised to explain how a univocal expression could make distinct truth-conditional contributions in its various occurrences. The idea was to treat context as a parameter at which a sentence is semantically evaluated. But the revolution has stalled. One salient problem comes from recurring demonstratives: "He is tall and he is not tall". For the sentence to be true at a context, each occurrence of the demonstrative must make a different truth-conditional contribution. (...) But this difference cannot be accounted for by standard parameter sensitivity. Semanticists, consoled by the thought that this ambiguity would ultimately be needed anyhow to explain anaphora, have been too content to posit massive ambiguities in demonstrative pronouns. This article aims to revived the parameter revolution by showing how to treat demonstrative pronouns as univocal while providing an account of anaphora that doesn't end up re-introducing the ambiguity. (shrink)