Jared Warren

A historically popular response to the liar paradox (“this sentence is false”) is to say that the liar sentence is meaningless (or semantically defective, or malfunctions, or…). Unfortunately, like all other supposed solutions to the liar, this approach faces a revenge challenge. Consider the revenge liar sentence, “this sentence is either meaningless or false”. If it is true, then it is either meaningless or false, so not true. And if it is not true, then it can’t be either meaningless or false, so it must be true. Either way, we are back in a paradox. This paper provides a detailed and exhaustive discussion of the options for responding to revenge on behalf of “meaningless” theories. Though I attempt to discuss all of the options fairly, I will ultimately opt for one specific response and discuss some of its challenges. Various technical and logical matters will be discussed throughout the paper, but my focus will be philosophical, throughout. My overall conclusion is that the “meaningless” strategy is at least as well off in the face of revenge as any other approach to the liar and related paradoxes.

Neural decoding studies seem to show that the “private” experiences of others are more accessible than philosophers have traditionally believed. While these studies have many limitations, they do demonstrate that by capturing patterns in brain activity, we can discover a great deal about what a subject is experiencing. We present a thought experiment about a super-decoder — the Atlantis machine — and argue that given plausible assumptions, an Atlantis machine could one day be built. On the basis of this argument, we then argue for the rejection of robust notions of consciousness, which have generated numerous puzzles, including puzzles about the possibility of philosophical zombies. In light of the Atlantis machine, it can be seen that robust notions of consciousness do not earn their explanatory or descriptive keep. More modest concepts of consciousness are sufficient to account for all phenomena — in both senses of the term. This kind of antirobustness about consciousness is a deflationary approach to conscious experience that differs in important ways from illusionist approaches.

Talk of ”mental representations” is ubiquitous in the philosophy of mind, psychology, and cognitive science. A slogan common to many different approaches says that representations ”stand in for” the things they represent. This slogan also attaches to most talk of "internal models" in cognitive science. We argue that this slogan is either false or uninformative. We then offer a new slogan that aims to do better. The new slogan ties the role of representations to the cognitive role played by the deliverances of perception. After clarifying the new slogan and warding off some misunderstandings, we discuss how the new slogan still captures the seed of truth in the old, point to some specific misunderstandings that can be avoided, and then suggest some ways that the new slogan is useful in the project of giving a satisfying philosophical theory of representation.

Once upon a time, logical conventionalism was the most popular philosophical theory of logic. It was heavily favored by empiricists, logical positivists, and naturalists. According to logical conventionalism, linguistic conventions explain logical truth, validity, and modality. And conventions themselves are merely syntactic rules of language use, including inference rules. Logical conventionalism promised to eliminate mystery from the philosophy of logic by showing that both the metaphysics and epistemology of logic fit into a scientific picture of reality. For naturalists of all stripes, this was paradise. Alas, paradise was lost. By the end of the twentieth century, logical conventionalism had been almost universally abandoned. But more recently, it has been revitalized. This chapter provides an overview of logical conventionalism and its history, clears away misunderstandings, and briefly responds to both the canonical objections to conventionalism (from Quine, Dummett, Boghossian, and many others) as well as new objections (from Field and Golan). From paradise lost, to paradise regained: logical conventionalism is back.

We face reality presented with the data of conscious experience and nothing else. The project of early modern philosophy was to build a complete theory of the world from this starting point, with no cheating. Crucial to this starting point is the data of conscious sensory experience – sense data. Attempts to avoid this project often argue that the very idea of sense data is confused. But the sense-data way of talking, the sense-data language, can be freed from every blemish using ideas from contemporary metaontology. We can adopt a sense-data framework that vindicates the traditional claims of sense-data theories and leads to plausible theories of perception and color. We can, we should, and in a sense, we must. Yet when we do, we face the traditional problem of external world skepticism, head-on. The real challenge of skepticism is forced upon us; it cannot honestly be avoided using externalist tricks, burden of proof shifting, or other razzle dazzle. But the challenge can be met: we are rational to posit the external world as the best explanation of the many synchronic and diachronic patterns over our sense-data. This paper argues for all of these points and ends with a plea for analytic empiricism – a traditional sense-data version of empiricism that uses all of the tools of analytic philosophy while avoiding the more questionable doctrines of the Vienna Circle (phenomenalism, verificationism). Analytic empiricism is our last best hope for completing the great philosophical project of early modern philosophy.

If we want to retain classical logic and standard syntax in light of the liar, we are forced to restrict the T-schema. The traditional philosophical justification for this is sentential – liar sentences somehow malfunction. But the standard formal way of implementing this is conditional, our T-sentences tell us that if “p” does not malfunction, then “p” is true if and only if p. Recently Bacon and others have pointed out that conditional T-restrictions like this flirt with incoherence. If we want to keep the “malfunction” motivation, our only other option is to non-conditionally restrict the T-schema, but Field and others have given powerful philosophical and technical arguments against this kind of approach. Here I argue that if we really take the philosophical motivation for restricting T-sentences seriously, we can explain why conditional restrictions fail, answer Field's argument, and reason in a coherent way about truth using a non-conditional restriction strategy. This cracks the door open for a fully classical response to the liar and related paradoxes. In closing, I argue that, when properly understood, this kind of “restriction” is not really a restriction at all. If this is right, then the holy grail of liar studies (classical logic, naïve truth, and standard syntax) may yet be attainable. (Note for readers: when this paper was first put online, the typesetters had changed some instances of corners to brackets, leading to confusion. The paper has now been corrected online by PPR, so please make sure you have the corrected version before reading or citing.)

The paper presents a comprehensive solution to the new riddle of induction. Gruesome induction is blocked because “grue” is not independent of our sampling and observation methods. Before presenting my theory, I critically survey previous versions of what I call the “independence strategy”, tracing the strategy to three different papers from the 1970s by (respectively) Wilkerson, Moreland, and Jackson. Next I critically examine recent approaches by Okasha, Godfrey-Smith, Schramm, and Freitag. All of these approaches have their virtues, but none of them rules out every problem case. Nor do any of them alone explain exactly what goes wrong in all types of gruesome reasoning. My account aims to do both. Learning lessons from my criticisms of previous theories, I argue that there are several crucial types of independence. All of them are needed to rule out every problem case. I close by suggesting that the independence solution can also be adopted by proponents of other approaches—Bayesians, fans of natural kinds, and pragmatists.

In the last 35 years many philosophers have appealed to reference magnetism to explain how it is that we mean what we mean. The idea is that it is a constitutive principle of metasemantics that the interpretation that assigns the more natural meanings is correct, ceteris paribus. Among other things, magnetism has been used to answer the challenges of grue and quus, Quine’s indeterminacy of translation argument, and Putnam’s model-theoretic argument against realism. Critics of magnetism have usually objected to the base notion of naturalness. Here I assume naturalness for the sake of argument, but argue that even still, reference magnetism should be rejected. The supposed force of reference magnetism is arbitrarily weak, and the best explanation of this is that it simply does not exist.

What is the role of imagination in a priori knowledge? Here I provide a partial answer, arguing that imagination can be used to shed light on which experiences merely enable knowledge, versus which are evidential. I reach this partial answer by considering in detail Timothy’s Williamson’s recent argument that the a priori/a posteriori distinction is insignificant. There are replies to the argument by Boghossian and Casullo that might work on their own terms, but my reply examines the assumptions that Williamson makes about the role of imagination in knowledge generation. I show that Williamson’s argument does not account for important distinctions from recent discussions of imaginative content. When these distinctions are not ignored, we can see that Williamson’s argument attributes a subject knowledge on the basis of a faulty application of universal generalization. I close by connecting my positive account of the role of imagination in the a priori to a debate about the role of memory in the a priori that played out 25 years ago.

In the mid twentieth century, logical positivists and many other philosophers endorsed a simple equation: something was necessary just in case it was analytic just in case it was a priori. Kripke’s examples of a posteriori necessary truths showed that the simple equation is false. But while positivist-style inferentialist approaches to logic and mathematics remain popular, there is no inferentialist account of necessity a posteriori. I give such an account. This sounds like an anti-Kripkean project, but it is not. Some of Kripke’s remarks even suggest this kind of approach. This inferentialist approach reinstates neither the simple equation nor pure conventionalism about necessity a posteriori. But it does lead to something near enough, a type of impure conventionalism. In recent years, metaphysically heavyweight approaches to modality have been popular, while other approaches have lagged behind. The inferentialist, impure conventionalist theory of necessity I describe aims to provide a metaphysically lightweight option in modal metaphysics.

The distinction between the a priori and the a posteriori is an old and influential one. But both the distinction itself and the crucial notion of a priori knowledge face powerful philosophical challenges. Many philosophers worry that accepting the a priori is tantamount to accepting epistemic magic. In contrast, this Element argues that the a priori can be formulated clearly, made respectable, and used to do important epistemological work. The author's conception of the a priori and its role falls short of what some historical proponents of the notion may have hoped for, but it allows us to accept and use the notion without abandoning either naturalism or empiricism, broadly understood. This Element argues that we can accept and use the a priori without magic.

Inferences are familiar movements of thought, but despite important recent work on the topic, we do not yet have a fully satisfying theory of inference. Here I provide a functionalist theory of inference. I argue that the functionalist framework allows us the flexibility to meet various demands on a theory of inference that have been proposed (such as that it must explain inferential Moorean phenomena and epistemological ‘taking’). While also allowing us to compare, contrast, adapt, and combine features of extant theories of inference into one unified theory. In fleshing out the inference role, I also criticize the common assumption that inference requires rule-following.

Daniel Dennett’s Consciousness Explained is probably the most widely read book about consciousness ever written by a philosopher. Despite this, the book has had a surprisingly small influence on how most philosophers of mind view consciousness. This might be because many philosophers badly misunderstand the book. They claim it does not even attempt to explain consciousness, but instead denies its very existence. Outside of philosophy the book has had more influence, but is saddled by the same misunderstanding. Now, 30 years after publication, Consciousness Explained deserves reconsideration from anyone interested in consciousness. Here I make a case for this. To start, I will clear up the central misunderstanding of the book. With that done, I will explain and update Dennett’s tantalizing approach to consciousness and the mind. The result brings us very, very close to explaining consciousness. Or so I will argue.

Quantifier variance holds that different languages can have unrestricted quantifier expressions that differ in meaning, where an expression is a “quantifier” just in case it plays the right inferential role. Several critics argued that J.H. Harris’s “collapse” argument refutes variance by showing that identity of inferential role is incompatible with meaning variance. This standard, syntactic collapse argument has generated several responses. More recently, Cian Dorr proved semantic collapse theorems to generate a semantic collapse argument against variance. The argument is significantly different from standard collapse, so it requires a new response. Here I clarify and analyze the semantic collapse argument, and explain how variantists can and should respond to it. The paper also includes an appendix showing the difficulties of positing identity variance without quantifier variance. The argument in the appendix has yet to appear in print, but is familiar to specialists.

Several recent epistemologists have used understanding-assent links in theories of a priori knowledge and justification, but Williamson influentially argued against the existence of such links. Here I (1) clarify the nature of understanding-assent links and their role in epistemology; (2) clarify and clearly formulate Williamson’s arguments against their existence; (3) argue that Williamson has failed to successfully establish his conclusion; and (4) rebut Williamson’s claim that accepting understanding-assent links amounts to a form of dogmatism.

In many ontological debates there is a familiar challenge. Consider a debate over X s. The “small” or anti-X side tries to show that they can paraphrase the pro-X or “big” side’s claims without any loss of expressive power. Typically though, when the big side adds whatever resources the small side used in their paraphrase, the symmetry breaks down. The big side plus small’s resources is a more expressively powerful and thus more theoretically fruitful theory. In this paper, I show that there is a very general solution to this problem, for the small side. Assuming the resources of set theory, small can successfully paraphrase big. This result depends on a theorem about models of set theory with urelements. After proving this theorem, I discuss some of its philosophical ramifications.

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge.

Our relationship to the infinite is controversial. But it is widely agreed that our powers of reasoning are finite. I disagree with this consensus; I think that we can, and perhaps do, engage in infinite reasoning. Many think it is just obvious that we can't reason infinitely. This is mistaken. Infinite reasoning does not require constructing infinitely long proofs, nor would it gift us with non-recursive mental powers. To reason infinitely we only need an ability to perform infinite inferences. I argue that we have this ability. My argument looks to our best current theories of inference and considers examples of apparent infinite reasoning. My position is controversial, but if I'm right, our theories of truth, mathematics, and beyond could be transformed. And even if I'm wrong, a more careful consideration of infinite reasoning can only deepen our understanding of thinking and reasoning. (Note for readers: the paper's brief discussion of uniform reflection and omega inconsistency is misleading. The imagined interlocutor's argument makes an assumption about the PA-provability of provability generalizations that, while true for the Godel sentence's instances, is unjustified, in general. This means my position is stronger against this objection than the paper suggests, since omega inconsistent theories are not automatically inconsistent with their uniform reflection principles, you also need to assume the arithmetically true Pi-2 sentences.)

The standard account of ontological commitment is quantificational. There are many old and well-chewed-over challenges to the account, but recently Kit Fine added a new challenge. Fine claimed that the ‘‘quantificational account gets the basic logic of ontological commitment wrong’’ and offered an alternative account that used an existence predicate. While Fine’s argument does point to a real lacuna in the standard approach, I show that his own account also gets ‘‘the basic logic of ontological commitment wrong’’. In response, I offer a full quantificational account, using the resources of plural logic, and argue that it leads to a complete theory of natural language ontological commitment.

This paper discusses the relevance of supertask computation for the determinacy of arithmetic. Recent work in the philosophy of physics has made plausible the possibility of supertask computers, capable of running through infinitely many individual computations in a finite time. A natural thought is that, if supertask computers are possible, this implies that arithmetical truth is determinate. In this paper we argue, via a careful analysis of putative arguments from supertask computations to determinacy, that this natural thought is mistaken: supertasks are of no help in explaining arithmetical determinacy.

In the work of both Matti Eklund and John Hawthorne there is an influential semantic argument for a maximally expansive ontology that is thought to undermine even modest forms of quantifier variance. The crucial premise of the argument holds that it is impossible for an ontologically "smaller" language to give a Tarskian semantics for an ontologically "bigger" language. After explaining the Eklund-Hawthorne argument (in section I), we show this crucial premise to be mistaken (in section II) by developing a Tarskian semantics for a mereological universalist language within a mereological nihilist language (a case which we, and Eklund and Hawthorne, take as representative). After developing this semantics we step back (in section III) to discuss the philosophical motivations behind the Eklund- Hawthorne argument’s demand for a semantics. We ultimately conclude that quantifier variantists can meet any demand for a semantics that might reasonably be imposed upon them.

Unrestricted inferentialism holds both that any collection of inference rules can determine a meaning for an expression and meaning constituting rules are automatically valid. Prior's infamous tonk connective refuted unrestricted inferentialism, or so it is universally thought. This paper argues against this consensus. I start by formulating the metasemantic theses of inferentialism with more care than they have hitherto received; I then consider a tonk language — Tonklish — and argue that the unrestricted inferentialist's treatment of this language is only problematic if it is mistakenly assumed that Tonklish can be homophonically translated into English. Next, I discuss the proper, non-homophonic, translation of Tonklish into English, rebut various objections, and consider several variants of Tonklish. The paper closes by highlighting the philosophical advantages that unrestricted inferentialism has over its competitors once the terrors of tonk have been tamed.

Rudolf Carnap famously distinguished between the external meanings that existence questions have when asked by philosophers and the internal meanings they have when asked by non-philosophers. Carnap’s overall position involved various controversial commitments, but relatively uncontroversial interpretative principles also lead to a Carnap-style distinction between internal and external questions. In section 1 of this paper I offer arguments for such a distinction in several particular cases; in section 2 I defend my arguments from numerous objections and motivate them by using points drawn from the general theory of interpretation; and in section 3 I discuss the meanings of external questions, ultimately arguing that they are best understood as involving primitive metaphysical notions, and that when so understood, it is natural to adopt a general error theory about philosophical ontology.

Theodore Sider’s recent book, “Writing the Book of the World”, employs a primitive notion of metaphysical structure in order to make sense of substantive metaphysics. But Sider and others who employ metaphysical primitives face serious epistemological challenges. In the first section I develop a specific form of this challenge for Sider’s own proposed epistemology for structure; the second section develops a general reliability challenge for Sider’s theory; and the third and final section argues for the rejection of Siderean structure in the course of answering a transcendental argument against such rejection.

Conventionalism about mathematics claims that mathematical truths are true by linguistic convention. This is often spelled out by appealing to facts concerning rules of inference and formal systems, but this leads to a problem: since the incompleteness theorems we’ve known that syntactic notions can be expressed using arithmetical sentences. There is serious prima facie tension here: how can mathematics be a matter of convention and syntax a matter of fact given the arithmetization of syntax? This challenge has been pressed in the literature by Hilary Putnam and Peter Koellner. In this paper I sketch a conventionalist theory of mathematics, show that this conventionalist theory can meet the challenge just raised , and clarify the type of mathematical pluralism endorsed by the conventionalist by introducing the notion of a semantic counterpart. The paper’s aim is an improved understanding of conventionalism, pluralism, and the relationship between them.

Recently a number of works in meta-ontology have used a variant of J.H. Harris's collapse argument in the philosophy of logic as an argument against Eli Hirsch's quantifier variance. There have been several responses to the argument in the literature, but none of them have identified the central failing of the argument, viz., the argument has two readings: one on which it is sound but doesn't refute quantifier variance and another on which it is unsound. The central lesson I draw is that arguments against quantifier variance must pay strict attention to issues of translation and interpretation. The paper also has a substantial appendix in which I prove the equivalence of plural mereological nihilism and standard first-order atomistic mereology; results of this kind are often appealed to in the literature on quantifier variance but without many details on the nature or proof of the result.

An influential argument against the possibility of truth by linguistic convention holds that while conventions can determine which proposition a given sentence expresses, they (conventions) are powerless to make propositions true or false. This argument has been offered in the literature by Lewy, Yablo, Boghossian, Sider and others. But despite its influence and prima facie plausibility, the argument: (i) equivocates between different senses of “making true”; (ii) mistakenly assumes hyperintensional contexts are intensional; and (iii) relies upon an implausible vision of the way that language works.