The use of tensed language and the metaphor of set ‘formation’ found in informal descriptions of the iterative conception of set are seldom taken at all seriously. Both are eliminated in the nonmodal stage theories that formalise this account. To avoid the paradoxes, such accounts deny the Maximality thesis, the compelling thesis that any sets can form a set. This paper seeks to save the Maximality thesis by taking the tense more seriously than has been customary (although not literally). A (...) modal stage theory, MST, is developed in a bimodal language, governed by a tenselike logic. Such a language permits a very natural axiomatisation of the iterative conception, which upholds the Maximality thesis. It is argued that the modal approach is consonant with mathematical practice and a plausible metaphysics of sets and shown that MST interprets a natural extension of Zermelo set theory less the axiom of Infinity and, when extended with a further axiom concerning the extent of the hierarchy, interprets Zermelo–Fraenkel set theory. (shrink)

Context: Strict finitism is usually not taken seriously as a possible view on what mathematics is and how it functions. This is due mainly to unfamiliarity with the topic. Problem: First, it is necessary to present a “decent” history of strict finitism and, secondly, to show that common counterarguments against strict finitism can be properly addressed and refuted. Method: For the historical part, the historical material is situated in a broader context, and for the argumentative part, an evaluation of arguments (...) and counterarguments is presented. Results: The main result is that strict finitism is indeed a viable option, next to other constructive approaches, in mathematics. Implications: Arguing for strict finitism is more complex than is usually thought. For future research, strict finitist mathematics itself needs to be written out in more detail to increase its credibility. In as far as strict finitism is a viable option, it will change our views on such “classics” as the platonist-constructivist discussion, the discovery-construction debate and the mysterious applicability problem . Constructivist content: Strict finitism starts from the idea that counting is an act of labeling, hence the mathematician is an active subject right from the start. It differs from other constructivist views in that the finite limitations of the human subject are taken into account. (shrink)

This paper is devoted to the study of some subvarieties of the variety Q of Q-Heyting algebras, that is, Heyting algebras with a quantifier. In particular, a deeper investigation is carried out in the variety Q subscript 3 of three-valued Q-Heyting algebras to show that the structure of the lattice of subvarieties of Q is far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q subscript 3 and we construct (...) the lattice of subvarieties lambda (Q subscript 3) of the variety Q subscript 3. (shrink)

In ‘The nature of moral judgments and the extent of the moral domain’, Fraser criticises findings by Kelly et al. that speak against the moral/conventional distinction, arguing that the experiment was confounded. First, we note that the results of that experiment held up when confounds were removed . Second, and more importantly, we argue that attempts to prove the existence of a M/C distinction are systematically confounded. In contrast to Fraser, we refer to data that support our view. We highlight (...) the implications for the moral/conventional theory. (shrink)

The solution of the outer multiplicity problem in the tensor product of U(3) irreducible representations (irreps) developed by Biedenharn et al.(1–7) and realized through the well-known Draayer-Akiyama (DA) computer code(8) is extended to the quantum algebra Uq(3). An analytic formula for special stretched Uq(3) Wigner coefficients, $$\left\langle {(\lambda _1 \mu _1 ) H_1 , (\lambda _2 \mu _2 ) \varepsilon _2 \Lambda _2 m_2 \left| { (\lambda _3 \mu _3 ) H_3 } \right.} \right\rangle _{\max }^q $$ is derived using (...) a projection operator method.(9–10) In this expression Hi denotes the highest weight vector of the (λiμi) irrep; the subscript “max” means coefficients corresponding to a unit tensor operator with a maximal characteristic null space; and q is the usual quantum label so the standard U(3) Wigner coefficient, which is required in the DA code, can be obtained in the q→1 limit of the theory. To illustrate the theory, some Uq(3) Wigner coefficients for the tensor product (22)×(22) are calculated. The procedure for evaluating nonhighest weight Wigner Uq(3) coefficients follow the DA prescription. (shrink)

This paper is devoted to the study of some subvarieties of the variety Qof Q-Heyting algebras, that is, Heyting algebras with a quantifier. In particular, a deeper investigation is carried out in the variety Q 3 of three-valued Q-Heyting algebras to show that the structure of the lattice of subvarieties of Qis far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q 3 and we construct the lattice of subvarieties (...) (Q 3 ) of the variety Q 3. (shrink)

Can business humanize its stakeholders? And if so, how does this relate to moral consideration for stakeholders? In this paper we compare two business orientations that are relevant for current business theory and practice: a stakeholder orientation and a profit orientation. We empirically investigate the causal relationships between business orientation, humanization, and moral consideration. We report the results of six experiments, making use of different operationalizations of a stakeholder and profit orientation, different stakeholders, and different participant samples. Our findings support (...) the prediction that individual stakeholders observing a stakeholder-oriented firm see the firm’s other stakeholders as more human than individual stakeholders observing a profit-oriented firm. This humanization, in turn, increases individual stakeholders’ moral consideration for the firm’s other stakeholders. Our findings underscore the importance of humanization for stakeholders’ moral consideration for each other. This paper contributes to a deeper understanding of the firm as a moral community of stakeholders. Specifically, we move away from a focus on managers, and how they can make business more moral. Instead we direct attention to stakeholders, and how business can make these stakeholders more moral. (shrink)

Health care workers with needlestick exposures to patients' blood often request a test of the patient for evidence of infection with human immunodeficiency virus. If the patient refuses the test, a conflict develops between the interests of the health care worker and those of the patient. Traditional approaches to this dilemma attempt to balance the rights or utilities of abstract patients and health care workers. While these approaches have the advantage of offering clear guidelines in advance of conflict, the interests (...) of the actual participants may differ from those used to create the guidelines. In nonmedical settings, conflicts are often resolved efficiently through negotiation and monetary exchanges. Although negotiated monetary settlements between health care workers and patients may be an impractical way to resolve medical conflicts, models developed from these perspectives provide insights into the individual interests of physicians and patients. Changing existing rules about medical record documentation, or increasing the penalties for the misuse of medical information, may satisfy the interests on both sides of the conflict and so represent integrative bargaining solutions. Even so, as the relationship between health care workers and their patients evolves, more explicit strategies for negotiation may become a reasonable solution to the problem of conflict. (shrink)

We present in this article a new logical system inspired from linear logic. This system is designed in order to express causality and dynamism. The cut elimination theorem holds for this logic. Examples of applications are given.

In a previous article, I argue that on the assumption that God exercises libertarian agency, a primary causal divine miracle could, in principle, leave a scientifically detectable gap in the natural world. In a subsequent publication, Evan Fales offered a critique of my argument and this article is my rejoinder. I justify my employment of Divine libertarian agency and respond to Fales’s two, closely-related questions: How much energy could one add to a room by making a lot of decisions? Would (...) the increase in energy be measurable? (shrink)