Gillian Russell

Anti-exceptionalists about formal logic think that logic is continuous with the sciences. Many philosophers of science think that there is feminist science. Putting these together: can anti-exceptionalism make space for feminist logic? The answer depends on the details of the ways logic is like science and the ways science can be feminist. This paper wades into these details, examines five different approaches, and ultimately argues that anti-exceptionalism makes space for feminist logic in several different ways.

Nancy Cartwright's 1983 book How the Laws of Physics Lie argued that theories of physics often make use of idealisations, and that as a result many of these theories were not true. The present paper looks at idealisation in logic and argues that, at least sometimes, the laws of logic fail to be true. That might be taken as a kind of skepticism, but I argue rather that idealisation is a legitimate tool in logic, just as in physics, and recognising this frees logicians up to use false laws where these are helpful.

A barrier to entailment exists if you can't get conclusions of a certain kind from premises of another. One of the most famous barriers in philosophy is Hume's Law, which says that you can't get normative conclusions from descriptive premises, or in slogan form: you can't get an ought from an is. This barrier is highly controversial, and many famous counterexamples were proposed in the last century. But there are other barriers which function almost as philosophical platitudes: no Universal conclusions from Particular premises, no Future conclusions from premises about the Past, and no claims that attribute Necessity from premises that merely tell us how things happen to be in the Actual world. Barriers to Entailment proposes a unified logical account of five barriers that have played important roles in philosophy, in the process showing how to diagnose proposed counterexamples and arguing that the case for Hume's Law is as strong as that for the platitudinous barriers. The first two parts of the book employ techniques from formal logic, but present them in an accessible way, suitable for any reader with some background in first-order model theory (of the kind that might be taught in a first class in logic). Gillian Russell introduces tense, modal, indexical, and deontic formal logics, but always avoids unneeded complexity. Each barrier is connected to broader philosophical topics: universality, time, necessity, context-sensitivity, and normativity. Russell brings out under-recognised connections between the domains and lays the groundwork for further work at the intersections. The last part of the book transposes the formal work to informal barrier theses in the philosophy of language, in the process doing new work on the concept of logical consequence, and providing new responses to proposed informal counterexamples to Hume's Law which employ hard-to-formalise tools from natural language, such as speech acts and thick normative expressions.

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.

Logical pluralism is the view that there is more than one logic. Logical normativism is the view that logic is normative. These positions have often been assumed to go hand-in-hand, but we show that one can be a logical pluralist without being a logical normativist. We begin by arguing directly against logical normativism. Then we reformulate one popular version of pluralism—due to Beall and Restall—to avoid a normativist commitment. We give three non-normativist pluralist views, the most promising of which depends not on logic’s normativity but on epistemic goals.

This paper looks at what David Kaplan's work on indexicals can teach us about logic and the philosophy of logic, and also what Kaplan's logic (i.e. the Logic of Demonstratives) can teach us about indexicals. The lessons are i) that logical consequence is not necessary truth-preservation, ii) that that the linguistic doctrine of necessary truth (also called conventionalism about modality) fails, and iii) that there is a kind of barrier to entailment between non-context-sensitive and context-sensitive claims.

This paper is about the putative theoretical virtue of strength, as it might be used in abductive arguments to the correct logic in the epistemology of logic. It argues for three theses. The first is that the well-defined property of logical strength is neither a virtue nor a vice, so that logically weaker theories are not—all other things being equal—worse or better theories than logically stronger ones. The second thesis is that logical strength does not entail the looser characteristic of scientific strength, and the third is that many modern logics are on a par—or can be made to be on a par—with respect to scientific strength.

Sider offers a new take on a linguistic account of necessity. In this paper, I assess his view’s vulnerability to objections made against more traditional linguistic accounts, especially an argument I call the “indexical problem.” I conclude that the indexical problem has no force against Sider’s approach because the view is able to attribute modal properties directly to propositions, rather than indirectly via analytic sentences that express them. However, Sider also argues that traditional linguistic accounts fail because of two well-known problems, and I argue that the same two problems undermine his own account.

When I was eleven, my form teacher, Mr Howard, showed some of my class how to punch. We were waiting for the rest of the class to finish changing after gym, and he took a stance that I would now call shizentai yoi and snapped his right fist forward into a head-level straight punch, pulling his left back to his side at the same time. Then he punched with his left, pulling back on his right. We all lined up in our ties and sensible shoes (this was England) and copied him—left, right, left, right—and afterwards he told us that if we practised in the air with sufficient devotion for three years, then we would be able to use our punches to kill a bull with one blow. I worshipped Mr Howard (though I would sooner have died than told him that) and so, as a skinny, eleven-year-old girl, I came to believe that if I practised, I would be able to kill a bull with one blow by the time I was fourteen. This essay is about epistemic viciousness in the martial arts, and this story is illustrates just that. Though the word ‘viciousness’ normally suggests deliberate cruelty and violence, I will be using it here with the more old-fashioned meaning, possessing of vices. Vices (such as avarice, alcoholism and nail-biting) are common, and most of us struggle with a few, but ‘epistemic’ means ‘having to do with knowledge and the justification of belief’ and so epistemic viciousness is the possession of vices that make one bad at acquiring true beliefs, or give one a tendency to form false ones. My eleven-year-old self possessed the epistemic vice of gullibility and hence showed a streak of epistemic viciousness, which led to the formation of a false belief. Other kinds of epistemic vice can lead to us failing to form true beliefs when we ought to. Consider the internet-surfing karate-sensei who stumbles upon an article claiming that chocolate milk is better than water or sports drinks for promoting recovery after strenuous exercise, and describing an experiment using stationary bikes performed at the University of Indiana, purporting to support this claim..

The analytic/synthetic distinction looks simple. It is a distinction between two different kinds of sentence. Synthetic sentences are true in part because of the way the world is, and in part because of what they mean. Analytic sentences - like all bachelors are unmarried and triangles have three sides - are different. They are true in virtue of meaning, so no matter what the world is like, as long as the sentence means what it does, it will be true. -/- This distinction seems powerful because analytic sentences seem to be knowable in a special way. One can know that all bachelors are unmarried, for example, just by thinking about what it means. But many twentieth-century philosophers, with Quine in the lead, argued that there were no analytic sentences, that the idea of analyticity didn't even make sense, and that the analytic/synthetic distinction was therefore an illusion. Others couldn't see how there could fail to be a distinction, however ingenious the arguments of Quine and his supporters. -/- But since the heyday of the debate, things have changed in the philosophy of language. Tools have been refined, confusions cleared up, and most significantly, many philosophers now accept a view of language - semantic externalism - on which it is possible to see how the distinction could fail. One might be tempted to think that ultimately the distinction has fallen for reasons other than those proposed in the original debate. -/- In Truth in Virtue of Meaning, Gillian Russell argues that it hasn't. Using the tools of contemporary philosophy of language, she outlines a view of analytic sentences which is compatible with semantic externalism and defends that view against the old Quinean arguments. She then goes on to draw out the surprising epistemological consequences of her approach.

Is it harder to acquire knowledge about things that really matter to us than it is to acquire knowledge about things we don't much care about? Jason Stanley 2005 argues that whether or not the relational predicate 'knows that' holds between an agent and a proposition can depend on the practical interests of the agent: the more it matters to a person whether p is the case, the more justification is required before she counts as knowing that p. The evidence for Stanley's thesis includes a number of intuitive judgments about examples. In this paper we provide parallel examples for which Stanley's thesis requires unwelcome knowledge-attributions, and argue that this is possible because his thesis conflicts with familiar and plausible principles about knowledge.

My target in this paper is a view that has sometimes been called the ‘ Linguistic Doctrine of Necessary Truth ’ and sometimes ‘Conventionalism about Necessity’. It is the view that necessity is grounded in the meanings of our expressions—meanings which are sometimes identified with the conventions governing those expressions—and that our knowledge of that necessity is based on our knowledge of those meanings or conventions. In its simplest form the view states that a truth, if it is necessary, is necessary because it is analytic. It is widely recognized that this simple version of the view faces a prima facie problem with the existence of the necessary a posteriori. Assuming that all analytic truths are a priori, if there are necessary a posteriori truths then there are necessary synthetic truths—contradicting the view’s claim that all necessary truths are analytic. Contemporary L-DONTers have things to say about the problem, but in this paper I want to suggest that there is a different, more serious, problem which arises from the phenomenon of indexicality, which L-DONTers have not taken account of. Though there are many versions of the problem, a simple one is this. Consider Kaplan’s celebrated sentence

Philosophy of language is the branch of philosophy that examines the nature of meaning, the relationship of language to reality, and the ways in which we use, learn, and understand language. _The Routledge Companion to Philosophy of Language _provides a comprehensive and up-to-date survey of the field, charting its key ideas and movements, and addressing contemporary research and enduring questions in the philosophy of language. Unique to this _Companion _is clear coverage of research from the related disciplines of formal logic and linguistics, and discussion of the applications in metaphysics, epistemology, ethics and philosophy of mind. Organized thematically, the _Companion _is divided into seven sections: Core Topics; Foundations of Semantics; Parts of Speech; Methodology; Logic for Philosophers of Language; Philosophy of Language for the Rest of Philosophy; and Historical Perspectives. Comprised of 70 never-before-published essays from leading scholars--including Sally Haslanger, Jeffrey King, Sally McConnell-Ginet, Rae Langton, Kit Fine, John MacFarlane, Jeff Pelletier, Scott Soames, Jason Stanley, Stephen Stich and Zoltan Gendler Szabo--the _Routledge Companion to Philosophy of Language_ promises to be the most comprehensive and authoritative resource for students and scholars alike.

This paper points out a tension between Agustín Rayo's criteria for singulartermhood and his explicit views on the status of Hybrid Identities, that is, identity statements that use singular terms from two different Systems of Representation, such as "7=Julius Caesar" or more suggestively "I am b" where "b" is a singular term referring to my brain. It argues that non-trivial Hybrid Identities are common and important in philosophy and elsewhere, and it suggests a friendly alternative that involves treating Hybrid Identities on the model of Rayo's "Just Is" statements. The last section of the paper points out that even this friendly alternative has counterintuitive consequences when combined with the metaphysical conventionalism that Rayo finds attractive, when it comes to questions of personal identity over time

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