This book brings together several directions of work in model theory between the late 1950s and early 1980s.

Bringing together powerful new tools from set theory and the philosophy of language, this book proposes a solution to one of the few unresolved paradoxes from antiquity, the Paradox of the Liar. Treating truth as a property of propositions, not sentences, the authors model two distinct conceptions of propositions: one based on the standard notion used by Bertrand Russell, among others, and the other based on J.L. Austin's work on truth. Comparing these two accounts, the authors show that while the (...) Russellian conception of the relation between sentences, propositions, and truth is crucially flawed in limiting cases, the Austinian perspective has fruitful applications to the analysis of semantic paradox. In the course of their study of a language admitting circular reference and containing its own truth predicate, Barwise and Etchemendy also develop a wide range of model-theoretic techniques--based on a new set-theoretic tool, Peter Aczel's theory of hypersets--that open up new avenues in logical and formal semantics. (shrink)

The present volume collects some of Barwise's papers written since then, those directly concerned with relations among logic, situation theory, and situation semantics. Several papers appear here for the first time.

The chapter explores whether, or to what extent, recent work in experimental philosophy puts pressure on the idea that the concept of causation is ‘egalitarian’. Causal selection – where experimental subjects tend to rate the causal strength of (for example) a norm-violator more strongly than a non-norm-violator – is a well established phenomenon, and is in prima facie tension with an egalitarian conception of causation; it also, indirectly, puts prima facie pressure on the idea that causation is a worldly phenomenon (...) whose obtaining is independent of facts about norms. The chapter explores both the various psychological mechanisms and the broadly pragmatic approaches to explaining causal selection. It argues that the answer to the question whether or not the concept of causation is egalitarian is currently significantly empirically underdetermined, and suggests some avenues for further investigation. (shrink)

This book was first published in 1984, as the revised edition of a 1979 original. The text is composed of studies in a descending sequence from perfect rationality, through imperfect and problematical rationality, to irrationality. Specifically human rationality is characterized by its capacity to relate strategically to the future, in contrast to the myopic 'gradient climbing' of natural selection. There is trenchant analysis of some of the parallels proposed in this connection between the biological and the social sciences. In the (...) chapter on imperfect rationality the crucial notion is that of 'binding oneself', as Ulysses did before setting out to the Sirens, when weakness of will may prevent us from using our capacity for perfect rationality. The second half of the book deals with rational-actor theory, comparing its logical power and success to rival approaches, and with the varieties of irrationality expressed in contradictory beliefs and desires. (shrink)

Logic is a field studied mainly by researchers and students of philosophy, mathematics and computing. Inductive logic seeks to determine the extent to which the premises of an argument entail its conclusion, aiming to provide a theory of how one should reason in the face of uncertainty. It has applications to decision making and artificial intelligence, as well as how scientists should reason when not in possession of the full facts. In this work, Jon Williamson embarks on a quest to (...) find a general, reasonable, applicable inductive logic (GRAIL), all the while examining why pioneers such as Ludwig Wittgenstein and Rudolf Carnap did not entirely succeed in this task. (shrink)

This chapter provides an overview of a range of probabilistic theories of causality, including those of Reichenbach, Good and Suppes, and the contemporary causal net approach. It discusses two key problems for probabilistic accounts: counterexamples to these theories and their failure to account for the relationship between causality and mechanisms. It is argued that to overcome the problems, an epistemic theory of causality is required.

Hyperproof is a system for learning the principles of analytical reasoning and proof construction, consisting of a text and a Macintosh software program. Unlike traditional treatments of first-order logic, Hyperproof combines graphical and sentential information, presenting a set of logical rules for integrating these different forms of information. This strategy allows students to focus on the information content of proofs, rather than the syntactic structure of sentences. Using Hyperproof the student learns to construct proofs of both consequence and nonconsequence using (...) an intuitive proof system that extends the standard set of sentential rules to incorporate information represented graphically. Hyperproof is compatible with various natural-deduction-style proof systems, including the system used in the authors' Language of First-Order Logic. (shrink)

The orthodox view in statistics has it that frequentism and Bayesianism are diametrically opposed—two totally incompatible takes on the problem of statistical inference. This paper argues to the contrary that the two approaches are complementary and need to mesh if probabilistic reasoning is to be carried out correctly.

Practical reasoning requires decision—making in the face of uncertainty. Xenelda has just left to go to work when she hears a burglar alarm. She doesn’t know whether it is hers but remembers that she left a window slightly open. Should she be worried? Her house may not be being burgled, since the wind or a power cut may have set the burglar alarm off, and even if it isn’t her alarm sounding she might conceivably be being burgled. Thus Xenelda can (...) not be certain that her house is being burgled, and the decision that she takes must be based on her degree of certainty, together with the possible outcomes of that decision. (shrink)

Recent work in applied ethics has advanced a raft of arguments regarding individual responsibilities to address collective challenges like climate change or the welfare and environmental impacts of meat production. Frequently, such arguments suggest that individual actors have a responsibility to be more conscientious with their consumption decisions, that they can and should harness the power of the market to bring about a desired outcome. A common response to these arguments, and a challenge in particular to act-consequentialist reasoning, is that (...) it “makes no difference” if one takes conscious consumption action or not – that one is “causally impotent” to change an outcome. In this paper, I break causal impotence objections into three distinct lines of argument and present causal indeterminacy as a third, unexplored variation of much more common causal impotence lines. I suggest that the causal indeterminacy argument presents additional challenges to consequentialist moral theory because it acknowledges that individual actions can have an impact on outcome, but suggests instead that the outcome can neither be known nor secured by the action itself. (shrink)

The EBM+ programme is an attempt to improve the way in which present-day evidence-based medicine (EBM) assesses causal claims: according to EBM+, mechanistic studies should be scrutinised alongside association studies. This paper addresses two worries about EBM+: (i) that it is not feasible in practice, and (ii) that it is too malleable, i.e., its results depend on subjective choices that need to be made in order to implement the procedure. Several responses to these two worries are considered and evaluated. The (...) paper also discusses the question of whether we should have confidence in medical interventions, in the light of Stegenga’s arguments for medical nihilism. (shrink)

This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces. I discuss the ramifications of interpretations of probability and objective Bayesianism for the philosophy of mathematics in general.

A word-by-word human sentence processing complexity metric is presented. This metric formalizes the intuition that comprehenders have more trouble on words contributing larger amounts of information about the syntactic structure of the sentence as a whole. The formalization is in terms of the conditional entropy of grammatical continuations, given the words that have been heard so far. To calculate the predictions of this metric, Wilson and Carroll's (1954) original entropy reduction idea is extended to infinite languages. This is demonstrated with (...) a mildly context-sensitive language that includes relative clauses formed on a variety of grammatical relations across the Accessibility Hierarchy of Keenan and Comrie (1977). Predictions are derived that correlate significantly with repetition accuracy results obtained in a sentence-memory experiment (Keenan & Hawkins, 1987). (shrink)

We may define words or concepts, and we may also, as Aristotle and others have thought, define the things for which words stand and of which concepts are concepts. Definitions of words or concepts may be explicit or implicit, and may seek to report preexisting synonymies, as Quine put it, but they may instead be wholly or partly stipulative. Definition by abstraction, of which Hume’s principle is a much discussed example, seek to define a term-forming operator, such as the number (...) operator, by fixing the truth-conditions of identity-statements featuring terms formed by means of that operator. Such definitions are a species of implicit definition. They are typically at least partly stipulative. Definitions of things, or real definitions, are, by contrast, typically conceived as true or false statements about the nature or essence of their definienda, and so not stipulative. There thus appears to be an obvious and head-on clash between taking Hume’s principle as an implicit and at least partly stipultative definition of the number operator and taking it as a real definition, stating the nature or essence of cardinal numbers. This paper argues that this apparent tension can be resolved, and that resolving it sheds light on part of the epistemology or essence and necessity, showing how some of our knowledge of essence and necessity can be a priori. (shrink)

I investigate two asymmetrical approaches to knowledge of absolute possibility and of necessity--one which treats knowledge of possibility as more fundamental, the other according epistemological priority to necessity. Two necessary conditions for the success of an asymmetrical approach are proposed. I argue that a possibility-based approach seems unable to meet my second condition, but that on certain assumptions--including, pivotally, the assumption that logical and conceptual necessities, while absolute, do not exhaust the class of absolute necessities--a necessity-based approach may be able (...) to do so. (shrink)

Panic buying of toilet rolls in Australia began in early March 2020. This was related to the realisation that the novel coronavirus was spreading across the country. To the general population the impact of the virus was unknown. Gradually the federal government started closing the country’s borders. The panic buying of toilet rolls was not unique to Australia. It happened across all societies that used toilet paper rather than water to clean after defecation and urination. However, research suggests that the (...) panic buying was most extreme in Australia. This article argues that the panic buying was closely linked to everyday notions of Western civilisation. Pedestal toilets and toilet paper are key aspects of civilisation and the fear of the loss of toilet paper is connected to anxiety about social breakdown, the loss of civilisation. This is the fear manifested in the perceived threat posed by the virus. (shrink)

In “Double Vision Two Questions about the Neo-Fregean Programme”, John MacFarlane’s raises two main questions: (1) Why is it so important to neo-Fregeans to treat expressions of the form ‘the number of Fs’ as a species of singular term? What would be lost, if anything, if they were analysed instead as a type of quantifier-phrase, as on Russell’s Theory of Definite Descriptions? and (2) Granting—at least for the sake of argument—that Hume’s Principle may be used as a means of implicitly (...) defining the number operator, what advantage, if any, does adopting this course possess over a direct stipulation of the Dedekind-Peano axioms? This paper attempts to answer them. In response to the first, we spell out the links between the recognition of numerical terms as vehicles of singular reference and the conception of numbers as possible objects of singular, or object-directed, thought, and the role of the acknowledgement of numbers as objects in the neo-Fregean attempt to justify the basic laws of arithmetic. In response to the second, we argue that the crucial issue concerns the capacity of either stipulation—of Hume’s Principle, or of the Dedekind-Peano axioms—to found knowledge of the principles involved, and that in this regard there are crucial differences which explain why the former stipulation can, but the latter cannot, play the required foundational role. (shrink)

This article examines cognitive process models of human sentence comprehension based on the idea of informed search. These models are rational in the sense that they strive to find a good syntactic analysis quickly. Informed search derives a new account of garden pathing that handles traditional counterexamples. It supports a symbolic explanation for local coherence as well as an algorithmic account of entropy reduction. The models are expressed in a broad framework for theories of human sentence comprehension.

The EBM+ programme is an attempt to improve the way in which present-day evidence-based medicine (EBM) assesses causal claims: according to EBM+, mechanistic studies should be scrutinised alongside association studies. This paper addresses two worries about EBM+: (i) that it is not feasible in practice, and (ii) that it is too malleable, i.e., its results depend on subjective choices that need to be made in order to implement the procedure. Several responses to these two worries are considered and evaluated. The (...) paper also discusses the question of whether we should have confidence in medical interventions, in the light of Stegenga's arguments for medical nihilism. (shrink)

An early objection to Simon Blackburn’s first attempts to breathe new life into expressivism—by solving the Frege-Geach problem—was that whilst viewing compound sentences featuring moral components as expressive of attitudes towards combinations of attitudes might enable one to make out that a thinker who, to take the usual example, asserts the premisses but will not accept the conclusion of a moral modus ponens is at fault because they are involved in a “clash of attitudes”, this does no justice to the (...) data of the problem, since the failing here is logical, not just moral or more generally practical. Blackburn claims to have an effective answer to this objection—a way to see how, as he now puts it, expressivism can after all “deliver the mighty ‘musts’ of logic”. I remain unconvinced. (shrink)

Michael Dummett mounts, in Frege: Philosophy of Mathematics, a concerted attack on the attempt, led by Crispin Wright, to salvage defensible versions of Frege's platonism and logicism in which Frege's criterion of numerical identity plays a leading role. I discern four main strands in this attack—that Wright's solution to the Caesar problem fails; that explaining number words contextually cannot justify treating them as enjoying robust reference; that Wright has no effective counter to ontological reductionism; and that the attempt is vitiated (...) by the unavoidable impredicativity of its leading principle—and argue that none of them succeeds. (shrink)