Arithmetical Soundness and Completeness for $$\varvec{\Sigma }_{\varvec{2}}$$ Numerations

We prove that for each recursively axiomatized consistent extension T of Peano Arithmetic and \(n \ge 2\), there exists a \(\Sigma _2\) numeration \(\tau (u)\) of T such that the provability logic of the provability predicate \(\mathsf{Pr}_\tau (x)\) naturally constructed from \(\tau (u)\) is exactly \(\mathsf{K}+ \Box (\Box ^n p \rightarrow p) \rightarrow \Box p\). This settles Sacchetti’s problem affirmatively.     

A New Rootedness? Education in the Technological Age

This paper explores the challenges facing educators in a time when modern technology, and especially modern social technology, has an increasingly powerful hold on our lives. The educational challenge does not primarily concern questions concerning the use of technology in the classroom, or as part of the learning environment, but a changeover in the whole social environment that marks our time. Taking guidance from Heidegger, Wittgenstein, Dewey and Nietzsche, the essay explores what we want the education of children to achieve, and how, if at all, this can be achieved in an age of modern social technology. The central argument is that the most basic educational goal of human flourishing cannot be achieved today as long as the main criteria of “best practice” in the classroom foreground pupil enjoyment rather than endurance of suffering. The paradox is that any call for the latter is now largely heard in a way cultivated by the culture of the former: namely, poorly and vulgarly, associated only with bullying authoritarianism, rather than the devoted care of teachers who want to awaken their pupils to self-responsibility.     

Does ‘Ought’ Imply ‘Might’? How (not) to Resolve the Conflict between Act and Motive Utilitarianism

Utilitarianism has often been understood as a theory that concerns itself first and foremost with the rightness of actions; but many other things (e.g., moral rules, motives, laws, etc.) are also properly subject to moral evaluation, and utilitarians have long understood that the theory must be able to provide an account of these as well. In a landmark article from 1976, Robert Adams argues that traditional act utilitarianism faces a particular problem in this regard. He argues that a on a sensible utilitarian account of the rightness of an agent’s motives, right motives will sometimes conflict with right actions, leaving the theory internally incoherent. The puzzle Adams raises has received a good deal of attention but few proposed solutions. Fred Feldman, however, has offered a solution that seems to be gaining adherents. In this paper I argue that Feldman’s approach cannot succeed. At bottom, it relies on a version of the principle that ‘ought’ implies ‘can’—and subsequently an account of an agent’s alternatives—that is far too restrictive to be plausible. Despite the failure of this solution, however, I argue that the conflict Adams develops is not as theoretically troubling as he suggests. While traditional act utilitarianism may fail for other reasons, it will not fail due to the conflict between acts and motives.     

Moods,Colored Lenses,and Emotional Disconnection: a Comment on Gallegos

In “Moods Are Not Colored Lenses: Perceptualism and the Phenomenology of Moods” (2017) Francisco Gallegos presents a challenge to popular view about the phenomenology of being in a mood that he calls “perceptualism”. In this essay, I offer a partial defense of perceptualism about moods and argue that perceptualism and Gallegos’s preferred Heideggerian alternative need not be viewed as in opposition to one another.     

When the Arrow Came before the Trolley: Jewish Aspects of the Trolley Problem

In 2014 Bruers and Breckman addressed a series of subsidiary questions arising from the trolley problem and their answers. In this article I describe ancient and precedent treatments of some of these issues over thousands of years as found in Jewish literature and the original solutions that have been proposed throughout history by Jewish philosophers and legal scholars. I address questions that have been posed to Jewish halakhic authorities when two obligations clash — whether one may save the lives of many at the cost of killing an individual — and discuss whether this is permitted in order to save lives or forbidden owing to the prohibition of murder. I also present new problems that have been introduced into the halakhic and philosophical discussions around the trolley problem in Jewish literature.     

The Break-Up Check: Exploring Romantic Love through Relationship Terminations

People who experience love often experience break-ups as well. However, philosophers of love have paid little attention to the phenomenon. Here, I address that gap by looking at the grieving process which follows unchosen relationship terminations. I ask which one is the loss that, if it were to be recovered, would stop grief or make it unwarranted. Is it the beloved, the reciprocation of love, the relationship, or all of it? By answering this question I not only provide with an insight on the nature of break-ups, but also make a specific claim about the nature of love. I argue that the object that is universally lost in all break-ups is a person with certain intrinsic qualities, who is in a relationship characterised by certain shared activities and recognized as romantic. That means that, at least in romantic terminations, the beloved and the relationship are not independent objects of grief. So, plausibly, they may not independent objects of value in love. Hence, those who state otherwise (within the property view and the relationship view) should face up to this objection coming from the study of break-ups.     

The Flipped Curriculum: Dewey’s Pragmatic University

Recently Graham Badley (Stud High Educ 41(4):631–641, 2016) made the case that the "pragmatic university” represents a viable future for the post-modern institution. In his construction of the pragmatic university, Badley largely draws upon the vision laid out by Richard Rorty (Philosophy and social hope. Penguin Books, London, 1999). While Rorty’s neopragmatism offers an important perspective on the pragmatic institution, I believe that John Dewey’s classical pragmatism offers a richer and more capable vision of the university. The aim of this paper is to develop a view of the pragmatic university drawn from Dewey’s philosophy. His writings on the university offer a unique and viable path forward because he directly engages a reconstruction of the relationship between knowledge and experience in the context of post-secondary education.     

On Educating While Hoping for the Impossible: Gabriel Marcel’s Absolute Hope as a Rejection of Educational Instrumentalism

Over the last 20 years, there has been an increase in philosophical inquiries of hope both in philosophy of mind and of virtue as well as in the philosophy of education. This paper wishes to add to this discussion by presenting the analysis of hope by French existentialist philosopher and theologian Gabriel Marcel and examining its possible contribution to educational practices and beliefs. As one of the very few modern, systematic accounts of hope, Marcel’s provocative conception of it and his critique of its common “technical” use could prove promising when applied to educational theory and practice. Following Marcel, I argue that in hope we find a complex and possibly contradictory view of the future: as a result of planning and technical problem-solving on one hand, and on the other, as an inclination towards the mysterious and radically unexpected. I suggest that maintaining educational hope within the tension between the planned and the unexpected, and specifically rejecting a complete disenchantment of the educational act, could help in securing education from being reduced to instrumental training and socializing, opening it up to new and unimaginable possibilities.     

Empiricism without magic: transformational abstraction in deep convolutional neural networks

In artificial intelligence, recent research has demonstrated the remarkable potential of Deep Convolutional Neural Networks (DCNNs), which seem to exceed state-of-the-art performance in new domains weekly, especially on the sorts of very difficult perceptual discrimination tasks that skeptics thought would remain beyond the reach of artificial intelligence. However, it has proven difficult to explain why DCNNs perform so well. In philosophy of mind, empiricists have long suggested that complex cognition is based on information derived from sensory experience, often appealing to a faculty of abstraction. Rationalists have frequently complained, however, that empiricists never adequately explained how this faculty of abstraction actually works. In this paper, I tie these two questions together, to the mutual benefit of both disciplines. I argue that the architectural features that distinguish DCNNs from earlier neural networks allow them to implement a form of hierarchical processing that I call “transformational abstraction”. Transformational abstraction iteratively converts sensory-based representations of category exemplars into new formats that are increasingly tolerant to “nuisance variation” in input. Reflecting upon the way that DCNNs leverage a combination of linear and non-linear processing to efficiently accomplish this feat allows us to understand how the brain is capable of bi-directional travel between exemplars and abstractions, addressing longstanding problems in empiricist philosophy of mind. I end by considering the prospects for future research on DCNNs, arguing that rather than simply implementing 80s connectionism with more brute-force computation, transformational abstraction counts as a qualitatively distinct form of processing ripe with philosophical and psychological significance, because it is significantly better suited to depict the generic mechanism responsible for this important kind of psychological processing in the brain.