Giải quyết biến đổi khí hậu và ô nhiễm môi trường đang và sẽ là thách thức lớn của nhân loại trong thế kỷ 21. Con người không còn nhiều thời gian để sửa chữa, phục hồi đưa hệ sinh thái môi trường (tự nhiên) trở về trạng thái an toàn. Trong khi các nỗ lực trong thời gian qua chưa thực sự hiệu quả thì COP26 mở ra cơ hội lớn để nhân loại tiến gần đến mục tiêu kiềm (...) chế nhiệt độ của trái đất không vượt quá 1.5 độ C. Mặc dù Việt Nam cùng với 146 quốc gia trên thế giới đã có cam kết mạnh mẽ nhất trong việc giảm phát thải vào năm 2050, tuy nhiên việc cụ thể hóa cam kết thông qua các giải pháp sáng tạo là rất quan trọng. Sử dụng (áp dụng, vận dụng) hệ sáng tạo 3D và nguyên lý bán dẫn giá trị, tác giả đề xuất hệ sinh thái “giải pháp trụ cột” cần thực hiện gồm có tăng cường thông tin, truyền thông, nghiên cứu khoa học về môi trường (biến đổi khí hậu, ô nhiễm môi trường...); xây dựng, chuyển đổi và nâng cao văn hóa và môi trường; đẩy mạnh phát triển kinh tế gia tăng phúc lợi; xây dựng (chuyển đổi) lớp doanh nhân có văn hóa, trách nhiệm môi trường; tăng cường mở rộng sự hợp tác quốc tế về mọi mặt đặc biệt là trong lĩnh vực kinh tế, truyền thông và khoa học; và thực thi các giải pháp nêu trên một cách kỷ luật. (shrink)

Cải tiến phương pháp lượng giá tài nguyên và di sản sử dụng nguyên lý bán dẫn giá trị và hệ xử lý thông tin SM3D. Lý thuyết sử dụng trong bài: • Total economic value (Adger et al., 1995) • Mindsponge theory (Quan-Hoang Vuong, 2023) và khung ra quyết định mindspongeconomics (Khuc, 2022) • Tháp văn hóa (Khuc, 2023) • Lý thuyết nguyên lý bán dẫn giá trị (Q.-H. Vuong, 2021) • Hệ xử lý thông tin (lý (...) thuyết quản trị tri thức) SM3D (Nguyen, 2023; Q. H. Vuong et al., 2022) . (shrink)

Cảm xúc là yếu tố cơ bản thúc đẩy con người đưa ra quyết định và xử lý thông tin. Sợ hãi là một trong những cảm xúc phổ biến nhất ảnh hưởng đến hành vi của nhà đầu tư cá nhân trên thị trường chứng khoán. Mặc dù nhiều nghiên cứu đã được thực hiện để khám phá tác động của nỗi sợ hãi đối với hiệu quả đầu tư và hành vi giao dịch của nhà đầu tư (...) cá nhân, nhưng vẫn còn rất ít thông tin về các yếu tố ảnh hưởng đến nỗi sợ hãi của nhà đầu tư cá nhân trong thời kỳ thị trường sụt giảm (hoặc những giai đoạn cực kỳ biến động). Vì thế, nghiên cứu này được thực hiện để tìm hiểu liệu các nguồn thông tin ảnh hưởng đến quyết định đầu tư của nhà đầu tư có ảnh hưởng đến sự sợ hãi của họ khi khủng hoảng xảy ra hay không. Nghiên cứu đã sử dụng phương pháp phân tích Bayesian Mindsponge Framework (BMF) trên bộ dữ liệu từ 1526 nhà đầu tư Trung Quốc và Việt Nam. Kết quả nghiên cứu chỉ ra rằng các nhà đầu tư tiếp cận các loại thông tin khác nhau khi đưa ra quyết định đầu tư sẽ ảnh hưởng đến tần suất phản ứng sợ hãi khác nhau. Cụ thể, các nhà đầu tư tham khảo thông tin từ chuyên gia hoặc tự phân tích khi đưa ra quyết định đầu tư ít bị đóng băng (biểu hiện của tâm lý sợ hãi) hơn trong thời kỳ thị trường sụt giảm. Ngược lại, những người đưa ra quyết định đầu tư dựa trên thông tin từ người quen hay bạn bè và trực giác sẽ bị đóng băng thường xuyên hơn. Kết quả nghiên cứu này giúp gợi ý nhà đầu tư cá nhân nên trang bị cho mình các kiến thức về tài chính cũng như tham khảo các ý kiến chuyên gia trên thị trường, hoặc những nguồn thông tin đáng tin cậy, khi đưa ra quyết định đầu tư. Bên cạnh đó, cơ quan quản lý thị trường cần có hoạt động phổ cập kiến thức về thị trường chứng khoán, hạn chế ảnh hưởng của các kênh thông tin không chính thống, và khuyến khích nhà đầu tư ít kinh nghiệm mua chứng chỉ quỹ của các quỹ đầu tư. (shrink)

Hiện tại, hệ thống JSTOR đã có một giao diện web rất thân thiện. Họ cũng đã tăng cường các mục thông tin bài vở phổ thông, có tính cách phổ biến cập nhật thông tin khoa học. Nhiều thông tin khai thác từ lịch sử dữ liệu hàn lâm cũng rất lý thú, nhờ vào hệ thống lớn tích lũy lâu ngày của 2600 tạp chí hàn lâm hàng đầu, từ 1200 nhà xuất bản của (...) 57 quốc gia. (shrink)

Dưới đây là một số quan sát từ dữ liệu giao dịch trái phiếu sơ cấp từ hệ thống thông tin trực tuyến của Sở Giao dịch Chứng khoán Hà Nội (HNX). HNX đảm nhiệm chức năng giao dịch sơ cấp tập trung đối với thị trường trái phiếu chính phủ.

This paper is a discussion note on Isaacs et al. (2022), who have claimed to offer a new motivation for imprecise probabilities, based on the mathematical phenomenon of non-measurability. In this note, I clarify some consequences of their proposal. In particular, I show that if their proposal is applied to a bounded 3-dimensional space, then they have to reject at least one of the following: (i) If A is at most as probable as B and B is at most as (...) probable as C, then A is at most as probable as C. (ii) Let A ∩ C = B ∩ C = ∅. A is at most as probable as B iff (A ∪ C) is at most as probable as (B ∪ C). But rejecting either statement seems unattractive. (shrink)

In this paper, we rigorously prove the existence of type-level ordered pairs in Quine’s New Foundations with atoms, augmented by the axiom of infinity and the axiom of choice (NFU + Inf + AC). The proof uses the cardinal squaring principle; more precisely, its instance for the (infinite) universe (VCSP), which is a theorem of NFU + Inf + AC. Therefore, we have a justification for proposing a new axiomatic extension of NFU, in order to obtain type-level ordered pairs almost (...) from the beginning. This axiomatic extension is NFU + Inf + AC + VCSP, which is equivalent to NFU + Inf + AC, but easier to reason about. (shrink)

The main feature of NF/NFU is the notion of stratification, which sets it apart from other set theories. We define stratification and prove constructively that every stratified formula has the (unique) least assignment of types. The basic notion of stratification is concerned only with variables, but we extend it to abstraction terms in order to simplify further development. We reflect on nested abstraction terms, proving that they get the expected types. These extensions enable us to check whether some complex formula (...) is stratified without rewriting it in the basic language. We also introduce natural numbers and a variant of the axiom of infinity, in order to precisely introduce type level ordered pairs, which are crucial in simplifying the definitions in the last part of the article. Using these notions we can easily define the sets of ordinal and cardinal numbers, which we show at the end of the article. The same approach can be readily applied to NF. (shrink)

The filtration method is often used to prove the finite model property of modal logics. We adapt this technique to the generalized Veltman semantics for interpretability logics. In order to preserve the defining properties of generalized Veltman models, we use bisimulations to define adequate filtrations. We give an alternative proof of the finite model property of interpretability logic with respect to Veltman models, and we prove the finite model property of the systems and with respect to generalized Veltman models.

Cách mạng 4.0 đã và đang mang đến sự thay đổi lớn trong đời sống của người dân Việt Nam. Sự tiện dụng của Grab, khả năng cập nhật 24/24 của Facebook, hay sự đa dạng về nội dung của YouTube thúc đẩy xã hội tiến tới thời đại mới của khởi nghiệp điện toán (Vuong, 2019). Ở đó, mỗi cá nhân đều có cơ hội để khởi nghiệp thông qua sự kết nối đến khắp mọi nơi trên thế (...) giới của Internet và sức mạnh tính toán nằm gọn trong long bàn tay. Hiện nay, sản xuất video trên YouTube, cho thuê nhà qua AirBnb, hay chạy xe cho Grab tạo ra công việc có khả năng tạo lợi nhuận cho người tham gia thị trường, dù là người lao động, hay tổ chức cung ứng dịch vụ. (shrink)

A possibility of defining logical constants within abstract logical frameworks is discussed, in relation to abstract definition of logical consequence. We propose using duals as a general method of applying the idea of invariance under replacement as a criterion for logicality.

A phenomenon is that which appears. In his phenomenology, Jean-Luc Marion shows how a phenomenon that appears in and out of itself evades the metaphysical demand of grounding. Classical philosophy has acknowledged phenomena only in so far as they can be sanctioned by the concepts of the intellect. This holds good also of Husserl’s constitutive ego. Now, Marion distinguishes between such intuitively “poor phenomena” and the “saturated phenomena” that exceed the intentional consciousness; they are given not by the consciousness but (...) to the consciousness in an excess of intuition. This “gift of appearance” is Marion’s main concern, in the visible in general, and in painting in particular. But whereas idols only reflect our own desire to see and to be seen, icons surprise us by the gaze the saint directs on us. A picture is the scene of a possible revelation; and the revelation is nothing but the phenomenon taken in its fullest meaning: intuitive saturation at its maximum. A crucial question, nonetheless, remains: What is the relation between revelation as a phenomenological possibility, and Revelation as a theological dogma of the utmost importance? (shrink)

Rational agents seem more confident in any possible event than in an impossible event. But if rational credences are real-valued, then there are some possible events that are assigned 0 credence nonetheless. How do we differentiate these events from impossible events then when we order events? de Finetti (1975), Hájek (2012) and Easwaran (2014) suggest that when ordering events, conditional credences and subset relations are as relevant as unconditional credences. I present a counterexample to all their proposals in this paper. (...) While their proposals order possible and impossible events correctly, they deliver the wrong verdict for disjoint possible events assigned equal positive credence. (shrink)

Formalizing commonsense knowledge for reasoning about time has long been a central issue in AI. It has been recognized that the existing formalisms do not provide satisfactory solutions to some fundamental problems, viz. the frame problem. Moreover, it has turned out that the inferences drawn do not always coincide with those one had intended when one wrote the axioms. These issues call for a well-defined formalism and useful computational utilities for reasoning about time and change. Yoav Shoham of Stanford University (...) introduced in his 1986 Yale doctoral thesis an appealing temporal nonmonotonic logic and identified a class of theories, causal theories, which have computationally simple model-theoretic properties. This paper is a study towards building upon Shoham's work on causal theories. We concentrate on improving computational aspects of causal theories while preserving their model-theoretic properties. (shrink)

We extend causal theories and study actions in domains involving multiple agents. Causal theories, invented by Yoav Shoham, are based on a temporal nonmonotonic logic and have computationally tractable aspects. Since Shoham's formalism does not provide an adequate mechanism for representing simultaneous actions and specifying their consequences, we introduce the notion of counteractions while preserving the efficiency and model-theoretic properties of causal theories.

A class of Kripke models is modally definable if there is a set of modal formulas such that the class consists exactly of models on which every formula from that set is globally true. In this paper, a class is also considered definable if there is a set of formulas such that it consists exactly of models in which every formula from that set is satisfiable. The notion of modal definability is then generalized by combining these two. For thus obtained (...) types of modal definability on the level of Kripke models, we give characterization theorems in the usual form, in terms of algebraic closure conditions. As some consequences of these, various preservation results are presented. Also, some characterizations are strengthened by replacing closure under ultraproducts with closure under ultrapowers. (shrink)

New Foundations with Urelements (NFU) is a theory that extends Quine’s original theory (New Foundations) by adding “urelements” (atoms). It was discovered by Jensen in 1969, who proved that NFU is relatively consistent with Peano arithmetic and consequently with Zermelo–Fraenkel set theory (ZF). Jensen’s proof is rather hard to follow, so Boffa introduced a more straightforward method of constructing models for NFU from a model of ZF. However, Boffa’s presentation of his construction is extremely terse with many essential details omitted, (...) since he probably only wanted to emphasize the differences from Jensen’s construction. Our main goal is to elaborate on this construction in great detail, and also to prove that the said construction yields some results that are either not present in the contemporary literature, or are accepted as true at face value. Namely, besides proving that this construction gives a model for NFU, we will also use it to define models for NFU with the Axiom of Infinity, NFU with the Axiom of Choice, and NFU with both of those axioms. (shrink)

In recent years there has been an increasing interest in museum studies in exhibitions on what is termed Difficult Matters —such as rape and mass murder—and how such exhibitions may evoke ethical change. This raises the question about the conditions on which such exhibitions can lead to an ethical change. By developing a conceptual framework this article contributes to museum studies on Difficult Matters demonstrating how vulnerability can work as a key concept in a relational pedagogical understanding of the conditions (...) for ethical change. Inspired by feminist ethics the article suggests that there is an “ambivalent potentiality” of the concept of vulnerability and forwards a double perspective on vulnerability as condition: vulnerability is inherent to the human condition and always situational. From this point of departure vulnerability is fleshed out as a key concept in museum pedagogy via pedagogical thinkers inspired by the philosopher Emmanuel Lévinas’ ethics. Concepts like heteronomy, incarnation, Face and Saying/Said are introduced to define vulnerability and the relation between exhibition and visitor is defined as a teaching–learning relation conditioned by vulnerability. Vulnerability is defined as openness to an encounter with the Other as being different, which is conditional of an ethical transformation of existing perceptions of self, others and the world. Finally, inspired by feminist philosophy a norm critical is introduced. It is argued that displaying Difficult Matters in order to evoke an ethical transformation museum professionals need consider critically the norms of vulnerability at play in particular situations. On this basis, the concept of vulnerability can serve as a lever for discussions on the pedagogy of exhibitions on Difficult Matters and the ethical responsibility of museum professionals in public museums in this regard. (shrink)

We can formalize judgments as logical formulas. Judgment aggregation deals with judgments of several agents, which need to be aggregated to a collective judgment. There are several logical formalizations of judgment aggregation. This paper focuses on a modal formalization which nicely expresses classical properties of judgment aggregation rules and famous results of social choice theory, like Arrow’s impossibility theorem. A natural deduction system for modal logic of judgment aggregation is presented in this paper. The system is sound and complete. As (...) an example of derivation, a formal proof of Arrow’s impossibility theorem is given. (shrink)

After a review of situation theory and previous attempts at 'computational' situation theory, we present a new programming environment, BABY-SIT, which is based on situation theory. We then demonstrate how problems requiring formal temporal reasoning can be solved in this framework. Specifically, the Yale Shooting Problem, which is commonly regarded as a canonical problem for nonmonotonic temporal reasoning, is implemented in BABY-SIT using Yoav Shoham's causal theories.

Recently, there have been some attempts towards developing programming languages based on situation theory. These languages employ situation-theoretic constructs with varying degrees of divergence from the ontology of the theory. In this paper, we review three of these programming languages.

Serious thinking about the computational aspects of situation theory is just starting. There have been some recent proposals in this direction (viz. PROSIT and ASTL), with varying degrees of divergence from the ontology of the theory. We believe that a programming environment incorporating bona fide situation-theoretic constructs is needed and describe our very recent BABY-SIT implementation. A detailed critical account of PROSIT and ASTL is also offered in order to compare our system with these pioneering and influential frameworks.

While situation theory and situation semantics provide an appropriate framework for a realistic model-theoretic treatment of natural language, serious thinking on their 'computational' aspects has just started. Existing proposals mainly offer a Prolog- or Lisp-like programming environment with varying degrees of divergence from the ontology of situation theory. In this paper, we introduce a computational medium (called BABY-SIT) based on situations. The primary motivation underlying BABY-SIT is to facilitate the development and testing of programs in domains ranging from linguistics to (...) artificial intelligence in a unified framework built upon situation-theoretic constructs. (shrink)

Situation theory has been developed over the last decade and various versions of the theory have been applied to a number of linguistic issues. However, not much work has been done in regard to its computational aspects. In this paper, we review the existing approaches towards 'computational situation theory' with considerable emphasis on our own research.

While situation theory and situation semantics provide an appropriate framework for a realistic model-theoretic treatment of natural language, serious thinking on their 'computational' aspects has only recently started. Existing proposals mainly offer a Prolog- or Lisp-like programming environment with varying degrees of divergence from the ontology of situation theory. In this paper, we introduce a computational medium (called BABY-SIT) based on situations. The primary motivation underlying BABY-SIT is to facilitate the development and testing of programs in domains ranging from linguistics (...) to artificial intelligence in a unified framework built upon situation-theoretic constructs. (shrink)

We describe a novel approach to the analysis of pronominal anaphora in Turkish. A computational medium which is based on situation theory is used as our implementation tool. The task of resolving pronominal anaphora is demonstrated in this environment which employs situation-theoretic constructs for processing.

This note follows up an earlier paper in which a possibility of defining logical constants within abstract logical frameworks was discussed, by using duals as a general method of applying the idea of invariance under replacement as a criterion for logicality. In the present note, this approach is applied to the discussion on logicality of generalized quantifiers. It is demonstrated that generalized quantifiers are logical constants by this criterion.

Sobre la base de una línea interpretativa propiciada por la misma doctrina de Plotino, este trabajo pretende estudiar el problema que conlleva el fin último del alma humana en vista de su ascenso hacia el Uno-Bien. En varios pasajes de su obra, el filósofo sostiene que, conociendo el propio sí-mismo, se puede tomar contacto con un principio supremo, anterior incluso a la potencia intelectiva, en virtud de cuya visión es dable gozar de un amor sin medida. El remate en la (...) unificación no depende en última instancia del acierto racional, sino de concordar en el mismo centro con aquello de semejante al Uno-Bien que hay en el alma. Estas distinciones abonarían la posibilidad de una unión mística dentro del sistema plotiniano. Sin embargo, desde el punto de vista epistemológico, el estatuto místico es controvertido y plantea una serie dificultades teóricas que es necesario dilucidar. Para el análisis de los tópicos mentados se desarrolla una lectura a la vez hermenéutica y crítica tanto de las fuentes como de la bibliografía erudita. (shrink)

The current study aimed to investigate the extent to which familial history of reading and math difficulties have an impact on children’s academic outcomes within a 3-year longitudinal study, which evaluated their core reading and math skills after first and second grades, as well as performance on complex academic tasks after second and third grades. At baseline, parents were asked to complete the Adult Reading History Questionnaire and its adaption, Adult Math History Questionnaire, to index familial history of reading and (...) math difficulties, respectively. Preliminary findings established the psychometric properties of the AMHQ, suggesting that it is a reliable and valid scale. Correlation analyses indicated that the ARHQ was negatively associated with children’s reading skills, whereas the AMHQ was negatively related to math outcomes. Path results revealed that the ARHQ predicted children’s performance on complex reading tasks indirectly via their core reading skills, and the AMHQ was linked to complex math outcomes indirectly via core math abilities. The ARHQ was also found to be negatively correlated with measures of children’s math performance, with path findings suggesting that these relations were indirectly explained by differences in their core reading skills. These results suggest that assessing familial risk for academic difficulties may be crucial to understanding comorbid etiological and developmental associations between reading and math differences. (shrink)

A 4-valued framework is proposed to distinguish intuitionistically valid formulas within classical validities.

We prove an existential analogue of the Goldblatt‐Thomason Theorem which characterizes modal definability of elementary classes of Kripke frames using closure under model theoretic constructions. The less known version of the Goldblatt‐Thomason Theorem gives general conditions, without the assumption of first‐order definability, but uses non‐standard constructions and algebraic semantics. We present a non‐algebraic proof of this result and we prove an analogous characterization for an alternative notion of modal definability, in which a class is defined by formulas which are satisfiable (...) under any valuation (the so‐called existential validity). Continuing previous work in which model theoretic characterization for this type of definability of elementary classes was proved, we give an analogous general result without the assumption of the first‐order definability. Furthermore, we outline relationships between sets of existentially valid formulas corresponding to several well‐known modal logics. (shrink)

Over the past six decades, Antarctic Treaty Consultative Parties have developed legal agreements to protect various aspects of the Antarctic environment. Strong anthropocentrism (e.g., unsustainable harvesting of marine living resources) is generally rejected, and stewardship (e.g., minimizing risks of contamination) is accepted while protection of nonanthropocentric values (e.g., wilderness and intrinsic values) is evoked when it furthers human interests. As one of the world’s remaining large wildernesses, Antarctica is under threat from the continuous expansion of the human footprint and is (...) in need of attention from the wider society, including the environmental ethics community. The interdependence of all life on this planet means that problems in Antarctica are not as far away and trivial as it may seem. Furthermore, Antarctica’s extreme position at the edge of civilization challenges humans as moral agents to think about where our moral duties and rights begin and end on this planet, and elsewhere in the universe. Considerations of wilderness and intrinsic values, equity, and abiotic ethics are some of the issues that environmental ethics can contribute toward the protection of the Antarctic wilderness. (shrink)

This paper introduces a new theory of constant regions, which generalizes that of interstices, in nonstandard models of arithmetic. In particular, we show that two homogeneity notions introduced by Richard Kaye and the author, namely, constantness and pregenericity, are equivalent. This led to some new characterizations of generic cuts in terms of existential closedness.

Recent decades have witnessed widespread agrarian transitions in mainland Southeast Asia. This paper examines how agrarian transitions are shaped by multiple drivers of change, and how these interwoven processes have triggered shifts in agricultural extension practices in three countries in the Lower Mekong Basin: Laos, Cambodia, and Vietnam. Drawing on interviews with experts working on the fields of agrarian studies and rural development, this paper argues that agrarian transitions not only put a strain on agricultural extension systems in responding to (...) evolving needs, but they also stimulate the co-production of innovative agricultural extension models to address gaps left by the limited presence of extensionists. The study gains insight into challenges faced by extensionists, including a lack of resources, skills, and capacities to meet growing needs, which simultaneously urged them to excel in their work performance. The paper highlights the proactive role of ‘champions’ in orchestrating collective efforts towards the co-production of innovative agricultural extension models (e.g. Metkasekor), and the formulation of pluralistic extension platforms in enabling such ‘co-learning-to-act’ practices. By translating these insights into the broader contexts of agricultural and rural development in the Mekong region and beyond, this paper aims to make a two-fold contribution. First, it will assert how the ‘business-as-usual’ extension model has failed to adequately address emerging needs as a result of agrarian transitions. Second, it will provide pathways for the recognition and legitimisation of the pluralistic extension approach that fosters stakeholders’ co-learning and productive engagement in extension practices. (shrink)

China’s phenomenal economic development since 1979 has caught the attention and envy of the rest of the world. 500 million Chinese have been lifted out of poverty since then.1 Yet, it has come with a huge price which threatens not only China but the rest of the world. These challenges include corruption, environmental issues, social inequalities and a rapidly aging population. If China is not able to overcome any of these, then its development will not be sustainable and the impact (...) will be immensely negative just as its development over the last three decades have been positive on the rest of the world. The purpose of this article is to show that there is a little-known transformation happening in China which may address the above issues. It is the thesis of the author that China’s present developmental challenges are fundamentally a problem of misplaced values, i.e. unsustainable priorities. And the little known transformation is that tens of millions of Chinese are quickly embracing a new set of values and accepting a biblical worldview.2 Rodney Stark, socialogist and popular author, has shown through his many works, such as For the Glory of God: How Monotheism Led to Reformations, Science, Witch-Hunts, and the End of Slavery,3 that societies which have espoused the monotheistic belief system are able to successfully overcome similar social challenges and remain viable. (shrink)

In a fair finite lottery with n tickets, the probability assigned to each ticket winning is 1/n and no other answer. That is, 1/n is unique. Now, consider a fair lottery over the natural numbers. What probability is assigned to each ticket winning in this lottery? Well, this probability value must be smaller than 1/n for all natural numbers n. If probabilities are real-valued, then there is only one answer: 0, as 0 is the only real and non-negative value that (...) is smaller than 1/n for all natural numbers n. However, this answer seems counter-intuitive, as it violates Regularity: for all possible events A that are assigned a probability, A is assigned a positive probability. It is possible for ticket i to win in the second lottery. So, the set {i} should be assigned a positive probability and not 0. Consequently, in order to satisfy Regularity, probabilities must be allowed to take on `non-real' values, e.g. a positive infinitesimal x that is smaller than 1/n for all natural numbers n. So, what regular probability is assigned to {i} in the second lottery? This probability value must be positive but smaller than 1/n for all natural numbers n. Given the definition of x, x is a correct answer. But x isn't unique, because every other positive infinitesimal is a correct answer as well and there are uncountably many positive infinitesimals. After all, every positive infinitesimal is strictly between 0 and 1/n for all natural numbers n. Nothing about a fair lottery over the natural numbers uniquely determines x as the correct answer and nothing about the lottery rules out other positive infinitesimals as a correct answer as well. What probability to assign to {i} is underdetermined. -/- In this thesis, I explore this difference between fair finite lotteries and fair infinite lotteries. The constraints governing the former uniquely determine the probabilities assigned to events in those lotteries, but this isn't true for the latter lotteries, when Regularity is a constraint on probabilities. Now, although there are uncountably many correct probability values that can be assigned to {i} in the second lottery, there are some applications of probability theory, for which at least one correct probability value must be chosen in order to accomplish that application, e.g. calculation of expected utilities. In this thesis, I spell out sufficient conditions for when a choice like that is problematic. These conditions apply to precise probabilities, imprecise probabilities, and qualitative probabilities. So, I will consider Benci et al. (2018)'s and Pruss (2021)'s suggestion of allowing probabilities to be imprecise, as well as resorting to qualitative probabilities, to overcome the choice problem. I will argue that both don't solve the problem. Furthermore, there's a hitherto unnoticed difficulty in deriving imprecise probabilities by supervaluating over precise `non-real' probability values. To avoid this difficulty, precise probability values should be real-valued. Thus, Regularity cannot be a constraint on probabilities. But as it turns out, dropping Regularity as a constraint and requiring precise probabilities to be real-valued solve the choice problem. (shrink)

This paper starts by investigating Ackermann's interpretation of finite set theory in the natural numbers. We give a formal version of this interpretation from Peano arithmetic (PA) to Zermelo-Fraenkel set theory with the infinity axiom negated (ZF−inf) and provide an inverse interpretation going the other way. In particular, we emphasize the precise axiomatization of our set theory that is required and point out the necessity of the axiom of transitive containment or (equivalently) the axiom scheme of ∈-induction. This clarifies the (...) nature of the equivalence of PA and ZF−inf and corrects some errors in the literature. We also survey the restrictions of the Ackermann interpretation and its inverse to subsystems of PA and ZF−inf, where full induction, replacement, or separation is not assumed. The paper concludes with a discussion on the problems one faces when the totality of exponentiation fails, or when the existence of unordered pairs or power sets is not guaranteed. (shrink)

Interpretability logic is a modal formalization of relative interpretability between first‐order arithmetical theories. Verbrugge semantics is a generalization of Veltman semantics, the basic semantics for interpretability logic. Bisimulation is the basic equivalence between models for modal logic. We study various notions of bisimulation between Verbrugge models and develop a new one, which we call w‐bisimulation. We show that the new notion, while keeping the basic property that bisimilarity implies modal equivalence, is weak enough to allow the converse to hold in (...) the finitary case. To do this, we develop and use an appropriate notion of bisimulation games between Verbrugge models. (shrink)

Australia’s punitive policy towards people seeking asylum deliberately causes severe psychological harm and meets recognised definitions of torture. Consequently, there is a tension between doctors’ obligation not to be complicit in torture and doctors’ obligation to provide best possible care to their patients, including those seeking asylum. In this paper, we explore the nature of complicity and discuss the arguments for and against a proposed call for doctors to boycott working in immigration detention. We conclude that a degree of complicity (...) is unavoidable when working in immigration detention, but that it may be ethically justifiable. We identify ways to minimise the harms associated with complicity and argue that it is ethical to continue working in immigration detention as long as due care and attention is paid to minimising the harms of complicity. (shrink)