The digital “4th Space” is a development of Oldenburg’s delineation of the 1st (home), 2nd place (work) and 3rd (social) places. Coworking spaces are presented as an example of space blurring within the knowledge economy, where digitalization, knowledge flows, flexibility and innovation play out at the micro level. Post-pandemic, they are likely to play a greater role as remote working remains a permanent feature. But how should we reassess their role in the advent of the 4th space, and what (...) might the 4th space mean for how the role of proximity itself is (re)conceptualized in relation to collaboration and innovation? To do so, providing examples, we suggest the journey from the telephone to extended reality (XR) video conferencing technologies as a means to understand the evolution of the 4th space. We discuss (XR) spaces and the opportunities to afford proximity and collaboration, thus providing an agenda for further research. (shrink)

Drawing on biosemiotic theory and the Peircean idea of ‘abduction’, I shall propose the idea of a layered structure of bio / semiotic evolution, in which humanknowledge is systemic and recursive — and thus emergent both from what is forgotten and from earlier evolutionary strata. I will argue that abductions are those processes by which we move creatively between often unacknowledged types of knowledge which are rooted in our natural and cultural evolutionary past (e.g., unconscious, preconscious, or tacit knowledge; knowledge (...) that is experienced affectively) and the more familiar types of knowledge associated with self-conscious deductive and inductive reasoning. I shall suggest that these processes of ‘hooking back’ into the past in order to make new sense in the light of subsequent experience, are characteristic of all human inventiveness in both the arts and the sciences, and are facilitated by what Peirce called ‘The Play of Musement’.My reasons for attempting this task are that I hope to offer a semiotic and biosemiotic corrective to the widespread and culturally dominant idea that the progress ofhuman knowledge and cultural evolution depends on self rational efficiency, conceived of in terms of self-conscious deduction and induction alone — a conception which runs the risk of excluding from the account what is actually the most creative part of human knowing. Second, I will suggest that a properly semiotically informed understanding of human creativity — i.e., one which understands the Peircean semiotic as triadic and which draws on the post-Peircean theory that the semiotic drive in nature and in culture derives from the need to model the world as accurately as possible — should provide a very stern warning against the dangers of confusing the map with the territory. For creative artists and scientists (and life-livers, in general) progress, I shall suggest, inasmuch as they ignore the utilitarian dogma in practice. A biosemiotic understanding of human reasoning as an evolutionary semiotic process should thus contribute to a removal of the impediments of modernity which lie in the failure to properly grasp both what language (and semiosis in general) is, as well as the historical and prehistorical evolution that makes such semiosis possible. (shrink)

Throughout the world, female students are less likely than males to take advanced physics courses. This mixed-methods study uses a concurrent, nested design to study an online homework intervention designed to address choice and achievement. A choice of three different contexts (biological, sports, and traditional) were offered to students for each physics problem, intending to stimulate females’ interest and enhance achievement. Informed by aspects of Artino’s social-cognitive model of academic motivation and emotion, we investigated: Which context of physics problems do (...) males and females select?; What explanations do students give for their choices?; Are there differences in the achievement of males and females?; and Is there a relationship between student achievement and the context selected? Fifty-two high school physics students from five U.S. states participated. Data included pre and post Force Concept Inventory scores, homework context choices and achievement, and rationales for choices. Findings indicate that females were most likely to select biology contexts; males, traditional. All students made more attempts on video questions over word questions, although females did not score as well. For all questions, students generally persisted until they answered them correctly, with females taking fewer attempts on problems. Context choice was mostly driven by interest, for males, and perceptions of difficulty level for females; however, rationales were indistinguishable by gender. On their first homework question attempt, females scored significantly better than the males. Initially, males had significantly higher FCI scores; post homework intervention, females increased their mean scores significantly on the FCI, erasing the initial gender gap, with no growth nor decline in males’ scores. Females with FCI growth were equally as likely to choose biology contexts as traditional contexts; males were more likely to choose biology contexts. Findings from this study suggest that modest changes to homework problems that provide choice and make the physics problems more contextually interesting - even without changes in classroom instruction - could increase interest and motivation students and increase achievement for both male and female students. Recommendations will be discussed. (shrink)

Henry Kyburg’s lottery paradox (1961, p. 197) arises from considering a fair 1000 ticket lottery that has exactly one winning ticket. If this much is known about the execution of the lottery it is therefore rational to accept that one ticket will win. Suppose that an event is very likely if the probability of its occurring is greater than 0.99. On these grounds it is presumed rational to accept the proposition that ticket 1 of the lottery will not win. Since (...) the lottery is fair, it is rational to accept that ticket 2 won’t win either—indeed, it is rational to accept for any individual ticket i of the lottery that ticket i will not win. However, accepting that ticket 1 won’t win, accepting that ticket 2 won’t win, . . . , and accepting that ticket 1000 won’t win entails that it is rational to accept that no ticket will win, which entails that it is rational to accept the contradictory proposition that one ticket wins and no ticket wins. (shrink)

According to Darwinian thinking, organisms are (for the most part) designed by natural selection, and so are (for the most part) integrated collections of adaptations, where an adaptation is a phenotypic trait that is a specialized response to a particular selection pressure. For animals that make their living in the Arctic, one adaptive problem is how to maintain body temperature above a certain minimum level necessary for survival. Polar bears' thick coats are a response to that selection pressure (surviving in (...) extreme cold). A thick coat makes a positive difference to a polar bear's fitness, since polar bears with very thin coats left fewer offspring than those with thicker coats. The foundational idea ofevolutionary psychologyis that brains are no different from any other organ with an evolutionary function, insofar as brains too are systems shaped by natural selection to solve adaptive problems. Thus brains have a particular functional organization because their behavioural effects tend, or once tended, to help maintain or increase the fitness of organisms with those brains. Prominent evolutionary psychologists (for example: Cosmides and Tooby, 1987; Cosmides and Tooby, 1994 and Symons, 1992) have endorsed the view that the last time any significant modifications were made by natural selection to the human brain's functional architecture, we were hunter-gatherers, inhabiting a world quite different from that which we now inhabit. That world was the Pleistocene epoch, between about 2 million years ago and 10 thousand years ago. On this view, then, the Pleistocene constitutes what evolutionary psychologists often call ourenvironment of evolutionary adaptedness(or EEA), and the information- processing structure and organization of our present-day cognitive architecture is no different from that of our recent huntergatherer ancestors. (shrink)

We analyze two problems in mathematics – the first (stated in our title) is extracted from Wittgenstein’s “Philosophy for Mathematicians”; the second (“What set of numbers is non-denumerable?”) is taken from Cantor. We then consider, by way of comparison, a problem in musical aesthetics concerning a Brahms variation on a theme by Haydn. Our aim is to bring out and elucidate the essentially riddle-like character of these problems.

In a rich and thought-provoking paper, Lambros Malafouris argues that taking material culture seriously means to be ‘systematically concerned with figuring out the causal efficacy of materiality in the enactment and constitution of a cognitive system or operation’ (Malafouris 2004, 55). As I understand this view, there are really two intertwined claims to be established. The first is that the things beyond the skin that make up material culture (in other words, the physical objects and artefacts in which cultural networks (...) and systems of human social relations are realized) may be essential to the enactment of, and be partly constitutive of, certain cognitive systems or operations. The consequence of establishing this claim is supposed to be that we have a mandate to recast the boundaries of the mind so as to include, as proper parts of the mind, things located beyond the skin. Thus, in talking about the contribution of the world to cognition, Malafouris (2004, 58) concludes that ‘what we have traditionally construed as an active or passive but always clearly separated external stimulus for setting a cognitive mechanism into motion, may be after all a continuous part of the machinery itself; at least ex hypothesi’. This is the position that, in philosophical circles, is known increasingly as the extended mind hypothesis (Clark & Chalmers 1998; Menary forthcoming). Henceforth I shall refer to this hypothesis as EM. A stock example will help bring the idea into view. Rumelhart et al. (1986) note that most of us solve difficult multiplication problems by using ‘pen and paper’ as an external resource. This environmental prop enables us to transform a difficult cognitive problem into a set of simpler ones, and to temporarily store the results of certain intermediate calculations. For the fan of EM, the distributed combination of this external resource and certain inner psychological processes constitutes a cognitive system in its own right. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in (...) the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

On the basis of careful textual exegesis and philosophical analysis, and contrary to the received view, Mark R. Wheeler demonstrates that Aristotle presents and systematically explicates his definition of the essence of the truth in the Metaphysics. Aristotle states the nominal definitions of the terms "truth" and "falsehood" as part of his arguments in defense of the logical axioms. These nominal definitions express conceptions of truth and falsehood his philosophical opponents would have recognized and accepted in the context of (...) dialectical argument. On the basis of these nominal definitions, Aristotle develops his definitions of the essences of truth and falsehood--his "real" definitions of truth and falsehood. Aristotle's methodical exposition of his essential definitions of truth and falsehood in the Metaphysics serves as a well-developed example of how his philosophical inquiry starts with nominal definitions and ends with real definitions. Wheeler also argues for the novel claim that Aristotle defines the most fundamental kind of truth in terms of accurate measurement. Aristotle's metrical conception of truth serves as the theoretical basis for specifying the truth conditions of various assertions, for identifying the sorts of beings implicated in these truth conditions, and for explaining the nature of approximate truth and falsehood. Far from offering us a minimal account of truth, Wheeler shows how Aristotle offers us a sophisticated and metrical theory of truth. (shrink)

Am 4. November 1915 legte EINSTEIN seine beriihmte Arbeit "Zur allgemeinen Relativitatstheorie" der PreuBischen Akademie der Wissenschaften zu Berlin vor. 50 Jahre spater organisierte die Deutsche Akademie der Wissenschaften im Andenken daran eine dreitagige Konferenz, in deren Verlauf auch eine Gedenkfeier abgehalten wurde. Ich hatte die Ehre, eine Gedenkrede iiber EINSTEIN und sein Werk zu halten. In der Zwischenzeit wurde unser Wissen urn viele wichtige neue Zusatze erweitert. Wir sehen nun, daB die Dynamik der Einsteinschen Theorie in einem Superraum ablauft. (...) Seine Struktur und seine Eigenschaften sind von graBter Bedeutung. Infolgedessen habe ich jenen Teil meines Berichtes von 1965, der iiber die Quantengeometrodynamik handelt, geandert und erweitert, urn vom § 12 an unser Wissen iiber den Super­ raum zusammenzufassen. Einige Teile des hier enthaltenen Materials sind schon friiher in anderer Form erschienen. Der Autor dankt fiir die Erlaubnis, dieses Material wieder ab­ drucken zu lassen, den folgenden Verlagen: Akademie-Verlag, Berlin; W. A. Benjamin, Inc., New York; Gordon and Breach, New York; und Springer-Verlag, New York und Heidelberg, sowie den Organisatoren jener Konferenzen, auf denen diese Beitrage vorgelegt wurden: Einstein-Symposium aus Deutsche Akademie der Wissenschaften zu Berlin, 1965; International School of Non-Linear Mathematics and Physics, Miinchen, J uli 1966; Academie Internationale de Philo sophie des Sciences, Oberwolfach/Freiburg i. Br., Juli 1966; Society of Engineering Science, Raleigh, North Carolina, Oktober 1966; Colloque Internationale sur Fluides et Champ Gravitationel en Relativite Generale, Paris, J uni 1967; und Battelle Ren­ contres in Mathematics and Physics, Seattle, Juli 1967. (shrink)

Coherentism maintains that coherent beliefs are more likely to be true than incoherent beliefs, and that coherent evidence provides more confirmation of a hypothesis when the evidence is made coherent by the explanation provided by that hypothesis. Although probabilistic models of credence ought to be well-suited to justifying such claims, negative results from Bayesian epistemology have suggested otherwise. In this essay we argue that the connection between coherence and confirmation should be understood as a relation mediated by the causal relationships (...) among the evidence and a hypothesis, and we offer a framework for doing so by fitting together probabilistic models of coherence, confirmation, and causation. We show that the causal structure among the evidence and hypothesis is sometimes enough to determine whether the coherence of the evidence boosts confirmation of the hypothesis, makes no difference to it, or even reduces it. We also show that, ceteris paribus, it is not the coherence of the evidence that boosts confirmation, but rather the ratio of the coherence of the evidence to the coherence of the evidence conditional on a hypothesis. (shrink)

The first section of this chapter discusses the one essay Davidson wrote specifically about the theory of literature, including his criticisms of Kripke's account of names in fiction. The second section describes his intentionalism, anticonventionalism, and account of metaphor. The third section discusses to what extent Davidson's views are taken into account by contemporary literary theorists, such as Michaels and Fish. After discussing how texts are prima facie different from speech, the fourth section presents some problems for Davidson's account of (...) texts, using Biblical texts as examples. The fifth section speculates on a Davidsonian response to those problems. (shrink)

Examines the philosophical, scientific, and theological aspects of the character of the human mind.

David Bohm, in his "causal theory", made the correct Hegelian synthesis of Einstein's thesis that there is a "there" there, and Bohr's antithesis of "thinglessness" (Nick Herbert’s term). Einstein was a materialist and Bohr was an idealist. Bohm showed that quantum reality has both. This is “physical dualism” (my term). Physical dualism may be a low energy approximation to a deeper monism of cosmic consciousness called "the super-implicate order" (Bohm and Hiley’s term), “pregeometry” (Wheeler’s term), “substratum” (Dirac’s term), “funda-MENTAL (...) space” (Hameroff’s term), “Chi” (Chinese medicine & Falun Gong) etc., but for our immediate pragmatic purpose of constructing naturally conscious nano-computers and of virtually reverse engineering alleged reports of propellantless UFO propulsion (French Intelligence Report, 1999 [email protected] Vol. 5, No. 11, Part 1 -- August 1, 1999 & NIDS report "Best UFO Cases - Europe", I. Von Ludwiger) to the stars and beyond, physical dualism will work. (shrink)

One approach to hypnosis suggests that for hypnotic experience to occur frontal lobe activity must be attenuated. For example, cold control theory posits that a lack of awareness of intentions is responsible for the experience of involuntariness and/or the subjective reality of hypnotic suggestions. The mid-dorso-lateral prefrontal cortex and the ACC are candidate regions for such awareness. Alcohol impairs frontal lobe executive function. This study examined whether alcohol affects hypnotisability. We administered 0.8 mg/kg of alcohol or a placebo to 32 (...) medium susceptible participants. They were subsequently hypnotised and given hypnotic suggestions. All participants believed they had received some alcohol. Participants in the alcohol condition were more susceptible to hypnotic suggestions than participants in the placebo condition. Impaired frontal lobe activity facilitates hypnotic responding, which supports theories postulating that attenuation of executive function facilitates hypnotic response, and contradicts theories postulating that hypnotic response involves enhanced inhibitory, attentional or other executive function. (shrink)

Mark Richard Wheeler - Aristotle on Truth - Journal of the History of Philosophy 44:3 Journal of the History of Philosophy 44.3 469-470 Paolo Crivelli. Aristotle on Truth. Cambridge-New York: Cambridge University Press, 2004. Pp. xi + 340. Cloth, $85.00. A thorough contemporary study of Aristotle's theory of truth is welcome. Adopting a frankly analytic approach, Professor Crivelli addresses all of the most important Aristotelian texts on truth. He provides close and careful exegesis, attending to philological and interpretive difficulties (...) related to the manuscripts and alternative translations. In the spirit of Hintikka, Łukasiewicz, and Mignucci, the tools of contemporary logical analysis are applied effectively and yield rigorous restatements of Aristotle's.. (shrink)

We examined the hypothesis that a tendency to experience the world in terms of a sense of ‘special’ connection is responsible for the self-transcendent value dimension identified by multi-dimensional scaling and constitutes a common factor for different religious and non-religious interpretations of spirituality. Eight different groups were studied including: six different types of faith leaders in India and the UK, people who self-rated as spiritual but not religious, and those self-rating as neither spiritual nor religious. They completed a questionnaire that (...) assessed the strength of their spirituality irrespective of type and the experience of special connection to the following categories: people, nature, places and the universe, with and without using the term spiritual. For all eight samples the different types of connection were highly inter-correlated, and self-perceived spirituality correlated with the sum of connection items irrespective of whether items included the term spiritual or not. Variation between groups in the size of the latter correlation was consistent with different interpretations of spirituality in those groups. Although the meaning of spirituality is socially constructed, variability within faith leader groups suggests that its interpretation is also affected by personality. (shrink)

The creative process has the potential to increase wellbeing and foster human flourishing (Dolan and Metcalfe, 2012 ; Forgeard and Eichner, 2014 ; O’Brien and Murray, 2015 ; Conner et al., 2018 ; Kaufman, 2018 ), yet has received little attention in the humanistic management literature. In this paper, we present three experiments showing that idea originators experience greater relationship conflict with counterparts who have committed perceived “idea theft”, i.e., proposed identical or related ideas. We test a model that identifies (...) a mechanism—self-threat—that mediates the relationship between idea theft and relationship conflict and identifies an intervention to ameliorate that self-threat via self-affirmation. Study 1 demonstrates the idea originator’s attribution of malign attributions to, and negative moral emotions toward, the counterpart. Study 2 demonstrates that idea originators ostracize both those who propose identical ideas and those who propose merely related ideas. In Study 3, evidence for self-threat as the mechanism underlying the negative relational consequences is provided via both a direct test of mediation as well as via moderation by self-affirmation. Our research contributes to the nascent idea theft literature and suggests a way to reduce its negative consequences. (shrink)

Recent advances in philosophy, artificial intelligence, mathematical psychology, and the decision sciences have brought a renewed focus to the role and interpretation of probability in theories of uncertain reasoning. Henry E. Kyburg, Jr. has long resisted the now dominate Bayesian approach to the role of probability in scientific inference and practical decision. The sharp contrasts between the Bayesian approach and Kyburg's program offer a uniquely powerful framework within which to study several issues at the heart of scientific inference, decision, and (...) reasoning under uncertainty. The commissioned essays for this volume take measure of the scope and impact of Kyburg's views on probability and scientific inference, and include several new and important contributions to the field. Contributors: Gert de Cooman, Clark Glymour, William Harper, Isaac Levi, Ron Loui, Enrique Miranda, John Pollock, Teddy Seidenfeld, Choh Man Teng, Mariam Thalos, Gregory Wheeler, Jon Williamson, and Henry E. Kyburg, Jr. (shrink)

Michael Tonry, Sentencing Matters (New York: Oxford University Press, 1996, 240pp.

This chapter contains sections titled: Is Philosophy Part of Web Science?; Representations and the Web; Enactive Search; Cognitive Extension and Cognitive Intelligence; From the Extended Mind to the Web; and the Web as Collective Intelligence.

Two compelling principles, the Reasonable Range Principle and the Preservation of Irrelevant Evidence Principle, are necessary conditions that any response to peer disagreements ought to abide by. The Reasonable Range Principle maintains that a resolution to a peer disagreement should not fall outside the range of views expressed by the peers in their dispute, whereas the Preservation of Irrelevant Evidence Principle maintains that a resolution strategy should be able to preserve unanimous judgments of evidential irrelevance among the peers. No standard (...) Bayesian resolution strategy satisfies the PIE Principle, however, and we give a loss aversion argument in support of PIE and against Bayes. The theory of imprecise probability allows one to satisfy both principles, and we introduce the notion of a set-based credal judgment to frame and address a range of subtle issues that arise in peer disagreements. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Response to Masafumi Ogawa, “Music Teacher Education in Japan: Structure, Problems, and Perspectives”Peggy WheelerMasafumi Ogawa's paper presents challenge after challenge facing the teacher and the teacher educator in Japan. One has the sense that a lifetime of frustrations with the national curriculum, the set-up of student teaching, and the definition of music as a school subject each made its way into the paper. Even choosing to focus on teacher (...) training still leaves a very broad topic for a relatively short paper. The central challenge seems to be the curriculum. How does the curriculum impact the teacher and the teacher training process? How does the underlying definition of music as well as the purpose that definition implies affect the curriculum? His paper also identifies a series of dualities or tensions that exist between two important components: the curriculum or teacher education. The fact that Japanese and American music education systems seem to be at opposite ends of some of these dualities is a compelling reason for exploring and discussing them.In the arena of teacher preparation, the dualities as they appear in their relative proportion of the teacher education curriculum are (1) performance versus academic music courses, such as history, theory, and composition, and (2) education versus music courses—a familiar lament among music education students. In student teaching, modeling in the classroom by the cooperating teacher is contrasted with providing opportunities for the student teacher to experiment with the teaching process. Evaluation of student teaching is a three-way tension involving the student teacher, the cooperating teacher, and the university professor.In his discussion of the school curriculum, Ogawa deplores the triumph of attitude over skill, and pleads for discernment in the application of national standards to meet the needs of the community and students. He returns to the nature of music and music education at several points in his paper, expanding the meaning and function of music beyond music as art. His dissatisfaction with the seemingly teacher-proof curriculum peaks when he advocates for the autonomy of the teacher in the classroom. Giving teachers the opportunity to devise their own curriculum seems to go to the other extreme. Having taught with colleagues who had virtually no training in music, a standard curriculum at the district or national level provides some essential boundaries.Ogawa's discussion of the impact of the national Course of Study on Japanese music education was particularly intriguing. As teacher certification in the United [End Page 205] States has begun to promote and reward National Board Certification, it is striking to consider the restrictions and disempowerment that Ogawa describes and credits to the omnipresent Course of Study. For someone unfamiliar with the Japanese system of education, some of the descriptions were enticing but brief. Other descriptions were a bit confusing, but after visiting the MEXT website, I think most of this confusion is due to translation. It is difficult to take any phrase that is packed with meaning in one culture and find a suitable phrase in another culture that will convey the associations that are connected with it. I would recommend quoting complete descriptions or including an appendix. A reference to the history of Japanese music education on Kensho Takeshi's website would also provide more context, particularly for the connection between emotion, music, and ethics.I want to thank Ogawa for stimulating me to consider issues of curriculum including how I have changed my views of curriculum since I returned to school teaching. First, I will describe my change of perspective. Then I would like to close by describing an aspect of curriculum and teacher education that has surfaced this past year. I would call this the meta-curriculum, and I wonder how we can prepare new teachers for this part of teaching. It seems to me that the world of philosophy is the quintessential and perhaps the only appropriate arena for this preparation.Beyond Curriculum in the ClassroomLike the first spring rain on newly cut grass, music education has a fresh and vital look to me. I returned to public school teaching this year after a hiatus of seventeen years. After focusing on viola performance and liberal arts... (shrink)

Jim Joyce argues for two amendments to probabilism. The first is the doctrine that credences are rational, or not, in virtue of their accuracy or “closeness to the truth” (1998). The second is a shift from a numerically precise model of belief to an imprecise model represented by a set of probability functions (2010). We argue that both amendments cannot be satisfied simultaneously. To do so, we employ a (slightly-generalized) impossibility theorem of Seidenfeld, Schervish, and Kadane (2012), who show that (...) there is no strictly proper scoring rule for imprecise probabilities. -/- The question then is what should give way. Joyce, who is well aware of this no-go result, thinks that a quantifiability constraint on epistemic accuracy should be relaxed to accommodate imprecision. We argue instead that another Joycean assumption — called strict immodesty— should be rejected, and we prove a representation theorem that characterizes all “mildly” immodest measures of inaccuracy. (shrink)

This impressive volume of essays that includes contributions from Herbert Dreyfus, Sean Kelly, Mike Wheeler, Dan Zahavi, and Shaun Gallagher reflects an emerging trend in cognitive science, and explores this new approach to cognitive science informed by Heidegger's thoughts on human existence.

Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is stochastically (...) independent of F (for all F in a partition of the underlying state space) is sufficient to avoid dilation, but (2) stochastic independence is not the only independence concept at play within imprecise probability models. In this paper we give a simple characterization of dilation formulated in terms of deviation from stochastic independence, propose a measure of dilation, and distinguish between proper and improper dilation. Through this we revisit the most sensational examples of dilation, which play up independence between dilator and dilatee, and find the sensationalism undermined by either fallacious reasoning with imprecise probabilities or improperly constructed imprecise probability models. (shrink)

Analyzing geometric properties of high-dimensional loss functions, such as local curvature and the existence of other optima around a certain point in loss space, can help provide a better understanding of the interplay between neural network structure, implementation attributes, and learning performance. In this work, we combine concepts from high-dimensional probability and differential geometry to study how curvature properties in lower-dimensional loss representations depend on those in the original loss space. We show that saddle points in the original space are (...) rarely correctly identified as such in lower-dimensional representations if random projections are used. In such projections, the expected curvature in a lower-dimensional representation is proportional to the mean curvature in the original loss space. Hence, the mean curvature in the original loss space determines if saddle points appear, on average, as either minima, maxima, or almost flat regions. We use the connection between expected curvature and mean curvature (i.e., the normalized Hessian trace) to estimate the trace of Hessians without calculating the Hessian or Hessian-vector products as in Hutchinson’s method. Because random projections are not able to correctly identify saddle information, we propose to study projections along Hessian directions that are associated with the largest and smallest principal curvatures. We connect our findings to the ongoing debate on loss landscape flatness and generalizability. Finally, we illustrate our method in numerical experiments on different image classifiers with up to about 7 × 10^6 parameters. (shrink)

In this paper, we present a new semantic challenge to the moral error theory. Its first component calls upon moral error theorists to deliver a deontic semantics that is consistent with the error-theoretic denial of moral truths by returning the truth-value false to all moral deontic sentences. We call this the ‘consistency challenge’ to the moral error theory. Its second component demands that error theorists explain in which way moral deontic assertions can be seen to differ in meaning despite necessarily (...) sharing the same intension. We call this the ‘triviality challenge’ to the moral error theory. Error theorists can either meet the consistency challenge or the triviality challenge, we argue, but are hard pressed to meet both. (shrink)

Recent debate about the error theory has taken a ‘formal turn’. On the one hand, there are those who argue that the error theory should be rejected because of its difficulties in providing a convincing formal account of the logic and semantics of moral claims. On the other hand, there are those who claim that such formal objections fail, maintaining that arguments against the error theory must be of a substantive rather than a formal kind. In this paper, we argue (...) that formal objections to the error theory cannot be eschewed but must be met head-on. (shrink)

Samuel C. Wheeler, III; The Extension of Deconstruction, The Monist, Volume 69, Issue 1, 1 January 1986, Pages 3–21, https://doi.org/10.5840/monist19866913.

Using a two-part instrument consisting of eight vignettes and twenty character traits, the study sampled 141 employees of a mid-west financial firm regarding their predispositions to prefer utilitarian or formalist forms of ethical reasoning. In contrast with earlier studies, we found that these respondents did not prefer utilitarian reasoning. Several other hypotheses were tested involving the relationship between people's preferences for certain types of solutions to issues and the forms of reasoning they use to arrive at those solutions; the nature (...) of the relationship between utilitarian and formalist categories ; and the possibility of measuring ethical predispositions using different methods. (shrink)