1. It is a fact that developing a good proof theory for modal logics is a difficult task. The problem is not in having deductive systems. In fact, all the main modal logics enjoy an axiomatic prese...

When young children attempt to locate numbers along a number line, they show logarithmic (or other compressive) placement. For example, the distance between “5” and “10” is larger than the distance between “75” and “80.” This has often been explained by assuming that children have a logarithmically scaled mental representation of number (e.g., Berteletti, Lucangeli, Piazza, Dehaene, & Zorzi, 2010; Siegler & Opfer, 2003). However, several investigators have questioned this argument (e.g., Barth & Paladino, 2011; Cantlon, Cordes, Libertus, & (...) Brannon, 2009; Cohen & Blanc-Goldhammer, 2011). We show here that children prefer linear number lines over logarithmic lines when they do not have to deal with the meanings of individual numerals (i.e., number symbols, such as “5” or “80”). In Experiments 1 and 2, when 5- and 6- year-olds choose between number lines in a forced-choice task, they prefer linear to logarithmic and exponential displays. However, this preference does not persist when Experiment 3 presents the same lines without reference to numbers, and children simply choose which line they like best. In Experiments 4 and 5, children position beads on a number line to indicate how the integers 1 100 are arranged. The bead placement of 4- and 5-year-olds is better fit by a linear than by a logarithmic model. We argue that previous results from the number line task may depend on strategies specific to the task. (shrink)

Now in a thoroughly revised and expanded third edition, this authoritative Handbook reviews current knowledge about all aspects of emotion and its role in human ...

Disagreement is a pervasive feature of human discourse and a crucial force in shaping our social reality. From mundane squabbles about matters of taste to high-stakes disputes about law and public policy, the way we express and navigate disagreement plays a central role in both our personal and political lives. Legal discourse, in particular, is rife with disagreement - it is the very bread and butter of courtroom argument and legal scholarship alike. Consider a debate between two legal philosophers, Ronald (...) and Herbert, about the Eighth Amendment of the U.S. Constitution, which prohibits ‘cruel and unusual punishment’. Ronald asserts: ‘It is the law that capital punishment is prohibited’. In response, Herbert states: ‘It is not the law that capital punishment is prohibited’. We intuitively think Ronald and Herbert are disagreeing, which reveals in the fact that they are licensed to use ex¬pressions like no (it isn’t) and nuh-uh when responding to their opponent’s claim. But despite the ubiquity and significance of legal disagreement, its precise nature remains elusive. This chapter discusses what exactly is going on when two people disagree about what the law requires, and how can hybrid theory may answer this question. (shrink)

This article discusses the role of moment-to-moment affect dynamics in mental disorder and aims to integrate recent literature on this topic in the context of complex dynamical system theory. First, we will review the relevance of temporal and contextual aspects of affect dynamics in relation to psychopathology. Related to this, we will discuss recent insights resulting from a network view on affect dynamics in psychopathology. Next, we explore how we can reconcile literature findings from a perspective of complex dynamical system (...) theory. Finally, future directions with regard to personalized assessment of risk and diagnostic use are discussed. (shrink)

According to the hypothesis of extended phenomenal consciousness, although the material vehicles that realize phenomenal consciousness include neural elements, they are not restricted to such elements. There will be cases in which those material vehicles additionally include not only non-neural bodily elements, but also elements located beyond the skull and skin. In this paper, I examine two arguments for ExPC, one due to Noë and the other due to Kiverstein and Farina. Both of these arguments conclude that ExPC is true (...) on the basis of an analysis of sensory substitution, the phenomenon in which technological augmentation enables one sensory modality, for instance touch, to support the kind of environmental access and interaction ordinarily supported by a different sensory modality, for instance vision. I develop considerations which reveal that, as they stand, both of these arguments fall short. If the phenomenon of sensory substitution provides evidence for the truth of ExPC, it is not because of the specific arguments offered by these authors. (shrink)

This interview with M. Beatrice Fazi explores in detail her work on computation. Focusing in particular upon her recent publications, it covers the themes of contingency and indeterminacy. The questions explore Fazi’s perspectives on computational aesthetics, abstraction and experience. Through an interrogation of the conceptual insights that Fazi’s recent work offers, the interview outlines an agenda for future work in the philosophy of computation and sets forward a series of conceptual policies for seeing the digital, software and data in a (...) fresh light. (shrink)

Mathematics and logic are indispensable in science, yet how they are deployed and why they are so effective, especially in the natural sciences, is poorly understood. In this paper, I focus on the how by analysing Jean Piaget’s application of mathematics to the empirical content of psychological experiment; however, I do not lose sight of the application’s wider implications on the why. In a case study, I set out how Piaget drew on the stock of mathematical structures to model psychological (...) content, namely, the operations of thought involved in reasoning. In particular, I show how operations of thought form structured wholes that initially resisted modelling by either lattices or groups but could be modelled adequately by modifications of these mathematical structures. Piaget coined the term ‘grouping’ for the modified structure, and I conclude that it represents a non-canonical application of mathematics to the empirical content of experimental psychology. I also touch on the role external factors played in Piaget’s development of the grouping. According to the genetic epistemology conceived by Piaget, the origin of intelligence lies in the biological organism and develops in stages over time, and, via the grouping, Piaget established a genetic relationship between two stages of reasoning. I show how this relationship explains why mathematics and logic fit the psychological content of reasoning whilst simultaneously making their successful deployment in the natural sciences more mysterious. Finally, I turn to the explanation Piaget envisaged for the unreasonable effectiveness of mathematics in the natural sciences and consider some consequences for naturalism and Pythagoreanism. (shrink)

"The availability of a paperback version of Boyle's philosophical writings selected by M. A. Stewart will be a real service to teachers, students, and scholars with seventeenth-century interests. The editor has shown excellent judgment in bringing together many of the most important works and printing them, for the most part, in unabridged form. The texts have been edited responsibly with emphasis on readability.... Of special interest in connection with Locke and with the reception of Descarte's Corpuscularianism, to students of the (...) Scientific Revolution and of the history of mechanical philosophy, and to those interested in the relations among science, philosophy, and religion. In fact, given the imperfections in and unavailability of the eighteenth-century editions of Boyle’s works, this collection will benefit a wide variety of seventeenth-century scholars." --Gary Hatfield, University of Pennsylvania. (shrink)

M. R. Ayers; V*—Some Thoughts, Proceedings of the Aristotelian Society, Volume 73, Issue 1, 1 June 1973, Pages 69–86, https://doi.org/10.1093/aristotelian/73.1.

Quilts with "a black-and-white checked" pattern "for the NASCAR market" are stitched together by an Amish woman whose family uses an outdoor privy because church rules stipulate "no indoor plumbing"; an Amish man delivers cans of his milk to an Amish-owned neighborhood collection tank cooled by electricity because state laws require the refrigeration of milk. These are just a few of the images Karen Johnson-Weiner presents of the New York State Amish and their continuing effort to maintain a life disconnected (...) from the surrounding society upon which they are, to varying degrees, economically dependent. The Amish's struggle to preserve separate-from-the world communities and the diversity among the various Amish... (shrink)

To carry on reasoning in the face of the implications of skepticism is what Fred Parker calls “sceptical thinking.” Not to be confused with the engineered vacillation leading to a tranquillizing suspense of judgement, it involves the double perspective of someone conducting a life, believing and reasoning as we do, while acutely aware that the whole endeavor is, in a sense, untenable. If, as Sir Philip Sidney famously said, an imaginative writer “nothing affirms, and therefore never lieth,” then the dilemma (...) posed by skepticism might be less embarrassing for that kind of writer than for philosophers. The latter purport to offer tenets valued according to their truth, however variously defined; the former, on the other hand, create “speaking pictures,” or verbal imitations. Skeptically thinking imaginative writers can create speaking pictures of a life in which knowledge is unavailable though people must reason, believe, and act. In a famous letter Keats went so far as to deem a kind of ataraxy to be a condition of the highest art, adducing Shakespeare’s “Negative Capability... of being in uncertainties, Mysteries, doubts, without any irritable reaching after fact & reason”. Parker does not discuss the possibility that negative capability might conduce to the highest flights of literature. He is concerned with the unresolved tensions of skeptical thinking that he sees as complicating key works of literature in the Hanoverian reigns. For their authors and readers, the negativity of skepticism was “disillusioning and destabilizing” if not ameliorated by a humor like Sterne’s or an irony like Hume’s. Humor or irony arises from the oddity that skepticism is put in its place only when we give up and allow nature to reassert itself. Not heroic measures, but backgammon and making merry with friends prevail over doubt. Sometimes, when the confrontation with skepticism gives rise to the precept of following nature, skepticism can result in “a surprising confidence of assertion”. (shrink)

In teaching introductory ethics courses it is a struggle to find ways to ground the theoretical approach in a context accessible to students. Two way to provide this context are to use feature films and service learning. Each approach has advantages and disadvantages. Feature films provide students with a consistentnarrative, the filmmaker’s intentions, and identical experiences. Service learning provides students with an open encounter with uncertain meaning, concrete human problems, and at best similar experiences. The benefits and weaknesses of each (...) approach depend upon the objectives of the course. Films allow for greater clarity in interpretation of ethical theory, while service makes possible an appreciation of the ambiguities of ethical actions. (shrink)