The use of cost-benefit analysis (CBA) in environmental decision-making and the contingent valuation (CV) technique as input into traditional CBA to elicit environmental values in monetary terms has stimulated an extensive debate. Critics have questioned the appropriateness of both the method and the technique. Some alternative suggestions for the elicitation of environmental values are based on a social process of deliberation. However, just like traditional economic theory, these alternative approaches may be questioned on their implicit value judgements regarding the legitimacy (...) of the social-political organisation of the process of value elicitation. Instead of making assumptions a priori, research efforts should be focused on the processes by which actual public attitudes and preferences towards the environment can best be elicited and fed into environmental or other public policy decision-making. In the study presented in this paper, support was found for both the individual WTP based approach and a participatory social deliberation approach to inform the environmental decision-making process, suggesting that a combination of both approaches is most appropriate. (shrink)

This note opens with brief evaluations of classical foundationalist endeavors – those of Frege, Russell, Brouwer and Hilbert. From there we proceed to some pluralist approaches to foundations, focusing on Putnam and Wittgenstein, making a note of what enables their pluralism. Then, I bring up approaches that find foundations potentially harmful, as expressed by Rav and Lakatos. I conclude with a brief discussion of a late medieval Indian case study in order to show what an “unfounded” mathematics could look (...) like. The general purpose is to re-evaluate the desiderata of foundational programs in mathematics. (shrink)

The eclipse riddle -- Seeing surfaces -- The disappearing act -- Spinning shadows -- Berkeley's shadow -- Para-reflections -- Para-refractions : shadowgrams and the black drop -- Goethe's colored shadows -- Filtows -- Holes in the light -- Black and blue -- Seeing in black and white -- We see in the dark -- Hearing silence.

In 2020, due to the Nightingale year and COVID‐19 crisis, nursing is in the public eye more than ever. Nurses often are being seen as compassionate helpers. The public image of nursing, however, also consists of stereotypes such as nursing being a ‘doing’ profession and care being a ‘female’ characteristic. Next to that, nursing is associated with images from the past, such as ‘the lady with the lamp’. Therefore, in the public eye at least, the nursing identity seems a simple (...) and straightforward enough construct, but nothing less is true. Looking at what a professional identity consists of, historic and social developments influence a group identity as a construct. In addition, individual, professional and contemporary societal moralities, including stereotypes, play its role. Nurses themselves reinforce stereotypes in order to fit into what is expected, even when they believe professional behaviour encompasses other features. They may do so individually as well as in a group context. But nursing actually seems to be better off when viewed upon as a diverse, autonomous profession. Moral values such as compassion motivate nurses to enter the profession. Research shows that if such values are addressed in daily practice, nursing could perhaps be saved from nurses leaving the profession because of feeling unfulfilled. Another aspect concerns the huge nursing body of knowledge. If seen as the ground on which nursing behaviour is standing, it would contribute to a different image of nursing than simplified stereotypes, which do not acknowledge the complex nature of the profession. This paper challenges the idea that the nursing identity is unchangeable and the notion that ‘a nurse will always be a nurse’. By doing so, the paper contributes to a debate on the supposed ‘true’ nature of the nursing identity and opens a discussion on the need for it to change. (shrink)

It is widely thought that the acceptability of an abstraction principle is a feature of the cardinalities at which it is satisfiable. This view is called into question by a recent observation by Richard Heck. We show that a fix proposed by Heck fails but we analyze the interesting idea on which it is based, namely that an acceptable abstraction has to “generate” the objects that it requires. We also correct and complete the classification of proposed criteria for acceptable abstraction.

We begin with a prepositional languageLpcontaining conjunction (Λ), a class of sentence names {Sα}αϵA, and a falsity predicateF. We (only) allow unrestricted infinite conjunctions, i.e., given any non-empty class of sentence names {Sβ}βϵB,is a well-formed formula (we will useWFFto denote the set of well-formed formulae).The language, as it stands, is unproblematic. Whether various paradoxes are produced depends on which names are assigned to which sentences. What is needed is a denotation function:For example, theLPsentence “F(S1)” (i.e.,Λ{F(S1)}), combined with a denotation functionδsuch (...) thatδ(S1)“F(S1)”, provides the (or, in this context, a)Liar Paradox.To give a more interesting example,Yablo's Paradox[4] can be reconstructed within this framework.Yablo's Paradoxconsists of an ω-sequence of sentences {Sk}kϵωwhere, for eachnϵω:WithinLPan equivalent construction can be obtained using infinite conjunction in place of universal quantification - the sentence names are {Si}iϵωand the denotation function is given by:We can express this in more familiar terms as:etc. (shrink)

A number of authors have argued that Peano Arithmetic supplemented with a logical validity predicate is inconsistent in much the same manner as is PA supplemented with an unrestricted truth predicate. In this paper I show that, on the contrary, there is no genuine paradox of logical validity—a completely general logical validity predicate can be coherently added to PA, and the resulting system is consistent. In addition, this observation lead to a number of novel, and important, insights into the nature (...) of logical validity itself. (shrink)

Logical pluralism is the view that there is more than one formal logic that correctly (or best, or legitimately) codifies the logical consequence relation in natural language. This essay provides a taxonomy of different variations on the logical pluralist theme based on a five-part structure, and then identifies an unoccupied position in this taxonomy: perspectival logical pluralism. Perspectival pluralism provides an attractive position from which to formulate a philosophy of logic from a feminist perspective (and from other, identity-based perspectives, such (...) as critical race theory). An example of how such an account might be developed is sketched. The essay concludes by defusing an obvious objection to the perspectival approach: the claim that the correct logic (or logics), in virtue of the formal nature of logic, should be independent of considerations regarding the identity of the reasoner. (shrink)

One of the main reasons for providing formal semantics for languages is that the mathematical precision afforded by such semantics allows us to study and manipulate the formalization much more easily than if we were to study the relevant natural languages directly. Michael Tye and R. M. Sainsbury have argued that traditional set-theoretic semantics for vague languages are all but useless, however, since this mathematical precision eliminates the very phenomenon (vagueness) that we are trying to capture. Here we meet this (...) objection by viewing formalization as a process of building models, not providing descriptions. When we are constructing models, as opposed to accurate descriptions, we often include in the model extra ‘machinery’ of some sort in order to facilitate our manipulation of the model. In other words, while some parts of a model accurately represent actual aspects of the phenomenon being modelled, other parts might be merely artefacts of the particular model. With this distinction in place, the criticisms of Sainsbury and Tye are easily dealt with—the precision of the semantics is artefactual and does not represent any real precision in vague discourse. Although this solution to this problem is independent of any particular semantics a detailed account of how we would distinguish between representor and artefact within Dorothy Edgington's degree-theoretic semantics is presented. (shrink)

One of the main problems plaguing neo-logicism is the Bad Company challenge: the need for a well-motivated account of which abstraction principles provide legitimate definitions of mathematical concepts. In this article a solution to the Bad Company challenge is provided, based on the idea that definitions ought to be conservative. Although the standard formulation of conservativeness is not sufficient for acceptability, since there are conservative but pairwise incompatible abstraction principles, a stronger conservativeness condition is sufficient: that the class of acceptable (...) abstraction principles be strictly logically symmetrically class conservative . The article concludes with an examination of which classes of abstraction principles meet this criteria. (shrink)

In “The Runabout Inference Ticket” AN Prior (1960) examines the idea that logical connectives can be given a meaning solely in virtue of the stipulation of a set of rules governing them, and thus that logical truth/consequence.

Truth values are, properly understood, merely proxies for the various relations that can hold between language and the world. Once truth values are understood in this way, consideration of the Liar paradox and the revenge problem shows that our language is indefinitely extensible, as is the class of truth values that statements of our language can take – in short, there is a proper class of such truth values. As a result, important and unexpected connections emerge between the semantic paradoxes (...) and the set-theoretic paradoxes. (shrink)

Reasoning about causation in fact is an essential element of attributing legal responsibility. Therefore, the automation of the attribution of legal responsibility requires a modelling effort aimed at the following: a thorough understanding of the relation between the legal concepts of responsibility and of causation in fact; a thorough understanding of the relation between causation in fact and the common sense concept of causation; and, finally, the specification of an ontology of the concepts that are minimally required for (automatic) common (...) sense reasoning about causation. This article offers a worked-out example of the indicated analysis. Such example consists of: a definition of the legal concept of responsibility (in terms of liability and accountability); a definition of the legal concept of causation in fact (in terms of the initiation of physical processes by an agent and of the provision of reasons and/or opportunities to other agents); CausatiOnt, an AI-like ontology of the common sense (causal) concepts that are minimally needed for reasoning about the legal concept of causation in fact (in particular, the concepts of category, dimension, object, agent, process, event and act). (shrink)

Fine and Antonelli introduce two generalizations of permutation invariance — internal invariance and simple/double invariance respectively. After sketching reasons why a solution to the Bad Company problem might require that abstraction principles be invariant in one or both senses, I identify the most fine-grained abstraction principle that is invariant in each sense. Hume’s Principle is the most fine-grained abstraction principle invariant in both senses. I conclude by suggesting that this partially explains the success of Hume’s Principle, and the comparative lack (...) of success in reconstructing areas of mathematics other than arithmetic based on non-invariant abstraction principles. (shrink)

When talking about decisionmaking for children with a life-threatening condition, the death of children with brain tumors deserves special attention. The last days of the lives of these children can be particularly harsh for bystanders, and raise questions about the suffering of these children themselves. In the Netherlands, these children are part of the group for whom a wide range of end-of-life decisions are discussed, and questions raised. What does the end-of-life for these children look like, and what motivates physicians (...) and parents to make decisions that may affect the life and death of these children? This article highlights the story of the parents of the sisters Roos and Noor. When both their daughters were diagnosed with a hereditary brain tumor, they had to make similar decisions twice. Their story sheds light on the suffering of children in the terminal phase, and how this suffering may motivate parents and physicians to make decisions that influence the end of life of these children’s lives.We argue that complete knowledge about suffering in the terminal phase of children with brain tumors is impossible. However, by collecting experiences like those of Roos and Noor, we can move toward an experienced-based understanding and better guide parents and physicians through these hardest of decisions. (shrink)

Michael Dummett argues that acceptance of potentially infinite collections requires that we abandon classical logic and restrict ourselves to intuitionistic logic. In this paper we examine whether Dummett is correct. After developing two detailed accounts of what, exactly, it means for a concept to be potentially infinite (based on ideas due to Charles McCarty and Øystein Linnebo, respectively), we construct a Kripke structure that contains a natural number structure that satisfies both accounts. This model supports a logic much stronger than (...) intuitionistic logic, demonstrating that Dummett was wrong. We conclude by briefly examining ways to extend the account(s) in question to indefinitely extensible concepts such as Cardinal, Ordinal, and Set. (shrink)

We consider domains with a natural property called top-circularity. We show that if such a domain satisfies either the maximal conflict property or the weak conflict property, then it is dictatorial. We obtain the result in Sato :331–342, 2010) as a corollary. Furthermore, it follows from our results that the union of a single-peaked domain and a single-dipped domain is dictatorial.

Positive thinkers love Watty Piper's The little engine that could. The story features a train laden with toys for deserving children on the other side of the mountain. After the locomotive breaks down, a sequence of snooty locomotives come up the track. Each engine refuses to pull the train up the mountain. They are followed by a weary old locomotive that declines, saying "I cannot. I cannot. I cannot." But then a bright blue engine comes up the track. He manages (...) to chug over the mountain by averring "I think I can. I think I can. I think can.". (shrink)

We expand on the fixed point semantic approach of Kripke via the addition of two unary intensional operators: a paradoxicality operator Π where Π(Φ) is true at a fixed point if and only if Φ is paradoxical (i.e., if and only if Φ receives the third, non-classical value on all fixed points that extend the current fixed point), and an unbounded truth operator Υ⊤ where Υ⊤(Φ) is true at a fixed point if and only if any fixed point extending the (...) current fixed point can be extended to one on which Φ receives the value true. We prove a generalized version of Kripke’s fixed point theorem guaranteeing the existence of models of this new language, as well as an expressive completeness result. We conclude with an exploration of the significant improvements in expressive power that result from the addition of these new operators, and we precisely identify what still cannot be said on this intensional extension of the Kripkean framework. (shrink)

A number of formal constraints on acceptable abstraction principles have been proposed, including conservativeness and irenicity. Hume’s Principle, of course, satisfies these constraints. Here, variants of Hume’s Principle that allow us to count concepts instead of objects are examined. It is argued that, prima facie, these principles ought to be no more problematic than HP itself. But, as is shown here, these principles only enjoy the formal properties that have been suggested as indicative of acceptability if certain constraints on the (...) size of the continuum hold. As a result, whether or not these higher-order versions of Hume’s Principle are acceptable seems to be independent of standard (ZFC) set theory. This places the abstractionist in an uncomfortable dilemma: Either there is some inherent difference between counting objects and counting concepts, or new criteria for acceptability will need to be found. It is argued that neither horn looks promising. (shrink)

It is sometimes suggested that impure sets are spatially co-located with their members (and hence are located in space). Sets, however, are in important respects like numbers. In particular, sets are connected to concepts in much the same manner as numbers are connected to concepts—in both cases, they are fundamentally abstracts of (or corresponding to) concepts. This parallel between the structure of sets and the structure of numbers suggests that the metaphysics of sets and the metaphysics of numbers should parallel (...) each other in relevant ways. This entails, in turn, that impure sets are not co-located with their members (nor are they located in space). (shrink)

Offering a Canadian perspective on the emotional health of servicemen and women, Military Operations and the Mind brings together researchers and practitioners from across the country to consider the impact that ethical issues have on the well-being of those who serve. Stemming from an initiative to enhance the lives of serving members by providing them with the best education and training in military ethics before and after deployments, this volume will better inform politics and public policies and enhance the welfare (...) of the soldiers, sailors, and airmen and women who serve in singular, often harsh, and sometimes dangerous conditions. By integrating into the analysis the critical issue of well-being, this emerging field demonstrates a more holistic approach and is distinct from other fields in military, historical, philosophical, and behavioural studies. The first study of its kind, Military Operations and the Mind presents a new and helpful way to focus on the life of soldiers not only in operations overseas, but also once they return home. (shrink)