BackgroundMedical ethics has recently seen a drive away from multiple prescriptive approaches, where physicians are inundated with guidelines and principles, towards alternative, less deontological perspectives. This represents a clear call for theory building that does not produce more guidelines. Phronesis (practical wisdom) offers an alternative approach for ethical decision-making based on an application of accumulated wisdom gained through previous practice dilemmas and decisions experienced by practitioners. Phronesis, as an ‘executive virtue’, offers a way to navigate the practice virtues for any (...) given case to reach a final decision on the way forward. However, very limited empirical data exist to support the theory of phronesis-based medical decision-making, and what does exist tends to focus on individual practitioners rather than practice-based communities of physicians.MethodsThe primary research question was: What does it mean to medical practitioners to make ethically wise decisions for patients and their communities? A three-year ethnographic study explored the practical wisdom of doctors (n = 131) and used their narratives to develop theoretical understanding of the concepts of ethical decision-making. Data collection included narrative interviews and observations with hospital doctors and General Practitioners at all stages in career progression. The analysis draws on neo-Aristotelian, MacIntyrean concepts of practice- based virtue ethics and was supported by an arts-based film production process.ResultsWe found that individually doctors conveyed many different practice virtues and those were consolidated into fifteen virtue continua that convey the participants’ ‘collective practical wisdom’, including the phronesis virtue. This study advances the existing theory and practice on phronesis as a decision-making approach due to the availability of these continua.ConclusionGiven the arguments that doctors feel professionally and personally vulnerable in the context of ethical decision-making, the continua in the form of a video series and app based moral debating resource can support before, during and after decision-making reflection. The potential implications are that these theoretical findings can be used by educators and practitioners as a non-prescriptive alternative to improve ethical decision-making, thereby addressing the call in the literature, and benefit patients and their communities, as well. (shrink)

A textbook for the undergraduate who is meeting the Lebesgue integral for the first time, relating it to the calculus and exploring its properties before deducing the consequent notions of measurable functions and measure.

Olav Gjelsvik: Quine on Observationality: This chapter discusses the role of the observationality of objects in Quine's philosophy. It does it by providing an overview of some of the milestones in Quine's thoughts about observation and observation sentences, and in connection with each milestone it identifies some of the philosophical problems Quine responds to and deals with. To help us understand how his thinking developed, the chapter discusses some of these problems and evaluates his responses. The final part discusses both (...) details and the bigger picture, partly by relating Quine to philosophers before him and after him. (shrink)

[Alan Weir] This paper addresses the problem of how to account for objective content-for the distinction between how we actually apply terms and the conditions in which we ought to apply them-from within a naturalistic framework. Though behaviourist or dispositionalist approaches are generally held to be unsuccessful in naturalising objective content or 'normativity', I attempt to restore the credibility of such approaches by sketching a behaviouristic programme for explicating objective content. /// [Alexander Miller] Paul Boghossian (1989, 1990) has (...) argued, on grounds concerning the holistic nature of belief fixation, that there are principled reasons for thinking that 'optimal conditions' versions of reductive dispositionalism about content cannot hope to satisfy a condition of extensional accuracy. I discern three separable strands of argument in Boghossian's work-the circularity objection, the open-endedness objection, and the certification objection-and argue that each of these objections fails. My conclusion is that for all that Boghossian has shown, 'optimal conditions' versions of reductive dispositionalism have to be assessed on a case-by-case basis. (shrink)

We examine George Boolos's proposed abstraction principle for extensions based on the limitation-of-size conception, New V, from several perspectives. Crispin Wright once suggested that New V could serve as part of a neo-logicist development of real analysis. We show that it fails both of the conservativeness criteria for abstraction principles that Wright proposes. Thus, we support Boolos against Wright. We also show that, when combined with the axioms for Boolos's iterative notion of set, New V yields a system equivalent to (...) full Zermelo-Fraenkel set theory with a principle of global choice. This advances Boolos's longstanding interest in the foundations of set theory. (shrink)

Neo-Fregeans argue that substantial mathematics can be derived from a priori abstraction principles, Hume's Principle connecting numerical identities with one:one correspondences being a prominent example. The embarrassment of riches objection is that there is a plurality of consistent but pairwise inconsistent abstraction principles, thus not all consistent abstractions can be true. This paper considers and criticizes various further criteria on acceptable abstractions proposed by Wright settling on another one—stability—as the best bet for neo-Fregeans. However, an analogue of the embarrassment of (...) riches objection resurfaces in the metatheory and I conclude by arguing that the neo-Fregean program, at least insofar as it includes a platonistic ontology, is fatally wounded by it. (shrink)

The neo-logicist argues tliat standard mathematics can be derived by purely logical means from abstraction principles—such as Hume's Principle— which are held to lie 'epistcmically innocent'. We show that the second-order axiom of comprehension applied to non-instantiated properties and the standard first-order existential instantiation and universal elimination principles are essential for the derivation of key results, specifically a theorem of infinity, but have not been shown to be epistemically innocent. We conclude that the epistemic innocence of mathematics has not been (...) established by the neo-logicist. (shrink)

Logicians interested in naive theories of truth or set have proposed logical frameworks in which classical operational rules are retained but structural rules are restricted. One increasingly popular way to do this is by restricting transitivity of entailment. This paper discusses a series of logics in this tradition, in which the transitivity restrictions are effected by a determinacy constraint on assumptions occurring in both the major and minor premises of certain rules. Semantics and proof theory for 3-valued, continuum-valued and surreal-valued (...) semantics are given and the proof theory for the systems outlined. The framework is robust in the sense that no conditional, defined or primitive, which sustains the contraction principles underlying Curry paradoxes can be expressed. Classical recapture is smoothly achievable in the system which however is expressively limited and not semantically closed. The conclusion considers the issue of how to extend the system to capture full naive set theory. (shrink)

Truth Through Proof defends an anti-platonist philosophy of mathematics derived from game formalism. Alan Weir aims to develop a more satisfactory successor to game formalism utilising a widely accepted, broadly neo-Fregean framework, in which the proposition expressed by an utterance is a function of both sense and background circumstance.

The guiding idea behind formalism is that mathematics is not a body of propositions representing an abstract sector of reality but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess. This idea has some intuitive plausibility: consider the tyro toiling at multiplication tables or the student using a standard algorithm for differentiating or integrating a function. It also corresponds to some aspects of the practice of (...) advanced mathematicians in some periods—for example, the treatment of imaginary numbers for some time after Bombelli's introduction of them, and perhaps the attitude of some contemporary mathematicians towards the higher flights of set theory. Finally, it is often the position to which philosophically naïve respondents will gesture towards, when pestered by questions as to the nature of mathematics. (shrink)

Starting with the distinction between epistemological and ontological naturalism, this chapter focuses most on Quine’s epistemological naturalism, not the ontological anti-naturalism he thought it leads to. It is argued that naturalised epistemology is not central to Quine’s epistemology. Quine’s key epistemological principle is:- follow the methods of science, and only those. Can Quine demarcate scientific methods from non-scientific ones? The problems which have been raised here, e.g. in the case of mathematics, are considered. A main theme is the relationship between (...) Quine’s naturalism and reductionist forms of ‘scientistic’ naturalism. Quine is generally taken to be an anti-reductionist, unsurprisingly given his explicit anti-reductionist pronouncements from ‘Two Dogmas’ onwards. It is argued that the situation is more complex than this and that key Quinean arguments are driven by a positivistic reductionism he never entirely broke free from. (shrink)

Mathematics poses a difficult problem for methodological naturalists, those who embrace scientific method, and also for ontological naturalists who eschew non-physical entities such as Cartesian souls. Mathematics seems both essential to science but also committed to abstract non-physical entities while methodologically it seems to have no place for experiment or empirical confirmation. The chapter critically reviews a number of responses naturalists have made including logicism, Quinean radical empiricism, and Penelope Maddy’s variant thereof and suggests some further problems both for ontological (...) and for methodological naturalists. (shrink)

Most of the time our quantifications generalise over a restricted domain. Thus in the last sentence, ‘most of the time’ is arguably not a generalisation over all times in the history of the universe but is restricted to a sub-group of times, those at which humans exist and utter quantified phrases and sentences, say. Indeed the example illustrates the point that quantificational phrases often carry an explicit restriction with them: ‘some people’, ‘all dogs’. Even then, context usually restricts to a (...) subdomain of the class specified by the count noun. Although teenagers like to have fun by being, they mistakenly think, overly literal— ‘Everyone is tired, let’s get to bed’: ‘everyone: you mean every person in the entire universe?’— competent language users have to be sensitive to context virtually all the time. But is it always the case that generalisation is over a restricted domain? On the face of it, to claim this is paradoxical. If we say. (shrink)

In this paper I argue for a theory of perception distinct both from classical sense-datum theories and from intentionalist theories, that is theories according to which one perceives external objects by dint of a relation with a propositional content. The alternative I propose completely rejects any representational element in perception. When one sees that an object has a property, the situation or state of affairs of its having that property is one's perception, so that the object and property are literally (...) part of one's mind. The most obvious objection to this view is that it embodies a rampant form of idealism. It is argued to the contrary, via consideration of the metaphysics of situations, that the theory is entirely consistent with a robustly realist view of the world. (shrink)

Gödel and others held that impredicative specification is illegitimate in a constructivist framework but legitimate elsewhere. Michael Dummett argues to the contrary that impredicativity, though not necessarily illicit, needs justification regardless of whether one assumes the context is realist or constructivist. In this paper I defend the Gödelian position arguing that Dummett seeks a reduction of impredicativity to predicativity which is neither possible nor necessary. The argument is illustrated by considering first highly predicative versions of the equinumerosity axiom for cardinal (...) number and Axiom V for sets, on the one hand, then classically consistent disjunctivised versions of Axiom V which are impredicative but can prove the well-foundedness of the semantics of weaker such systems, on the other. (shrink)

W.V. Quine's thesis of the indeterminacy of translation is the theory which launched a thousand doctorates. During the 1970s it sometimes seemed to be as firmly entrenched a dogma among North American philosophers as the existence of God was among medieval theologians. So what is the indeterminacy thesis? It is very tempting, of course, to apply a little reflexivity and deny that there is any determinate thesis of indeterminacy of translation; to charge Quine with championing a doctrine which has no (...) clear meaning, or which is hopelessly ambiguous. Such a charge is, it is argued in this article, false. His meaning is fairly clear and there is widespread agreement on what the thesis amounts to. The second section of the article looks at Quine's ‘argument from below’ for indeterminacy, then the ‘argument from above’, with concluding remarks in the last section. (shrink)

Gödel and others held that impredicative specification is illegitimate in a constructivist framework but legitimate elsewhere. Michael Dummett argues to the contrary that impredicativity, though not necessarily illicit, needs justification regardless of whether one assumes the context is realist or constructivist. In this paper I defend the Gödelian position arguing that Dummett seeks a reduction of impredicativity to predicativity which is neither possible nor necessary. The argument is illustrated by considering first highly predicative versions of the equinumerosity axiom for cardinal (...) number and Axiom V for sets, on the one hand, then classically consistent disjunctivised versions of Axiom V which are impredicative but can prove the well-foundedness of the semantics of weaker such systems, on the other. (shrink)

In this paper I highlight certain logical and metaphysical issues which arise in the characterisation of functionalism-in particular its ready coherence with a physicalist ontology, its structuralism and the impredicativity of functionalist specifications. I then utilise these points in an attempt to demonstrate fatal flaws in the functionalist programme. I argue that the brand of functionalism inspired by David Lewis fails to accommodate multiple realisability though such accommodation was vaunted as a key improvement over the identity theory. More standard accounts (...) of functionalism allow, by contrast, for far too much multiple realisability. Specifically, functionalist structures will be massively reduplicated in the human brain; so functionalism yields the absurd consequence that each human harbours large numbers of minds and exemplifies virtually all mental states. (shrink)

I revisit my 1993 paper on Putnam and mathematical realism focusing on the indispensability argument and how it has fared over the years. This argument starts from the claim that mathematics is an indispensable part of science and draws the conclusion, from holistic considerations about confirmation, that the ontology of science includes abstract objects as well as the physical entities science deals with.

I outline a variant on the formalist approach to mathematics which rejects textbook formalism's highly counterintuitive denial that mathematical theorems express truths while still avoiding ontological commitment to a realm of abstract objects. The key idea is to distinguish the sense of a sentence from its explanatory truth conditions. I then look at various problems with the neo-formalist approach, in particular at the status of the notion of proof in a formal calculus and at problems which Gödelian results seem to (...) pose for the tight link assumed between truth and proof. (shrink)

I outline a variant on the formalist approach to mathematics which rejects textbook formalism's highly counterintuitive denial that mathematical theorems express truths while still avoiding ontological commitment to a realm of abstract objects. The key idea is to distinguish the sense of a sentence from its explanatory truth conditions. I then look at various problems with the neo-formalist approach, in particular at the status of the notion of proof in a formal calculus and at problems which Gödelian results seem to (...) pose for the tight link assumed between truth and proof. (shrink)

In this article I discuss the 'procedural postulationist' view of mathematics advanced by Kit Fine in a recent paper. I argue that he has not shown that this view provides an avenue to knowledge of mathematical truths, at least if such truths are objective truths. In particular, more needs to be said about the criteria which constrain which types of entities can be postulated. I also argue that his reliance on second-order quantification means that his background logic is not free (...) of ontological commitment and that his doctrine of 'creative expansion' only makes sense from a radically anti-realist perspective. (shrink)

SummaryMany contemporary philosophers of language believe that realist metaphysics and a beha‐viouristic approach to language are incompatible, debate centring on which is to be given up. In this paper I argue that no incompatibility has been shown to exist. In the first section I attempt to give both a characterization of, and an argument for, behaviourism. Then I attempt to characterize realism more generally than is often done, evaluating the work of Dummett, Quine, Putnam and Wittgenstein, as recently interpreted, in (...) that light. Finally I attempt to sketch a behaviouristic justification of classical predicate logic and offer some programmatic remarks on behaviouristic accounts of mathematics and natural science.RésuméBien des philosophes contemporains du langage, estimant qu'une métaphysique réaliste et une approche behavioriste sont incompatibles, centrent le débat sur la question «lequel des deux doit‐il être sacrifité?» Je montre dans ce papier qu'on n'a jamais pu prouver l'existence d'une incompatibilité. Dans la première partie, je tente de caractériser et de défendre le behaviorisme. Puis j'essaie de caractériser le réalisme plus généralement que cela n'a été souvent fait et évalue dans cette perspective les oeuvres de Dummett, de Quine, de Putnam et de Wittgenstein à la lumière de leurs interprétations récentes. Finalement, je propose une justification behavioriste de la classique logique des prédicats et quelques remarques programmatiques quant à une approche behavioriste des mathématiques et des sciences naturelles.ZusammenfassungManche zeitgenössische Philosophen glauben, dass eine realistische Metaphysik nicht mit einer behavioristischen Betrachtungsweise der Sprache vereinbar sei, wobei sich der Streit um die Frage dreht, welche der beiden Haltungen aufgegeben werden müsse. Ich argurnentiere, dass die Unvereinbarkeit nicht wirklich nachgewiesen wurde. Im ersten Abschnitt versuche ich, den Beha‐viorismus genauer zu charakterisieren und zu seinen Gunsten zu argumentieren. Ich versuche dann, eine allgemeinere Charakterisierung des Realismus zu geben, als das üblich ist, indem ich die Werke von Dummett, Quine, Putnam und Wittgenstein, wie sie neuerdings unter diesen Gesichts‐punkt interpretiert werden, beurteile. lch versuche schliesslich, eine behavioristische Rechtferti‐gung der klassischen Prädikatenlogik zu skizzieren, und lege auch einige programmatische Bemerkungen zur behavioristischen Behandlung von Mathematik und Naturwissenschaft vor. (shrink)