Gillian Russell

Take a correct sequent of formal logic, perhaps a simple logical truth, like the law of excluded middle, or something with premises, like disjunctive syllogism, but basically a claim of the form \.Γ can be empty. If you don’t like my examples, feel free to choose your own, everything I have to say should apply to those as well. Such a sequent attributes the properties of logical truth or logical consequence to a schematic sentence or argument. This paper aims to answer the question of how beliefs in such attributions are justified, on both its descriptive and normative interpretations; I aim to say when we generally take ourselves to be justified in forming such beliefs, and to make it plausible that beliefs formed this way really are justified.We can ask such questions about many domains but there are special difficulties for answering them in logic. Some of the difficulties stem from the fact that logic is thought t..

Could it ever be right to say that a language---as opposed to a speaker of the language---makes, or presupposes or somehow commits itself to certain claims? Such as that certain kinds of objects exist, or that things are a certain way? It can be tempting to think not, to think that languages are just the neutral media through which speakers make claims. Yet certain, surprisingly diverse, phenomena---analyticity, racial epithets, object-involving direct reference, arithmetic, and semantic paradoxes like the Liar---have pushed philosophers towards views according to which languages can have presuppositions or commitments of their own---to things like the existence of numbers, the marital status of bachelors, the existence of water, and even to contradictions or morally abhorrent views. In this paper I want to present some recent data from linguistics that supports a less commonly discussed, and rather surprising version of this idea: namely that English presupposes the existence of locations or places. In section one I do some work to clarify what this claim could possibly mean by identifying some central ways in which languages have been thought to presuppose various things about the world. In section two I present the core of the linguistic data and theory from the work of Susan Rothstein. In section three I compare it to some older work by David Kaplan, arguing that the significance of the new results is greater for the issue at hand, and then in the final section I examine the philosophical significance of this work. One might attempt to draw quite impressive conclusions: such as that the existence of space is analytic, and hence a priori. I will argue that such a conclusion here would be over hasty, and that what we really have is just a surprising fact about our not-so-neutral natural language

Deductive Logic is an introductory textbook in formal logic. The book is divided into four parts covering (i) truth-functional logic, (ii) monadic quantifi- cation, (iii) polyadic quantification and (iv) names and identity, and there are exercises for all these topics at the end of the book. In the truth-functional logic part, the reader learns to produce paraphrases of English statements and arguments in logical notation (this subsection is called “analysis”), then about the semantic properties of such paraphrased statements and arguments, such as satisfiability, implication and equivalence (“logical assessment”) and finally (“reflection”) there is an axiomatic proof method and some important extras such as disjunctive normal form and expressive adequacy. Parts two and three mirror this analysis/assessment/reflection structure for monadic and polyadic quantification, though this time the proof system is a natural deduction one, and part three contains a completeness proof for that system. The fourth part of the book introduces names, the identity predicate and descriptions and examines the additional expressive power which these provide.

This paper investigates, formulates and proves an indexical barrier theorem, according to which sets of non-indexical sentences do not entail (except under specified special circumstances) indexical sentences. It surveys the usual difficulties for this kind of project, as well some that are specific to the case of indexicals, and adapts the strategy of Restall and Russell's "Barriers to Implication" to overcome these. At the end of the paper a reverse barrier theorem is also proved, according to which an indexical sentence will not, except under specified circumstances, entail a non-indexical one

Machine generated contents note: -- Series Editors' PrefaceAcknowledgementsNotes on ContributorsHow Things Are Elsewhere; W. Schwarz Information Change and First-Order Dynamic Logic; B.Kooi Interpreting and Applying Proof Theories for Modal Logic; F.Poggiolesi & G.Restall The Logic(s) of Modal Knowledge; D.Cohnitz On Probabilistically Closed Languages; H.Leitgeb Dogmatism, Probability and Logical Uncertainty; B.Weatherson & D.Jehle Skepticism about Reasoning; S.Roush, K.Allen & I.HerbertLessons in Philosophy of Logic from Medieval Obligations; C.D.Novaes How to Rule Out Things with Words: Strong Paraconsistency and the Algebra of Exclusion; F.Berto Lessons from the Logic of Demonstratives; G.RussellThe Multitude View on Logic; M.Eklund Index.

Recent work on analyticity distinguishes two kinds, metaphysical and epistemic. This paper argues that the distinction allows for a new view in the philosophy of logic according to which the claims of logic are metaphysically analytic and have distinctive modal profiles, even though their epistemology is holist and in many ways rather Quinean. It is argued that such a view combines some of the more attractive aspects of the Carnapian and Quinean approaches to logic, whilst avoiding some famous problems