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.

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.

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 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 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.

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.

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)

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.

Theoria, Volume 87, Issue 4, Page 971-985, August 2021.

In this article we present a notion of “logical perfection”. We first describe through examples a notion of logical perfection extracted 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)

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.

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

Presenting a fascinating analysis of the idea of what can't be said, this book ascertains whether the notion of there being a truth, or a state of affairs, or knowledge that can't be expressed linguistically is a coherent notion. The author distinguishes different senses in which it might be said that something can't be said. The first part looks at the question of whether ineffability is a coherent idea. Part two evaluates two families of arguments regarding whether ineffable states of (...) affairs actually exist: the argument from mysticism and the argument from epistemic boundedness. Part three looks more closely at the relation between mystic and non-mystic stances. In the fourth and final part the author distinguishes five qualitatively different types of ineffability. _Ineffability and Philosophy_ is a significant contribution to this area of research and will be essential reading for philosophers and those researching and studying the philosophy of language. (shrink)

Experiences of absence are common in everyday life, but have received little philosophical attention until recently, when two positions regarding the nature of such experiences surfaced in the literature. According to the Perceptual View, experiences of absence are perceptual in nature. This is denied by the Surprise-Based View, according to which experiences of absence belong together with cases of surprise. In this paper, I show that there is a kind of experience of absence—which I call frustrating absences—that has been overlooked (...) by the Perceptual View and by the Surprise Based-View and that cannot be adequately explained by them. I offer an alternative account to deal with frustrating absences, one according to which experiencing frustrating absences is a matter of subjects having desires for something to be present frustrated by the world. Finally, I argue that there may well be different kinds of experiences of absence. (shrink)

In this challenging study, André Gallois proposes and defends a thesis about the character of our knowledge of our own intentional states. Taking up issues at the centre of attention in contemporary analytic philosophy of mind and epistemology, he examines accounts of self-knowledge by such philosophers as Donald Davidson, Tyler Burge and Crispin Wright, and advances his own view that, without relying on observation, we are able justifiably to attribute to ourselves propositional attitudes, such as belief, that we consciously hold. (...) His study will be of wide interest to philosophers concerned with questions about self-knowledge. (shrink)

Lorenz proposed in his (1935) articulation of a theory of behavioral instincts that the objective of ethology is to distinguish behaviors that are “innate” from behaviors that are “learned” (or “acquired”). Lorenz’s motive was to open the investigation of certain “adaptive” behaviors to evolutionary theorizing. Accordingly, since innate behaviors are “genetic”, they are open to such investigation. By Lorenz’s light an innate/acquired or learned dichotomy rested on a familiar Darwinian distinction between genes and environments. Ever since Lorenz, ascriptions of innateness (...) have become widespread in the cognitive, behavioral, and biological sciences. The trend continues despite decades of strong arguments that show, in particular, the dichotomy that Lorenz invoked in his theory of behavioral instincts is literally false: no biological trait is the product of genes alone. Some critics suggest that the failure of Lorenz’s account shows that innateness is not well-defined in biology and the practice of ascribing innateness to various biological traits should be dropped from respectable science. Elsewhere (Ariew 1996) I argued that despite the arguments of critics, there really is a biological phenomenon underlying the concept of innateness. On my view, innateness is best understood in terms of C.H. Waddington’s concept of “canalization”, i.e. the degree to which a trait is innate is the degree to which its developmental outcome is canalized. The degree to which a developmental outcome is canalized is the degree to which the developmental process is bound to produce a particular endstate despite environmental fluctuations both in the development’s initial state and during the course of development. The canalization account differs in many ways to the traditional ways that ethologists such as Konrad Lorenz originally understood the concept of innateness. Most importantly, on the canalization account the distinction between innate and acquired is not a dichotomy, as Konrad Lorenz had it, but rather a matter of degree difference that lies along a spectrum with highly canalized development outcomes on the one end and highly environmentally sensitive development outcomes on the other end. Nevertheless, I justified the canalization account on the basis of a set of desiderata or criteria that I suggested falls-out of what seemed uncontroversial about Lorenz’s account of innateness (briefly): innateness is a property of a developing individual, innateness denotes environmental stability, and innate-ascriptions are useful in certain natural selection explanations (more below). From that same set of desiderata I argued (in my 1996) that neither the concept of heritability nor of norms of reactions—two concepts from population genetics—suffice to ground innateness. In this essay, I wish to provide further support of the canalization account in two ways. First, I wish to better motivate the desiderata by revisiting a debate between Konrad Lorenz and Daniel Lehrman over the meaning and explanatory usefulness of innate ascriptions in ethology. Second, I wish to compare my canalization account of innateness with accounts proposed by contemporary philosophers, one by Stephen Stich (1975), another by Elliott Sober (forthcoming), and a third by William Wimsatt (1986). (shrink)

This book presents a comprehensive and detailed exploration of the relationship between the thought of G.W.F. Hegel and that of John McDowell, the latter of whom is widely considered to be one of the most influential living analytic philosophers. It serves as a point of entry in McDowell’s and Hegel’s philosophy, and a substantial contribution to ongoing debates on perceptual experience and perceptual justification, naturalism, human freedom and action. The chapters gathered in this volume, as well as McDowell’s responses, make (...) it clear that McDowell’s work paves the way for an original reading of Hegel’s texts. His conceptual framework allows for new interpretive possibilities in Hegel’s philosophy which, until now, have remained largely unexplored. Moreover, these interpretations shed light on various aspects of continuity and discontinuity between the philosophies of these two authors, thus defining more clearly their positions on specific issues. In addition, they allow us to see Hegel’s thought as containing a number of conceptual tools that might be useful for advancing McDowell’s own philosophy and contemporary philosophy in general. (shrink)

Current work in language models (LMs) helps us speed up or even skip thinking by accelerating and automating cognitive work. But can LMs help us with critical thinking -- thinking in deeper, more reflective ways which challenge assumptions, clarify ideas, and engineer new concepts? We treat philosophy as a case study in critical thinking, and interview 21 professional philosophers about how they engage in critical thinking and on their experiences with LMs. We find that philosophers do not find LMs to (...) be useful because they lack a sense of selfhood (memory, beliefs, consistency) and initiative (curiosity, proactivity). We propose the selfhood-initiative model for critical thinking tools to characterize this gap. Using the model, we formulate three roles LMs could play as critical thinking tools: the Interlocutor, the Monitor, and the Respondent. We hope that our work inspires LM researchers to further develop LMs as critical thinking tools and philosophers and other 'critical thinkers' to imagine intellectually substantive uses of LMs. (shrink)

There is a growing awareness that there are many subtle forms of exclusion and partiality that affect the correct workings of a judicial system. The concept of epistemic injustice, introduced by the philosopher Miranda Fricker, is a useful conceptual tool to understand forms of judicial partiality that often go undetected. In this paper, we present Fricker’s original theory and some of the applications of the concept of epistemic injustice in legal processes. In particular, we want to show that the seed (...) planted by Fricker has flourished into a rich field of study in which the concept is used to analyze many different phenomena in law, not always following the original characterization provided by her. This has led to a distinction between what we will call the narrow version of the concept, which is closer to Fricker’s original account, and the wider version of epistemic injustice, which is a more controversial notion because it is always on the verge of morphing into other well-known concepts like sexism, racial discrimination, oppression, silencing, and gaslighting. We will show that the value of the narrow version is mostly theoretical, and that in order to use the concept of epistemic injustice one must adopt a more liberal understanding of it. (shrink)

This paper offers a new interpretation for Wittgenstein`s treatment of mathematical identities. As it is widely known, Wittgenstein`s mature philosophy of mathematics includes a general rejection of abstract objects. On the other hand, the traditional interpretation of mathematical identities involves precisely the idea of a single abstract object – usually a number –named by both sides of an equation.

The existence of causal explanations in science has been an issue of interest in Western philosophy from its very beginnings. That is the reason this work, following an idea of Mario Bunge, makes a historical review of this matter. The modern treatment of this subject takes place since the postulation by Popper and Hempel of the D-N model of scientific explanation, whose viability is scrutinized here from different points of view in the current philosophy of science. The main object of (...) this paper is to present two arguments against the possibility of causal explanations in theoretical physics. The first one concerns the existence, in certain cases, of inter-theoretical incompatibilities, and the second refers to the need to resort, in other cases, to concatenations of laws of different theories and disciplines. The final conclusion will be the defence of a form of theoretical explanation, which follows the Popper-Hempel model, but devoid of any ontological and metaphysical connotations. (shrink)

In this paper, I present a position that I call erotetic amelioration, according to which we must evaluate and, eventually, improve our answers to questions of the form “What is x?”. My focus will be on cases where x stands for a strongly social kind, such as marriage. Such a position is offered as an alternative to the idea-sometimes called conceptual engineering-according to which we should evaluate and, eventually, seek to improve our concepts. After introducing the idea of erotetic amelioration, (...) I will show how it can be put into work to deal with what I call the topic preservation challenge, and what advantages it has in relation to a similar position available in the literature, namely, Cappelen’s (2018) Austerity Framework. (shrink)

It is widely believed by philosophers that we human beings are capable of stepping back from inclinations to act in a certain way and consider whether we should do so. If we judge that there are enough reasons in favour of following our initial inclination, we are definitely motivated, and, if all goes well, we act. This view of human agency naturally leads to the idea that our actions are self-determined, or controlled by ourselves. Some go one step further to (...) the point of saying that we should extend the fundamental aspects of this view of human agency to the epistemic realm. This we call ‘the control-view”. Here we will make a strong case against the control-view. While we have a substantial control over our practical lives, it is very unlikely that this extends to our epistemic lives. Our discussion will proceed in three stages. We will present two asymmetries between our practical and epistemic lives which are followed by a general argument against the control-view. (shrink)

El uso de sistemas de machine learning en los procesos de selección laboral ha sido de gran utilidad para agilizarlos y volverlos más eficientes, pero al mismo tiempo ha generado problemas en términos de equidad, confiabilidad y transparencia. En este artículo comenzamos explicando los diferentes usos de la Inteligencia Artificial en los procesos de selección laboral en Estados Unidos. Presentamos los sesgos sexuales y raciales que han sido detectados en algunos de ellos y explicamos los obstáculos jurídicos y prácticos para (...) su detección y análisis. Un posible remedio jurídico a la discriminación algorítmica es el régimen de impacto diferencial sistémico utilizado en Estados Unidos. Usamos algunas características de este régimen para señalar los vacíos jurídicos frente a la discriminación en el acceso al empleo en el ámbito del derecho laboral colombiano, y ofrecemos algunas características generales que podría tener un régimen de esa naturaleza. (shrink)

Moore’s Paradox is a test case for any formal theory of belief. In Knowledge and Belief, Hintikka developed a multimodal logic for statements that express sentences containing the epistemic notions of knowledge and belief. His account purports to offer an explanation of the paradox. In this paper I argue that Hintikka’s interpretation of one of the doxastic operators is philosophically problematic and leads to an unnecessarily strong logical system. I offer a weaker alternative that captures in a more accurate way (...) our logical intuitions about the notion of belief without sacrificing the possibility of providing an explanation for problematic cases such as Moore’s Paradox. (shrink)

This paper raises three questions regarding the attribution of beliefs, desires, and intentions to robots. The first one is whether humans in fact engage in robot mindreading. If they do, this raises a second question: does robot mindreading foster trust towards robots? Both of these questions are empirical, and I show that the available evidence is insufficient to answer them. Now, if we assume that the answer to both questions is affirmative, a third and more important question arises: should developers (...) and engineers promote robot mindreading in view of their stated goal of enhancing transparency? My worry here is that by attempting to make robots more mind-readable, they are abandoning the project of understanding automatic decision processes. Features that enhance mind-readability are prone to make the factors that determine automatic decisions even more opaque than they already are. And current strategies to eliminate opacity do not enhance mind-readability. The last part of the paper discusses different ways to analyze this apparent trade-off and suggests that a possible solution must adopt tolerable degrees of opacity that depend on pragmatic factors connected to the level of trust required for the intended uses of the robot. (shrink)

But what are functions? Here, 15 leading scholars of philosophy of psychology and philosophy of biology present new essays on functions.

A. Selbstverortung: Der hermssche Blick auf andere Religionen -- b. Öffnung zu Anderen: Das Problem geschlossener Rationalitätsformen -- ii. Einheit in der Vielfalt. Die interpretative Vernunft -- III. 3.C. Schlussfolgerungen. Bildung der Weltanschauungen -- IV. Ergebnisse und Ausblicke -- IV. 1. Perspektiven des Theorievergleichs -- IV. 1.A. Eine 'Topik der Verständigung' - als Struktur der Forschungsfragen -- IV. 1.B. Vernunft und Religion als komplementäre Konkurrenz -- IV. 2. Möglichkeiten interkultureller Koexistenz -- IV. 2.A. Evangelischer Glaube im Horizont des globalen Wandels (...) -- IV. 2.B. Diskurskultur und Diskurs der Kulturen -- IV. 2.C. Konstitutionalisierung der Wirkungsgemeinschaft der Menschheit -- Bibliografie -- Literatur von Jürgen Habermas -- Literatur von Eilert Herms -- Weitere Literatur -- Personenregister -- Sachregister. (shrink)

Mathematical chemistry is often thought to be a 20th-century subdiscipline of chemistry, but in this paper we discuss several early chemical ideas and some landmarks of chemistry as instances of the mathematical way of thinking; many of them before 1900. By the mathematical way of thinking, we follow Weyl's description of it in terms of functional thinking, i.e. setting up variables, symbolizing them, and seeking for functions relating them. The cases we discuss are Plato's triangles, Geoffroy's affinity table, Lavoisier's classification (...) of substances and their relationships, Mendeleev's periodic table, Cayley's enumeration of alkanes, Sylvester's association of algebra and chemistry, and Wiener's relationship between molecular structure and boiling points. These examples show that mathematical chemistry has much more than a century of history. (shrink)

The first purpose of this article is to present a new theory of libertarian free will—the boundary theory of libertarian free will—which provides a new framework by means of employing boundaries as a “conceptual scheme” for understanding libertarian free will. This theory consists of two parts. One part suggests that the agent’s will should be viewed as the intermediate boundary between an agent’s reasons and his alternative choices. The second part is a model where the agent’s will is a faculty (...) that solely operates by permitting or resisting reasons (that are potential causes) to become actual causes for the agent’s choices. The second purpose of the paper is to argue that the boundary theory of libertarian free will has several advantages, the most important of which are: (a) it defeats the charge that libertarian free will is a mystery; (b) it defeats the standard objections against the compatibility of libertarian free will and indeterminism (that is, the luck argument, the roll-back argument, the difference argument, the assimilation argument, etc.); and (c) it is simultaneously an argument for indeterminism as such (that is, that determinism is false). (shrink)

IN the last decade deliberative democracy has developed rapidly from a “theoretical statement” into a “working theory.”1 Scholars and practitioners have launched numerous initiatives designed to put deliberative democracy into practice, ranging from deliberative polling to citizen summits.2 Some even advocate deliberation as a new “revolutionary now.”3 Deliberative democracy has also experienced the beginning of an empirical turn, making significant gains as an empirical (or positive) political science. This includes a small, but growing body of literature tackling the connection between (...) the normative standards of deliberation, how well they are met, and the empirical consequences of meeting them.4 This trend has, for instance, included the use of methods and frameworks borrowed from other fields, such as political and social psychology. Such studies suggest that cases approaching ideal deliberation are rare, but that group interaction sometimes works surprisingly well according to such ideals.5. (shrink)

Los sesgos cognitivos afectan negativamente la toma de decisiones en todas las esferas de la vida, incluyendo las decisiones de los jueces. La imposibilidad de eliminarlos por completo de la práctica del derecho, o incluso de controlar sus efectos, contrasta con el anhelo de que las decisiones judiciales sean el resultado exclusivo de un razonamiento lógico-jurídico correcto. Frente el efecto sistemático, recalcitrante y porfiado de los sesgos cognitivos, una posible estrategia para disminuir su efecto es enfocarse, no en modificar el (...) comportamiento de los agentes judiciales, sino en moldear su entorno para que los sesgos tengan menos oportunidades de aparecer. En particular, es más provechoso concentrar los esfuerzos en identificar aquellas reglas procesales que faciliten o limiten el efecto de los sesgos. En este ensayo propongo un diálogo fructífero entre el derecho y la psicología que puede llevar a mejorar la calidad de los sistemas judiciales. La propuesta está basada en la creación de guías de práctica judicial que puedan servir de base para la creación de protocolos procesales que limiten en la medida de lo razonable sus efectos negativos y conduzcan a mejores decisiones judiciales. (shrink)