Reconstructing the Topology of the Elementary Self-embedding Monoids of Countable Saturated Structures

Every transformation monoid comes equipped with a canonical topology, the topology of pointwise convergence. For some structures, the topology of the endomorphism monoid can be reconstructed from its underlying abstract monoid. This phenomenon is called automatic homeomorphicity. In this paper we show that whenever the automorphism group of a countable saturated structure has automatic homeomorphicity and a trivial center, then the monoid of elementary self-embeddings has automatic homeomorphicity, too. As a second result we strengthen a result by Lascar by showing that whenever \({\mathbf {A}}\) is a countable \(\aleph _0\)-categorical G-finite structure whose automorphism group has a trivial center and if \({\mathbf {B}}\) is any other countable structure, then every isomorphism between the monoids of elementary self-embeddings is a homeomorphism.     

A Logical Analysis of Monty Hall and Sleeping Beauty

Hintikka and Sandu’s independence-friendly (IF) logic is a conservative extension of first-order logic that allows one to consider semantic games with imperfect information. In the present article, we first show how several variants of the Monty Hall problem can be modeled as semantic games for IF sentences. In the process, we extend IF logic to include semantic games with chance moves and dub this extension stochastic IF logic. Finally, we use stochastic IF logic to analyze the Sleeping Beauty problem, leading to the conclusion that the thirders are correct while identifying the main error in the halfers’ argument.     

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.