What in the World are Possible Worlds?

Ted Sider writes that "many are impressed with the utility of possible worlds in linguistics and philosophy", and this is true, in particular, of those with an interest in modal logic. However, in the midst of the marvelous milieu brought on by the development of possible world semantics, some have stopped to ask just what it is that possible worlds are. They certainly seem useful, and we seem to understand how to use them and talk about them, but what precisely is it that we're talking about when we talk of possible worlds? In this thesis, I will attempt to outline the most significant and well-recognized view in this debate: that of David Lewis. Through my discussion of him, I will find occasion to discuss some alternative views that have arisen. After finishing my presentation of Lewis, I will discuss where people have begun to take this debate and address the question of whether progress can be made towards a substantive answer. In Chapter I, I begin by presenting the motivation of the question of possible worlds found in the study of modal logic. I then present the major approaches taken to answering the questions that were raised, leading into my discussion of David Lewis's famous and robust account. I present key features of Lewis's view and then move into his criticisms of the other major responses. This much should suffice as a relatively thorough treatment of the answers that have come before. In Chapter II, I discuss the current state of the debate. I begin by mentioning several problems that can be spotted in Lewis's views in particular. I then move to Menzel's account, which tries to answer the question of possible worlds from a new angle, jettisoning the direction taken by Lewis and his contemporaries. I explain why Menzel has taken this new approach, and then move into another new approach, this time given by Stephen Yablo. I discuss how these two approaches can help serve each other in helpful ways. But, at last, I present several hurdles these two views would have to overcome in order to play together nicely

Sketch-and-Project Meets Newton Method: Global O(k−2)\mathcal O(k^{-2}) Convergence with Low-Rank Updates

In this paper, we propose the first sketch-and-project Newton method with fast $\mathcal O(k^{-2})$ global convergence rate for self-concordant functions. Our method, SGN, can be viewed in three ways: i) as a sketch-and-project algorithm projecting updates of Newton method, ii) as a cubically regularized Newton ethod in sketched subspaces, and iii) as a damped Newton method in sketched subspaces. SGN inherits best of all three worlds: cheap iteration costs of sketch-and-project methods, state-of-the-art $\mathcal O(k^{-2})$ global convergence rate of full-rank Newton-like methods and the algorithm simplicity of damped Newton methods. Finally, we demonstrate its comparable empirical performance to baseline algorithms.Comment: 10 page

Extending the Harper Identity to Iterated Belief Change

The field of iterated belief change has focused mainly on revision, with the other main operator of AGM belief change theory, i.e. contraction, receiving relatively little attention. In this paper we extend the Harper Identity from single-step change to define iterated contraction in terms of iterated revision. Specifically, just as the Harper Identity provides a recipe for defining the belief set resulting from contracting A in terms of (i) the initial belief set and (ii) the belief set resulting from revision by ¬A, we look at ways to define the plausibility ordering over worlds resulting from contracting A in terms of (iii) the initial plausibility ordering, and (iv) the plausibility ordering resulting from revision by ¬A. After noting that the most straightforward such extension leads to a trivialisation of the space of permissible orderings, we provide a family of operators for combining plausibility orderings that avoid such a result. These operators are characterised in our domain of interest by a pair of intuitively compelling properties, which turn out to enable the derivation of a number of iterated contraction postulates from postulates for iterated revision. We finish by observing that a salient member of this family allows for the derivation of counterparts for contraction of some well known iterated revision operators, as well as for defining new iterated contraction operators

Experiential Education in the Lecture Hall

Legal education today is composed of two separate worlds. The first world includes clinical faculty, law skills faculty, and other related faculty. These faculty members have long embraced experiential education, and they organize and attend conferences like the Experience the Future symposium, hosted by Northeastern University School of Law and the Alliance for Experiential Learning in Law. The other world includes people like me- doctrinal faculty members who are still largely teaching the way we always have. As we see it, our role is to teach doctrine and legal analysis, leaving skills training and other experiential teaching to others. Experiential education is simply not a part of our professional conversation. It is only a slight exaggeration to say that these two worlds never meet. They speak in the hallways and they sit in the same faculty meetings, but they rarely meet as educators to discuss their collective ideas on how to teach their students. As a result, while different models of experiential education have been debated, studied, and critiqued by one group of legal educators, it is largely ignored by the other. This Essay argues that the push for experiential education in law schools is really a push for better teaching. Part I explains the relationship between experiential education and student learning. Part II explores different ways to use experiential education in traditional doctrinal courses. Part III examines ways to foster a culture of experiential education among doctrinal faculty

What in the World are Possible Worlds?

Ted Sider writes that "many are impressed with the utility of possible worlds in linguistics and philosophy", and this is true, in particular, of those with an interest in modal logic. However, in the midst of the marvelous milieu brought on by the development of possible world semantics, some have stopped to ask just what it is that possible worlds are. They certainly seem useful, and we seem to understand how to use them and talk about them, but what precisely is it that we're talking about when we talk of possible worlds? In this thesis, I will attempt to outline the most significant and well-recognized view in this debate: that of David Lewis. Through my discussion of him, I will find occasion to discuss some alternative views that have arisen. After finishing my presentation of Lewis, I will discuss where people have begun to take this debate and address the question of whether progress can be made towards a substantive answer. In Chapter I, I begin by presenting the motivation of the question of possible worlds found in the study of modal logic. I then present the major approaches taken to answering the questions that were raised, leading into my discussion of David Lewis's famous and robust account. I present key features of Lewis's view and then move into his criticisms of the other major responses. This much should suffice as a relatively thorough treatment of the answers that have come before. In Chapter II, I discuss the current state of the debate. I begin by mentioning several problems that can be spotted in Lewis's views in particular. I then move to Menzel's account, which tries to answer the question of possible worlds from a new angle, jettisoning the direction taken by Lewis and his contemporaries. I explain why Menzel has taken this new approach, and then move into another new approach, this time given by Stephen Yablo. I discuss how these two approaches can help serve each other in helpful ways. But, at last, I present several hurdles these two views would have to overcome in order to play together nicely

Infinite Value and the Best of All Possible Worlds

A common argument for atheism runs as follows: God would not create a world worse than other worlds he could have created instead. However, if God exists, he could have created a better world than this one. Therefore, God does not exist. In this paper I challenge the second premise of this argument. I argue that if God exists, our world will continue without end, with God continuing to create value-bearers, and sustaining and perfecting the value-bearers he has already created. Given this, if God exists, our world—considered on the whole—is infinitely valuable. I further contend that this theistic picture makes our world's value unsurpassable. In support of this contention, I consider proposals for how infinitely valuable worlds might be improved upon, focusing on two main ways—adding value-bearers and increasing the value in present value-bearers. I argue that neither of these can improve our world. Depending on how each method is understood, either it would not improve our world, or our world is unsurpassable with respect to it. I conclude by considering the implications of my argument for the problem of evil more generally conceived

Quantum Mechanics as Classical Physics

Here I explore a novel no-collapse interpretation of quantum mechanics which combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical predictions of quantum mechanics, the theory looks surprisingly classical. All there is at the fundamental level are particles interacting via Newtonian forces. There is no wave function. However, there are many worlds.Comment: 25 page

The actual future is open

Open futurism is the indeterministic position according to which the future is 'open,' i.e., there is now no fact of the matter as to what future contingent events will actually obtain. Many open futurists hold a branching conception of time, in which a variety of possible futures exist. This paper introduces two challenges to (branching-time) open futurism, which are similar in spirit to a challenge posed by Kit Fine to (standard) tense realism. The paper argues that, to address the new challenges, open futurists must (i) adopt an objective, non-perspectival notion of actuality and (ii) subscribe to an A-theoretic, dynamic conception of reality. Moreover, given a natural understanding of "actual future," (iii) open futurism is naturally coupled with the view that a unique, objectively actual future exists, contrary to a common assumption in the current debate. The paper also contends that recognising the existence of a unique actual future helps open futurists to avoid potential misconceptions

How Strong Is a Counterfactual?

The literature on counterfactuals is dominated by strict accounts and variably strict accounts. Counterexamples to the principle of Antecedent Strengthening were thought to be fatal to SA; but it has been shown that by adding dynamic resources to the view, such examples can be accounted for. We broaden the debate between VSA and SA by focusing on a new strengthening principle, Strengthening with a Possibility. We show dynamic SA classically validates this principle. We give a counterexample to it and show that extra dynamic resources cannot help SA. We then show VSA accounts for the counterexample if it allows for orderings on worlds that are not almost-connected, and that such an ordering naturally falls out of a Kratzerian ordering source semantics. We conclude that the failure of Strengthening with a Possibility tells strongly against Dynamic SA and in favor of an ordering source-based version of VSA

Fifty Million Elvis Fans Can’t be Wrong

This essay revisits some classic problems in the philosophy of space and time concerning the counting of possibilities. I argue that we should think that two Newtonian worlds can differ only as to when or where things happen and that general relativistic worlds can differ in something like the same way—the first of these theses being quaintly heterodox, the second baldly heretical, according to the mores of contemporary philosophy of physics