This paper continues the investigation of inconsistent arithmetical structures. In $\S2$ the basic notion of a model with identity is defined, and results needed from elsewhere are cited. In $\S3$ several nonisomorphic inconsistent models with identity which extend the (=, $\S4$ inconsistent nonstandard models of the classical theory of finite rings and fields modulo m, i.e. Z m , are briefly considered. In $\S5$ two models modulo an infinite nonstandard number are considered. In the first, it is shown how to (...) model inconsistently the arithmetic of the rationals with all names included, a strengthening of earlier results. In the second, all inconsistency is confined to the nonstandard integers, and the effects on Fermat's Last Theorem are considered. It is concluded that the prospects for a good inconsistent theory of fields may be limited. (shrink)

Three indexes have been compiled: authors of main articles (including our special departments such as ‘Projects in progress’ and ‘Notes and discussions’); essay reviews; and book reviews. Co-author...

Our world is a world of change. Children are born and grow into adults. Material possessions rust and decay with age and ultimately perish. Yet scepticism about change is as old as philosophy itself. Heraclitus, for example, argued that nothing could survive the replacement of parts, so that it is impossible to step into the same river twice. Zeno argued that motion is paradoxical, so that nothing can alter its location. Parmenides and his followers went even further, arguing that the (...) very concept of qualitative change is inconsistent. Change in any respect is impossible, they argued, as change requires difference and nothing differs from itself. Few today would accept the Eleatic conclusion that change is impossible. But the topic of change continues to be a source of much debate, as it brings together various issues that are central to metaphysics, language, and logic – including identity, persistence, time, tense, and temporal logic. Author Recommends Wasserman, Ryan. 'The Problem of Change.' Philosophy Compass 1 (2006): 1–10. This article presents the problem of change and provides a brief survey of potential solutions. Haslanger, Sally. 'Persistence Through Time.' The Oxford Handbook of Metaphysics . Eds. M. Loux and D. Zimmerman. Oxford: Oxford University Press, 2003. This article presents the problem of change and provides a detailed survey of potential solutions. Heller, Mark. 'Things Change.' Philosophy and Phenomenological Research 52 (1992): 695–704. This article presents, explains, and defends the temporal parts solution to the problem of change. Hinchliff, Mark. 'The Puzzle of Change.' Philosophical Perspectives 10 (1996): 119–36. This article presents, explains, and defends the presentist solution to the problem of change. Wasserman, Ryan. 'The Argument from Temporary Intrinsics.' Australasian Journal of Philosophy 81 (2003): 413–19. This article presents, explains, and defends the relationist solution to the problem of change. Sider, Theodore. Four-Dimensionalism . Oxford: Oxford University Press, 2001. This book provides an introduction to various issues related to the problem of change, including the nature of time, tense, and persistence. Chapter 5 presents, explains, and defends the stage-view solution to the problem of change. Online Materials Change. URL: http://plato.stanford.edu/entries/change/ The Stanford Encyclopedia of Philosophy entry on change, by Chris Mortensen. Time. URL: http://plato.stanford.edu/entries/time/ The Stanford Encyclopedia of Philosophy entry on time, by Ned Markosian. Temporal Parts. URL: http://plato.stanford.edu/entries/temporal-parts/ The Stanford Encyclopedia of Philosophy entry on temporal parts, by Katherine Hawley. Material Constitution. URL: http://plato.stanford.edu/entries/material-constitution/ The Stanford Encyclopedia of Philosophy entry on material constitution, by Ryan Wasserman. Persistence Bibliography. URL: http://tedsider.org/teaching/pp_bibliography.pdf A bibliography on change and related issues, by Theodore Sider. Sample Syllabus Books on Syllabus Rea, Michael. Material Constitution: A Reader . Lanham: Rowman & Littlefield, 1997. Sider, Theodore. Four-Dimensionalism . Oxford: Oxford University Press, 2001. van Inwagen, P. and Zimmerman, D. 2008. Metaphysics: The Big Questions . 2nd ed. Oxford: Blackwell, 2008. Week 1: Time and Tense Four-Dimensionalism , chapters 1 and 2. Markosian, Ned. 'A Defence of Presentism.' Oxford Studies in Metaphysics, Volume 1. Ed. D. Zimmerman. Oxford: Oxford University Press, 2004: 47–82. In van Inwagen, P. and Zimmerman, D. Metaphysics: The Big Questions. 2nd ed. Oxford: Blackwell, 2008: 116-123. In van Inwagen, P. and Zimmerman, D. Metaphysics: The Big Questions. 2nd ed. Oxford: Blackwell, 2008: 124-129. Week 2: Time and Persistence Four-Dimensionalism , chapter 3. McGrath, Matthew. 'Temporal Parts.' Philosophy Compass 2 (2007): 730–48. In van Inwagen, P. and Zimmerman, D. Metaphysics: The Big Questions. 2nd ed. Oxford: Blackwell, 2008: 265-267. Hawthorne, J, Scala, M., and Wasserman, R. 'Recombination, Humean Supervenience, and Causal Constraints: An Argument for Temporal Parts?' Oxford Studies in Metaphysics , Volume 1. Ed. D. Zimmerman, Oxford: Oxford University Press, 2004: 301-318. Week 3: Change and Presentism In van Inwagen, P. and Zimmerman, D. Metaphysics: The Big Questions. 2nd ed. Oxford: Blackwell, 2008: 141-149. In van Inwagen, P. and Zimmerman, D. Metaphysics: The Big Questions. 2nd ed. Oxford: Blackwell, 2008: 267-269. In van Inwagen, P. and Zimmerman, D. Metaphysics: The Big Questions. 2nd ed. Oxford: Blackwell, 2008: 269-281. Week 4: Change and Temporal Parts Four-Dimensionalism , pp. 92–8. Heller, Mark. 'Things Change.' Philosophy and Phenomenological Research 52 (1992): 695–704. Lombard, Lawrence. 'The Doctrine of Temporal Parts and the "No Change" Objection.' Philosophy and Phenomenological Research 54 (1994): 365–72. Week 5: Change, Relationism, and Adverbialism Hawley, Katherine. 'Why Temporary Properties are not Relations between Physical Objects and Times.' Proceedings of the Aristotelian Society 98 (1998): 211–16. Wasserman, Ryan. 'The Argument from Temporary Intrinsics.' Australasian Journal of Philosophy 81 (2003): 413–19. Lewis, David. 'Tensing the Copula.' Mind 111 (2002): 1–13. Caplan, Ben. 'Why so Tense about the Copula?' Mind 114 (2007): 703–8. Week 6: Change and Tropes Ehring, Douglas. 'Lewis, Temporary Intrinsics and Momentary Tropes.' Analysis 57 (1997): 254–8. MacBride, Fraser. 'Four New Ways to Change Your Shape.' Australasian Journal of Philosophy 79 (2001): 81–9. Simons, Peter. 'On Being Spread Out in Time: Temporal Parts and the Problem of Change.' Existence and Explanation . Eds. W. Spohn, B.C. van Fraassen, and B. Skyrms. Dordrecht: Kluwer, 1991: 131-147. Weeks 7 and 8: Special Topic – Material Change Four-Dimensionalism , chapter 5. Selections from Material Constitution: A Reader. Week 9: Special Topic – Change of Position In van Inwagen, P. and Zimmerman, D. Metaphysics: The Big Questions. 2nd ed. Oxford: Blackwell, 2008: 186-195. In van Inwagen, P. and Zimmerman, D. Metaphysics: The Big Questions. 2nd ed. Oxford: Blackwell, 2008: 195-215. Week 10: Special topic – Changing the Past In van Inwagen, P. and Zimmerman, D. Metaphysics: The Big Questions. 2nd ed. Oxford: Blackwell, 2008: 224-235. van Iwagen, Peter. 'Changing the Past.' Oxford Studies in Metaphysics , Volume 5 . Ed. D. Zimmerman. Oxford: Oxford University Press, 2009: 1-22. Hudson, H. and Wasserman, R. 'Van Inwagen on Time Travel and Changing the Past.' Oxford Studies in Metaphysics , Volume 5. Ed. D. Zimmerman. Oxford: Oxford University Press, 2009: 41-49. (shrink)

In 1934, Oscar Reutersvärd drew what is generally acknowledged to be the first impossible triangle. Over the course of his lifetime, Reutersvärd created thousands of impossible figures, three of which would later adorn a series of Swedish postage stamps. But despite his enormous, inventive output, Reutersvärd is not widely known. Instead, impossible figures are popularly associated with M. C. Escher—three of whose more famous works include impossible figures—and the mathematical physicist Roger Penrose, who published the first academic article about impossible (...) figures in 1958 after independently discovering the impossible triangle. For Escher and Penrose, however, impossible figures were merely a passing interest. And while Penrose was concerned primarily with the mathematics of impossible figures and Escher integrated them into familiar human scenes, Reutersvärd’s abstract, minimalistic renderings express a fascination with the figures themselves. Free of adornment, they attract and command the eye, and exhibit a strange and peculiar beauty. -/- In this chapter, I investigate why we find impossible figures so visually compelling. In other words, my concern here is the specifically aesthetic appeal of impossible figures. Mathematicians and logicians have studied them for their mathematical and logical properties (Mortensen 2010), psychologists for what they reveal about the visual system (Gregory 1997, chap. 10), and philosophers in part for what they tell us about the limits of the imagination (Elpidorou 2016, 11), but we value them mainly as things to look at. This is what I want to understand. -/- I will work in three stages, using three methods. First, I will define the domain of investigation. What exactly is an impossible figure? Answering this question requires a form of conceptual analysis and raises a variety of interesting philosophical issues. Second, I will ask about the experience of looking at impossible figures. Here I will proceed by introspection—a first-person study of my own experience. Finally, I will appeal to results from experimental psychology to develop an empirically-grounded hypothesis about the visual appeal of impossible figures. If things go well, we will learn something not only about impossible figures, but about ourselves, and how and why we look at visual art in general. (shrink)

This paper criticises necessitarianism, the thesis that there is at least one necessary truth; and defends possibilism, the thesis that all propositions are contingent, or that anything is possible. The second section maintains that no good conventionalist account of necessity is available, while the third section criticises model theoretic necessitarianism. The fourth section sketches some recent technical work on nonclassical logic, with the aim of weakening necessitarian intuitions and strengthening possibilist intuitions. The fifth section considers several a prioristic attempts at (...) demonstrating that there is at least one necessary proposition and finds them inadequate. The final section emphasises the epistemic aspect of possibilism. (shrink)

Klaus Peter Mortensen; The Double Call: on Bildung in a Literary and Reflective Perspective, Journal of Philosophy of Education, Volume 36, Issue 3, 16 December.

A typical theorem of conaexive logics is Aristotle''s Thesis(A), (AA).A cannot be added to classical logic without producing a trivial (Post-inconsistent) logic, so connexive logics typically give up one or more of the classical properties of conjunction, e.g.(A & B)A, and are thereby able to achieve not only nontriviality, but also (negation) consistency. To date, semantical modellings forA have been unintuitive. One task of this paper is to give a more intuitive modelling forA in consistent logics. In addition, while inconsistent (...) but nontrivial theories, and inconsistent nontrivial logics employing prepositional constants (for which the rule of uniform substitution US fails), have both been studied extensively within the paraconsistent programme, inconsistent nontrivial logics (closed under US) do not seem to have been. This paper gives sufficient conditions for a logic containingA to be inconsistent, and then shows that there is a class of inconsistent nontrivial logics all containingA. A second semantical modelling forA in such logics is given. Finally, some informal remarks about the kind of modellingA seems to require are made. (shrink)

Background Interest in strengthening residents’ autonomy in nursing homes is intensifying and professional caregivers’ experience ethical dilemmas when the principles of beneficence and autonomy conflict. This increased focus requires expanded knowledge of how residents experience decision-making in nursing homes and how being subject to paternalism affects residents’ dignity. Research question/aim This study explored how residents experience paternalism in nursing homes. Research design This study involved a qualitative interpretive design with participant observations and semi-structured interviews. The interpretations were informed by Gadamer’s (...) hermeneutics. Participants and research context Eleven residents were interviewed after a period of participant observation in two nursing homes. Ethical considerations The study was performed in accordance with the Helsinki declaration. The Regional Ethics Committee (REK) permitted the researcher to perform participant observation in the nursing homes. The use of audio recordings of interviews was registered and supervised by Sikt - Norwegian Agency for Shared Services in Education and Research. The resident’s consent was assessed continuously. Three interviews were terminated for ethical reasons. Findings The resident interviews revealed that residents found it obvious for caregivers to possess the decision-making authority in nursing homes. When residents explained their views, three main themes emerged: (1) To be included even though caregivers make the decisions, (2) Surrender to dependency, and (3) Adherence to nursing home norms. Conclusions Residents submit to their caregivers and give caregivers the responsibility and function as leaders. Paternalism was experienced as dignifying in situations where it contributed to residents being able to live according to second order desires and values, and when it implied respect and appraisal of residents’ capabilities. Paternalism was experienced as debasing when residents felt left out, and when residents felt that their capabilities were underestimated. This also included their capability to withstand paternalistic influence. (shrink)

The question of the interpretation of impossible pictures is taken up. Penrose's account is reviewed. It is argued that whereas this account makes substantial inroads into the problem, there needs to be a further ingredient. An inconsistent account using heap models is proposed.

The blindness to ontological questioning in feminist theory has left a lacuna in scholarly study that Touching Thought—a study at the intersection of ontological meditation and feminist theorizing on sexual difference—seeks to fill. Ellen Mortensen's new work critiques the language and theoretical pathways of contemporary feminist theorists such as Judith Butler, Rosi Braidotti, Elizabeth Grosz, Luce Irigaray, Theresa de Lauretis, and Donna Haraway to reveal a problematic predilection for technological language at the expense of ontological inquiry. The volume ranges (...) across feminist epistemology and ethics, the politics of performativity, the aesthetics of body/power, and the question of sexual difference and concludes with an examination of the different philosophical and theoretical attempts at undertaking an ontological questioning of sexual difference. This foundational work will serve as preparation for scholars of feminist and queer theory and continental philosophy seeking alternative pathways of feminist thought that encourage fundamental thinking on the subject of individual freedom. (shrink)

Chris Mortensen, Graham Nerlich, Garrett Cullity and Gerard O'Brien.

Popper's definition looked initially promising provided that the restriction of classical logic was removed. As we have seen, this promise is not fulfilled. The search for a satisfactory verisimilitude ordering must therefore be pursued along more mainstream lines. The present exercise ought, however, to make us aware of the possibility that breakdowns of proposed definitions might only occur because of strictly classical assumptions.

In this article we address the question of how many impossible images Escher produced. To answer requires us first to clarify a range of concepts, including content, ambiguity, illusion, and impossibility. We then consider, and reject, several candidates for impossibility before settling on an answer.

Nudging is a concept in behavioural science, political theory and economics that proposes indirect suggestions to try to achieve non-forced compliance and to influence the decision making and behaviour of groups and individuals. Researchers in medical ethics are currently discussing whether nudging is ethically permissible in healthcare. In this article, we examine current knowledge about how different decisions (rational and pre-rational decisions, major and minor decisions) are made and how this decision-making process pertains to patients. We view this knowledge in (...) light of the nursing project and the ongoing debate regarding the ethical legitimacy of nudging in healthcare. We argue that it is insufficient to discuss nudging in nursing and healthcare in light of free will and patient autonomy alone. Sometimes, nurses must take charge and exhibit leadership in the nurse–patient relationship. From the perspective of nursing as leadership, nudging becomes a useful tool for directing and guiding patients towards the shared goals of health, recovery and independence and away from suffering. The use of nudging in nursing to influence patients’ decisions and actions must be in alignment with the nursing project and in accordance with patients’ own values and goals. (shrink)

This is a brief note about the history of the analysis of the collection of theories, RM3modn, in Meyer and Mortensen "Inconsistent Models for Relevant Arithmetics" Journal of Symbolic Logic 49 (1984).

First, we consider an argument due to Popper for maximal strength in choice of logic. We dispute this argument, taking a lead from some remarks by Susan Haack; but we defend a set of contrary considerations for minimal strength in logic. Finally, we consider the objection that Popper presupposes the distinctness of logic from science. We conclude from this that all claims to logical truth may be in equal epistemological trouble.

This paper offers an inconsistent model of motion perception. It was prompted by work on inconsistent motion due to Hegel and, following him, Priest. But the paper skirts Hegel's full scale idealism, by proposing that the inconsistency is with the cognitive contents of motion perception. The paper draws on work in the psychology of perception, and in the theory of inconsistency. I begin by noting the prima facie argument that temporal change threatens inconsistency, and canvassing ways in which this might (...) be avoided. The orthodox reply to the prima facie argument is that one and the same thing can have different incompatible properties at different times. This is plausible when applied to motion in the physical world. However, applied to cognition, it can be seen that the phenomenon of phi or beta, combined with the mechanism of a Reichardt detector, lends support to one key step in the prima facie argument, namely re-identification over time. The inconsistency of the model is then seen to follow from application of the Fade Principle. Advantages of the model are stressed: including a simple explanation of the debilitating condition of akinetopsia, that is, motion blindness; and a suggestion as to how to account for the “moving now.”. (shrink)

In this paper, a survey is made of some of the contributionsto the interpretation of Hartle and Hawking's theory of thewave function of the universe and its beginning. It is arguedthat there are considerable difficulties with the interpretationof the theory, but that there is at least one interpretationhitherto not found in the literature which survives existingphilosophical objections.