Large cardinals arising from the existence of arbitrarily long end elementary extension chains over models of set theory are studied here. In particular, we show that the large cardinals obtained in this fashion (`unfoldable cardinals') lie in the boundary of the propositions consistent with `V = L' and the existence of 0 ♯ . We also provide an `embedding characterisation' of the unfoldable cardinals and study their preservation and destruction by various forcing constructions.

We study notions of independence appropriate for a stability theory of metric abstract elementary classes (for short, MAECs). We build on previous notions used in the discrete case, and adapt definitions to the metric case. In particular, we study notions that behave well under superstability‐like assumptions. Also, under uniqueness of limit models, we study domination, orthogonality and parallelism of Galois types in MAECs.

We study versions of limit models adapted to the context of metric abstract elementary classes. Under categoricity and superstability-like assumptions, we generalize some theorems from 7, 15-17. We prove criteria for existence and uniqueness of limit models in the metric context.

A long series of conversations interweaving mathematical, historical and philosophical aspects of categoricity in model theory took place between the author and Saharon Shelah in 2016 and 2017. In this excerpt of that long conversation, we explore the relationship between explicit and implicit aspects of categoricity. We also discuss the connection with definability issues.

We prove the following main theorem: Let be an abstract elementary class satisfying the joint embedding and the amalgamation properties with no maximal models of cardinality μ. Let μ be a cardinal above the the Löwenheim‐Skolem number of the class. If is μ‐Galois‐stable, has no μ‐Vaughtian Pairs, does not have long splitting chains, and satisfies locality of splitting, then any two ‐limits over M, for, are isomorphic over M.

The existence of End Elementary Extensions of models M of ZFC is related to the ordinal height of M, according to classical results due to Keisler, Morley and Silver. In this paper, we further investigate the connection between the height of M and the existence of End Elementary Extensions of M. In particular, we prove that the theory `ZFC + GCH + there exist measurable cardinals + all inaccessible non weakly compact cardinals are possible heights of models with no End (...) Elementary Extensions' is consistent relative to the theory `ZFC + GCH + there exist measurable cardinals + the weakly compact cardinals are cofinal in ON'. We also provide a simpler coding that destroys GCH but otherwise yields the same result. (shrink)

We provide here the first steps toward a Classification Theory ofElementary Classes with no maximal models, plus some mild set theoretical assumptions, when the class is categorical in some λ greater than its Löwenheim-Skolem number. We study the degree to which amalgamation may be recovered, the behaviour of non μ-splitting types. Most importantly, the existence of saturated models in a strong enough sense is proved, as a first step toward a complete solution to the o Conjecture for these classes. Further (...) results are in preparation. (shrink)

We prove a version of a small index property theorem for strong amalgamation classes. Our result builds on an earlier theorem by Lascar and Shelah. We then study versions of the small index property for various non-elementary classes. In particular, we obtain the small index property for quasiminimal pregeometry structures.

In this article we present a notion of “logical perfection”. We first describe through examples a notion oflogical perfectionextracted from the contemporary logical concept of categoricity. Categoricity (in power) has become in the past half century a main driver of ideas in model theory, both mathematically (stability theory may be regarded as a way of approximating categoricity) and philosophically. In the past two decades, categoricity notions have started to overlap with more classical notions of robustness and smoothness. These have been (...) crucial in various parts of mathematics since the nineteenth century. We postulate and present the category of logical perfection. We draw on various notions of perfection from mathematics of the 19th and 20th centuries and then trace the relation to the concept of categoricity in power as a logical notion of what a “mathematically perfect” structure is. (shrink)

In recent years, mathematical logic has developed in many directions, the initial unity of its subject matter giving way to a myriad of seemingly unrelated areas. The articles collected here, which range from historical scholarship to recent research in geometric model theory, squarely address this development. These articles also connect to the diverse work of Väänänen, whose ecumenical approach to logic reflects the unity of the discipline.

Theoria, Volume 87, Issue 4, Page 870-873, August 2021.

In the paper “Categoricity in abstract elementary classes with no maximal models”, we address gaps in Saharon Shelah and Andrés Villavecesʼ proof in [4] of the uniqueness of limit models of cardinality μ in λ-categorical abstract elementary classes with no maximal models, where λ is some cardinal larger than μ. Both [4] and [5] employ set theoretic assumptions, namely GCH and Φμ+μ+).Recently, Tapani Hyttinen pointed out a problem in an early draft of [3] to Villaveces. This problem stems from (...) the proof in Shelah and Villavecesʼ [4] that reduced towers are continuous. Residues of this problem also infect the proof of Proposition II.7.2 in VanDieren [5]. We respond to the issues in Shelah and Villaveces [4] and VanDieren [5] with alternative proofs under the strengthened assumption that the abstract elementary class is categorical in μ+. (shrink)

The idea of inclusive collective decision-making is important in establishing democratic legitimacy, but it fails when citizens are excluded. Stated-preference methods of valuation, which are commonly used in economics, have been criticised because the principle of willingness to pay may exclude low-income earners who do not have the capacity to pay. Deliberative valuation has been advocated as a way to overcome this problem, but deliberation may also be exclusive. In this review, two deliberative valuation frameworks are compared. The first is (...) grounded on the idea of rational discourse that emphasises argument at the expense of other communicative strategies. It seeks to secure inclusion through procedural rules and prerequisites, but fails to address the underlying democratic limitation of argumentation. The second does not rely on the distinction between rational and rhetorical speech, and therefore admits alternative forms of communication. This approach recognises differences in the communicative capacities and practices of those who take part in deliberation, and so is better equipped to improve, though not to guarantee, inclusion. (shrink)

I defend the view that circular definitions can be useful and illuminating by focusing on the fitting-attitudes analysis of value. This definition states that an item has value if and only if it is a fitting target of attitudes. Good items are the fitting targets of positive attitudes, and bad items are the fitting targets of negative ones. I shall argue that a circular version of this definition, defended by Rabinowicz and Rønnow-Rasmussen (2006), is preferable to its non-circular counterpart and (...) upholds reasonable standards of acceptability. The standards I will be discussing come from Humberstone (1997), who claims that definitions cannot be informative as long as they are inferentially circular. (shrink)

Plagiarism is a serious, yet widespread type of research misconduct, and is often neglected in developing countries. Despite its far-reaching implications, plagiarism is poorly acknowledged and discussed in the academic setting, and insufficient evidence exists in Latin America and developing countries to inform the development of preventive strategies. In this context, we present a longitudinal case study of seven instances of plagiarism and cheating arising in four consecutive classes of an Epidemiology Masters program in Lima, Peru, and describes the implementation (...) and outcomes of a multifaceted, “zero-tolerance” policy aimed at introducing research integrity. Two cases involved cheating in graded assignments, and five cases correspond to plagiarism in the thesis protocol. Cases revealed poor awareness of high tolerance to plagiarism, poor academic performance, and widespread writing deficiencies, compensated with patchwriting and copy-pasting. Depending on the events’ severity, penalties included course failure and separation from the program. Students at fault did not engage in further plagiarism. Between 2011 and 2013, the Masters program sequentially introduced a preventive policy consisting of: intensified research integrity and scientific writing education, a stepwise, cumulative writing process; honor codes; active search for plagiarism in all academic products; and a “zero-tolerance” policy in response to documented cases. No cases were detected in 2014. In conclusion, plagiarism seems to be widespread in resource-limited settings and a greater response with educational and zero-tolerance components is needed to prevent it. (shrink)

Literature reports that depressive symptoms may precede suicidal ideation. Several studies have identified social support and substance use as moderators of this relationship. However, no study has evaluated these variables together by testing how substance use can affect the moderating effect of social support in this relationship. The purpose of this article is to individually evaluate dimensions of social support (friends, family, significant others, and school) and substance use (alcohol, marijuana, and other illicit drugs), as moderators of the relationship between (...) depressive symptoms and suicidal ideation; as well as analyze the moderating role of substance use in the moderation exerted by social support in this relationship. This study, quantitative and cross-sectional, considered 775 adolescents [Average age = 15.48 (SD = 0.96), 45.9% women], from 20 randomly selected schools in Santiago de Chile. Simple moderation models were used to analyze possible moderators separately, and double moderation models were used to analyze the moderating role of substance use in the moderating effect of social support. The results show that the four dimensions of social support moderate the relationship between depressive symptomatology and suicidal ideation, showing the strongest interaction in the case of family support, followed by support of a significant person, support at school, and support of friends, in that order. On the other hand, alcohol was the only drug that moderated the relationship in question. In addition, the results show that the use of alcohol limits the moderating effect of social support in the fields of family, significant person, and school support, but not in the case of support of friends. The use of marijuana and other illicit drugs did not affect the moderating effects of social support for any of the areas evaluated. The results are discussed according to the different roles that alcohol use can play in adolescence, and how these, together with perceived social support, are related to the emergence of suicidal ideation from depressive symptoms. (shrink)

Andres Rosler's study looks at Aristotle and the question of political obligation and its limits. Rosler takes his exploration further, considering the ethical underpinning of Aristotle's political thought, the normativity of his ethical and political theory, and the concepts of political authority and obligation themselves"--Provided by publisher.

In this paper I argue that the search for explainable models and interpretable decisions in AI must be reformulated in terms of the broader project of offering a pragmatic and naturalistic account of understanding in AI. Intuitively, the purpose of providing an explanation of a model or a decision is to make it understandable to its stakeholders. But without a previous grasp of what it means to say that an agent understands a model or a decision, the explanatory strategies will (...) lack a well-defined goal. Aside from providing a clearer objective for XAI, focusing on understanding also allows us to relax the factivity condition on explanation, which is impossible to fulfill in many machine learning models, and to focus instead on the pragmatic conditions that determine the best fit between a model and the methods and devices deployed to understand it. After an examination of the different types of understanding discussed in the philosophical and psychological literature, I conclude that interpretative or approximation models not only provide the best way to achieve the objectual understanding of a machine learning model, but are also a necessary condition to achieve post hoc interpretability. This conclusion is partly based on the shortcomings of the purely functionalist approach to post hoc interpretability that seems to be predominant in most recent literature. (shrink)

In Lukács: Praxis and the Absolute, Daniel Andrés López reassembles Lukács’s philosophy of praxis on a Hegelian basis, as a conceptual-historical totality, both defending him and proposing an unprecedented, immanent critique that raises problems for Marxian philosophy as a whole.

The paper is a critical comment on D. Hoffman. The Scrambling Theorem: A simple proof of the logical possibility of spectrum inversion. Consciousness and Cognition, 2006, 15, 31–45.

The book is an undergraduate-level introduction to first-order logic and proposi­tional modal logic. The book presents symbolic logic in a way that is pedagogi­cally attractive and formally rigorous. The main concepts are formally defined, in­formally explained, and illustrated with several examples. The book is aimed at philosophy majors and it includes discussions of several problems in the philosophy of logic.

En este artículo describiremos la vitalidad del sistema fonológico del mapudungun hablado por escolares pewenches de la Provincia del Biobío, VIII Región. Específicamente, nos hemos propuesto: a) Determinar los fonos/fonemas, y su fonotaxis, que se relevan como indicadores de vitalidad, b) Identificar las transferencias fonético-fonológicas presentes en la fonología del pewenche hablado por estos escolares y c) Interpretar las transferencias encontradas en términos del grado de vitalidad de la fonología de la lengua. La muestra está conformada por un grupo de (...) 20 escolares bilingües de entre 12 y 15 años de edad, que se encuentran cursando 7° y 8° año básico en escuelas rurales pertenecientes a dos comunidades pewenches del valle del Queuco, en la comuna de Alto Biobío. Para la recolección del material fonológico, se aplicó a los participantes una lista léxica de 65 ítems, material que se complementó con la narración oral en mapudungun de un cuento. Según nuestros datos, hemos podido constatar la existencia de una serie de rasgos fónicos en el mapudungun hablado por los escolares pewenches que obedece a la influencia de las estructuras fonológicas del castellano. Sin embargo, el grado y la difusión de los fenómenos de transferencia se desarrollan de manera heterogénea en ambas comunidades en estudio, debido, entre otros factores, a la intensidad del contacto. In this article we will describe the vitality of the phonological system Mapudungun spoken by Pewenche schoolchildren from the Biobío province, VIII Region. We intend: a) To determine the phones/phonemes, and their phonotactics, which are revealed as vitality markers. b) To identify the phonetic-phonological transferences which are present in the Pewenche spoken by these schoolchildren, and, c) To interpret the transferences found in terms of the degree of the language phonological vitality. The sample is composed of 20 bilingual schoolchildren from 12 to 15 years old, who are in 7th and 8th grade in rural primary schools belonging to two Pehuenche comunities from Valle del Queuco, in the city of Alto Biobío. To collect the phonological material, we applied a 64-item lexical list, which was complemented with the oral narration of a tale in Mapudungun. According to our data, we have been able to verify the existence of a series of phonic features in the Mapudungun spoken by Pewenche schoolchildren, which originate because of the influence of the Spanish phonological structure. However, the degree and spread of the transference phenomena develop in a heterogeneous way in both of the studied communities. due to the contact intensity, among other possible factors. (shrink)

This paper tries to simplify the situation in modern epistemology, where the scientific method seems to be accomplished by different scientific methodologies. this is partially done by asserting that the popperian critical methodology can be seen as a special case of bayesianism. to this effect, it is firstly argued, that popper's corroboration degree measures the probabilistic support that evidence lends to universal hypotheses. then it is affirmed, that popper and miller have not established the impossibility of inductive probability. and it (...) is finally claimed, that bayesian probabilistic support encompasses popper's corroboration concept. (shrink)

Incommensurability has been for about forty years one of the most discussed topics on the contemporary philosophy of science. In order to tackle this issue I assume Howard Sankey’s characterization of incommensurability as “the thesis that the content of some alternative scientific theories is incomparable due to translation failure between the vocabulary the theories employ”. This kind of incomparability should pre- vent for instance the derivation of Newtonian mechanics from relativity theory, as Thomas Kuhn maintains. Since I have myself been (...) concerned with the comparison of Newtonian and Einsteinian mass concepts in Rivadulla, I focus in this short paper on the comparability of theories of contemporary theoretical physics.Thus, instead of dealing with the question of whether the theories of contemporary physics are definitely incommensurable with each other, the main aim of this paper is to provide an answer to the question of whether it makes any sense to think about the in- commensurability between contemporary physical theories, due to their obvious comparability. (shrink)

I would like to take this opportunity to concentrate on the notion of republican virtue, to specify what it consists of and, in passing, to clarify some of the misunderstandings that tend to appear about this fundamental concept for republican discourse.

This paper critically examines the forays into metaphysics of The Dual Nature of Technical Artifacts Program (henceforth, DNP). I argue that the work of DNP is a valuable contribution to the epistemology of certain aspects of artifact design and use, but that it fails to advance a persuasive metaphysic. A central problem is that DNP approaches ontology from within a functionalist framework that is mainly concerned with ascriptions and justified beliefs. Thus, the materiality of artifacts emerges only as the external (...) conditions of realizability of function ascription. The work of DNP has a strong programmatic aspect and much of its foray into metaphysics is tentative, so the intent of my argument is partly synthetic: to sum up these issues as they are presented in the literature and highlight some recognized problems. But I also go beyond that, suggesting that these problems are foundational, arising from the very way in which DNP poses the question of artifact metaphysics. Although it sets out to incorporate objective aspects of technology, DNP places a strong focus on the intentional side of the purported matter-mind duality, bracketing off materiality in an irretrievable manner. Thus, some of the advantages of dualism are lost. I claim that DNP is dualistic, not merely based on “duality”, but that its version of dualism does not appropriately account for the material “nature” of artifacts. The paper ends by suggesting some correctives and alternatives to Dual Nature theory. (shrink)

Rips et al. claim that the principles underlying the structure of natural numbers cannot be inferred from interactions with the physical world. However, in their target article they failed to consider an important source of interaction: finger counting. Here, we show that finger counting satisfies all the conditions required for allowing the concept of numbers to emerge from sensorimotor experience through a bottom-up process.

As society advances, the educational system remains linked to the traditional model focused on the transmission of information and must adapt to new times and new profile of students, with the students and learning centered education. Active pedagogies developed during the 20th century become a fundamental reference point for the implementation of education competencies.

Explanation and understanding are intimately connected notions, but the nature of that connection has generally not been considered a topic worthy of serious philosophical investigation. Most authors have avoided making reference to the notion of understanding in their accounts of explanation because they fear that any mention of the epistemic states of the individuals involved compromises the objectivity of explanation. Understanding is a pragmatic notion, they argue, and pragmatics should be kept at a safe distance from the universal features of (...) explanation. My main contention in this dissertation is that there is a sense in which it is meaningful and useful to talk about objective understanding, and that to characterize this notion it is necessary to formulate an account of objective explanation that makes reference to the beliefs and epistemic goals of the participants in a cognitive enterprise. ;My account of explanation is based on the belief-doubt model of inquiry first proposed by Peirce. Using the tools provided by decision theory, and the models of belief revision developed by Isaac Levi and by Alchourron, Gardenfors, and Makinson, I analyze the objective and pragmatic conditions that a piece of information must fulfill to be both explanatory and epistemically useful to an inquiring agent. The objective basis for an explanation is provided by the relation of probabilistic relevance that the fact described by the explanans bares to the fact described by the explanandum. But an explanation is much more than its foundation. As an epistemological notion, a potential explanation can only be a bona fide explanation if it becomes part of inquiry, that is, if an agent or a group of agents can see any value in it for their cognitive purposes. I provide a way to evaluate an explanation in terms of its credibility, its content, and its explanatory value. I argue that although an objective measure of the credibility and content of an explanation can be established, in many cases a complete determination of its explanatory value will ultimately depend on the interests and goals of the individual inquirers. (shrink)