8,990 research outputs found

    The socratic dialogue as a ritual of emotional purification

    Get PDF
    Abstract In the present paper, the role that emotions play in Socratic self-care, as it can be reconstructed from Plato's dialogues, is investigated and explored. In highlighting the fundamental role that emotions play in such a care, which is not mere repair of a fault (reparative care), but an active and constant attending to self- and others' improvement, it is emphasized how the Socratic care that is enacted in the Selected Dialogues exhibits marked religious qualities, which make Socrates a kind of priestly and demonic figure, as the reader can infer in particular from the two chapters devoted to the Critique and the Apology, respectively. The intent underlying this focus on the religious and especially initiatory aspects of Socratic care in the Platonic dialogues is, as explained at the beginning of the introduction to this work, to deepen the link between the emotional aspect of self-care, explored in depth by Professor L. Napolitano, and my personal interest in the relationship between philosophy and religion. In the present work this link has been found in the theme of 'aporia; this is interpreted in the introduction and in the following chapters as ritual death, that is, as an 'experience in which the initiate (in this case Socrates' interlocutor) witnesses his own death, that is, the disappearance of the firm attachment to his unreflective opinions. It follows that 'aporia is a positive element of self-care, since this ritual death makes it possible, if it is accepted and not rejected, to get rid of those obstacles from within that prevent one from looking forward to one's own improvement and the pursuit of happiness. Aporia is not only a logical impasse, but also an emotionally very dense moment; it therefore holds together the two fundamental components of this work, the focus on emotions in the Socratic dialogue and the focus on the initiatory aspects with which Plato cloaks this dialogue. Plato alludes to these initiatory aspects from time to time in the selected dialogues by appropriating now from Coribantism (Euthydemus), now from Orphism (Phaedo), now even from the rituals of transition from one age to another (the ephebia, as in the case of the Alcibiades); all these disparate experiences have in common the idea of a ritual death, a liminal phase between one life (the one about to leave) and the new one (about to embark on). In the Socratic dialogue enacted in Plato's works, precisely this initiatory death (the aporia) is II achieved; if the interlocutor accepts it, he or she will progress on the path of self care; if he or she is afraid or annoyed by it, he or she will derive no benefit. The introduction outlines the assumptions on which the following analysis are based: the first is the ritual and initiatory nature of refutation and the characterization of aporia as an emotionally connoted moment; the second, based on the analysis of the first book of the Republic, is the relational nature of caring and thus of the good that caring/caretaking pursues; therefore, one who cares for others necessarily also cares for himself. The intertwining of the ritual and emotional aspects, as well as the communal and relational nature of the good pursued by Socratic caring, is explored throughout the introduction and, more importantly, eight chapters, devoted to Euthydemus, Charmides, Alcibiades I, Lysis, Euthyphro, Apology, Critique, and Phaedo, respectively. In the introduction to the thesis, the reason for the choice of these dialogues is explained and what are the relationships between them in this work. In the conclusion, the scientific and especially moral reasons for the importance of emphasizing the role of emotions in Plato's Socrates and the ritual aspects of it are made clea

    Covering and Separation for Permutations and Graphs

    Get PDF
    This is a thesis of two parts, focusing on covering and separation topics of extremal combinatorics and graph theory, two major themes in this area. They entail the existence and properties of collections of combinatorial objects which together either represent all objects (covering) or can be used to distinguish all objects from each other (separation). We will consider a range of problems which come under these areas. The first part will focus on shattering k-sets with permutations. A family of permutations is said to shatter a given k-set if the permutations cover all possible orderings of the k elements. In particular, we investigate the size of permutation families which cover t orders for every possible k-set as well as study the problem of determining the largest number of k-sets that can be shattered by a family with given size. We provide a construction for a small permutation family which shatters every k-set. We also consider constructions of large families which do not shatter any triple. The second part will be concerned with the problem of separating path systems. A separating path system for a graph is a family of paths where, for any two edges, there is a path containing one edge but not the other. The aim is to find the size of the smallest such family. We will study the size of the smallest separating path system for a range of graphs, including complete graphs, complete bipartite graphs, and lattice-type graphs. A key technique we introduce is the use of generator paths - constructed to utilise the symmetric nature of Kn. We continue this symmetric approach for bipartite graphs and study the limitations of the method. We consider lattice-type graphs as an example of the most efficient possible separating systems for any graph

    A Political Theory of Engineered Systems and A Study of Engineering and Justice Workshops

    Get PDF
    Since there are good reasons to think that some engineered systems are socially undesirable—for example, internal combustion engines that cause climate change, algorithms that are racist, and nuclear weapons that can destroy all life—there is a well-established literature that attempts to identify best practices for designing and regulating engineered systems in order to prevent harm and promote justice. Most of this literature, especially the design theory and engineering justice literature meant to help guide engineers, focuses on environmental, physical, social, and mental harms such as ecosystem and bodily poisoning, racial and gender discrimination, and urban alienation. However, the literature that focuses on how engineered systems can produce political harms—harms to how we shape the way we live in community together—is not well established. The first part of this thesis contributes to identifying how particular types of engineered systems can harm a democratic politics. Building on democratic theory, philosophy of collective harms, and design theory, it argues that engineered systems that extend in space and time beyond a certain threshold subvert the knowledge and empowerment necessary for a democratic politics. For example, the systems of global shipping and the internet that fundamentally shape our lives are so large that people cannot attain the knowledge necessary to regulate them well nor the empowerment necessary to shape them. The second part of this thesis is an empirical study of a workshop designed to encourage engineering undergraduates to understand how engineered systems can subvert a democratic politics, with the ultimate goal of supporting students in incorporating that understanding into their work. 32 Dartmouth undergraduate engineering students participated in the study. Half were assigned to participate in a workshop group, half to a control group. The workshop group participants took a pretest; then participated in a 3-hour, semi-structured workshop with 4 participants per session (as well as a discussion leader and note-taker) over lunch or dinner; and then took a posttest. The control group participants took the same pre- and post- tests, but had no suggested activity in the intervening 3 hours. We find that the students who participated in workshops had a statistically significant test-score improvement as compared to the control group (Brunner-Munzel test, p \u3c .001). Using thematic analysis methods, we show the data is consistent with the hypothesis that workshops produced a score improvement because of certain structure (small size, long duration, discussion-based, over homemade food) and content (theoretically rich, challenging). Thematic analysis also reveals workshop failures and areas for improvement (too much content for the duration, not well enough organized). The thesis concludes with a discussion of limitations and suggestions for future theoretical, empirical, and pedagogical research

    Logical disagreement : an epistemological study

    Get PDF
    While the epistemic significance of disagreement has been a popular topic in epistemology for at least a decade, little attention has been paid to logical disagreement. This monograph is meant as a remedy. The text starts with an extensive literature review of the epistemology of (peer) disagreement and sets the stage for an epistemological study of logical disagreement. The guiding thread for the rest of the work is then three distinct readings of the ambiguous term ‘logical disagreement’. Chapters 1 and 2 focus on the Ad Hoc Reading according to which logical disagreements occur when two subjects take incompatible doxastic attitudes toward a specific proposition in or about logic. Chapter 2 presents a new counterexample to the widely discussed Uniqueness Thesis. Chapters 3 and 4 focus on the Theory Choice Reading of ‘logical disagreement’. According to this interpretation, logical disagreements occur at the level of entire logical theories rather than individual entailment-claims. Chapter 4 concerns a key question from the philosophy of logic, viz., how we have epistemic justification for claims about logical consequence. In Chapters 5 and 6 we turn to the Akrasia Reading. On this reading, logical disagreements occur when there is a mismatch between the deductive strength of one’s background logic and the logical theory one prefers (officially). Chapter 6 introduces logical akrasia by analogy to epistemic akrasia and presents a novel dilemma. Chapter 7 revisits the epistemology of peer disagreement and argues that the epistemic significance of central principles from the literature are at best deflated in the context of logical disagreement. The chapter also develops a simple formal model of deep disagreement in Default Logic, relating this to our general discussion of logical disagreement. The monograph ends in an epilogue with some reflections on the potential epistemic significance of convergence in logical theorizing

    Quantum-Classical hybrid systems and their quasifree transformations

    Get PDF
    The focus of this work is the description of a framework for quantum-classical hybrid systems. The main emphasis lies on continuous variable systems described by canonical commutation relations and, more precisely, the quasifree case. Here, we are going to solve two main tasks: The first is to rigorously define spaces of states and observables, which are naturally connected within the general structure. Secondly, we want to describe quasifree channels for which both the Schrödinger picture and the Heisenberg picture are well defined. We start with a general introduction to operator algebras and algebraic quantum theory. Thereby, we highlight some of the mathematical details that are often taken for granted while working with purely quantum systems. Consequently, we discuss several possibilities and their advantages respectively disadvantages in describing classical systems analogously to the quantum formalism. The key takeaway is that there is no candidate for a classical state space or observable algebra that can be put easily alongside a quantum system to form a hybrid and simultaneously fulfills all of our requirements for such a partially quantum and partially classical system. Although these straightforward hybrid systems are not sufficient enough to represent a general approach, we use one of the candidates to prove an intermediate result, which showcases the advantages of a consequent hybrid ansatz: We provide a hybrid generalization of classical diffusion generators where the exchange of information between the classical and the quantum side is controlled by the induced noise on the quantum system. Then, we present solutions for our initial tasks. We start with a CCR-algebra where some variables may commute with all others and hence generate a classical subsystem. After clarifying the necessary representations, our hybrid states are given by continuous characteristic functions, and the according state space is equal to the state space of a non-unital C*-algebra. While this C*-algebra is not a suitable candidate for an observable algebra itself, we describe several possible subsets in its bidual which can serve this purpose. They can be more easily characterized and will also allow for a straightforward definition of a proper Heisenberg picture. The subsets are given by operator-valued functions on the classical phase space with varying degrees of regularity, such as universal measurability or strong*-continuity. We describe quasifree channels and their properties, including a state-channel correspondence, a factorization theorem, and some basic physical operations. All this works solely on the assumption of a quasifree system, but we also show that the more famous subclass of Gaussian systems fits well within this formulation and behaves as expected

    Counterexample Guided Abstraction Refinement with Non-Refined Abstractions for Multi-Agent Path Finding

    Full text link
    Counterexample guided abstraction refinement (CEGAR) represents a powerful symbolic technique for various tasks such as model checking and reachability analysis. Recently, CEGAR combined with Boolean satisfiability (SAT) has been applied for multi-agent path finding (MAPF), a problem where the task is to navigate agents from their start positions to given individual goal positions so that the agents do not collide with each other. The recent CEGAR approach used the initial abstraction of the MAPF problem where collisions between agents were omitted and were eliminated in subsequent abstraction refinements. We propose in this work a novel CEGAR-style solver for MAPF based on SAT in which some abstractions are deliberately left non-refined. This adds the necessity to post-process the answers obtained from the underlying SAT solver as these answers slightly differ from the correct MAPF solutions. Non-refining however yields order-of-magnitude smaller SAT encodings than those of the previous approach and speeds up the overall solving process making the SAT-based solver for MAPF competitive again in relevant benchmarks

    Computing torsion for plane quartics without using height bounds

    Full text link
    We describe an algorithm that provably computes the rational torsion subgroup of the Jacobian of a curve without relying on height bounds. Instead, it relies on computing torsion points over small number fields. Both complex analytic and Chinese remainder theorem based methods are used to find such torsion points. The method has been implemented in Magma and used to provably compute the rational torsion subgroup for more than 98% of Jacobians of curves in a dataset due to Sutherland consisting of 82240 plane quartic curves.Comment: Copy of Magma code and data file repository included as ancillary file. Comments always welcome

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

    Get PDF
    LIPIcs, Volume 251, ITCS 2023, Complete Volum
    corecore