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.

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 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.

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.

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)

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.

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)

This reconsideration of Hume’s classic essay “Of Miracles” via the lens of American pragmatist ways of thinking about history and power shifts our attention from Hume’s epistemic concerns about the legitimacy of witnesses and testimony to his distaste for sacred history, his critical stance regarding the social force of revelation, and his disdain for religious authority. To view Hume’s essay both as an articulation of a critical philosophy of history and as an exercise in moral dynamism (social power or, authority, (...) is a result of epistemic transactions), is to intervene in both Hume studies and Contemporary Pragmatism. (shrink)

Under the lig ht of Being and Nothingness’s the o re t ical body – Sartre’s master piece –, it is intended to discuss the essential source of human reality as “n i h i l a t i o n” and ontological lack, as well as manifestations and cons e q u e nces from this primordial human passion to be transformed to coagulated transcendence, to be transformed in Being In-itself-For-itself: to be consciousness and, at the same t i (...) me, to be a complete and finished Being, with infinite de nsity and witho u t fissures. (shrink)

An examination of David Hume's philosophy of religion that situates his conception "true religion" within the context of his overall science of human nature, his rejection of popular religion, and his Ciceronian influence"--Provided by publisher.

Drawing on recent findings, this study examines whether valence concordant electromyography (EMG) responses can be explained as an unconditional effect of mere stimulus processing or as somatosensory simulation driven by task-dependent processing strategies. While facial EMG over the Corrugator supercilii and the Zygomaticus major was measured, each participant performed two tasks with pictures of album covers. One task was an affective evaluation task and the other was to attribute the album covers to one of five decades. The Embodied Emotion Account (...) predicts that valence concordant EMG is more likely to occur if the task necessitates a somatosensory simulation of the evaluative meaning of stimuli. Results support this prediction with regard to Corrugator supercilii in that valence concordant EMG activity was only present in the affective evaluation task but not in the non-evaluative task. Results for the Zygomaticus major were ambiguous. Our findings are in line with the view that EMG activity is an embodied part of the evaluation process and not a mere physical outcome. (shrink)

We analyze the connections of Lavoisier system of nomenclature with Leibniz’s philosophy, pointing out to the resemblance between what we call Leibnizian and Lavoisian programs. We argue that Lavoisier’s contribution to chemistry is something more subtle, in so doing we show that the system of nomenclature leads to an algebraic system of chemical sets. We show how Döbereiner and Mendeleev were able to develop this algebraic system and to find new interesting properties for it. We pointed out the resemblances between (...) Leibniz program and Lavoisier legacy, particularly regarding the lingua philosophica for understanding and thinking Nature, in this particular case, chemistry. In the second part we discuss, from the linguistic viewpoint, how Lavoisian algebraic system may be taken further to build a language. We study the constituents of such a chemical language. Finally, we formalize some of the ideas here presented by using elements of network theory and discrete mathematics. (shrink)

English summary: Marc Andre Wiegand analyzes the neo-Kantian premises of Gustav Radbruch's legal philosophy.

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)

Social constructionists maintain that we invent the properties of the world rather than discover them. Is reality constructed by our own activity? Do we collectively invent the world rather than discover it? André Kukla presents a comprehensive discussion of the philosophical issues that arise out of this debate, analysing the various strengths and weaknesses of a range of constructivist arguments and arguing that current philosophical objections to constructivism are inconclusive. However, Kukla offers and develops new objections to constructivism, distinguishing between (...) the social causes of scientific beliefs and the view that all ascertainable facts are constructed. (shrink)

Over the past fifteen years there has been a considerable amount of debate concerning what theoretical population dynamic models tell us about the nature of natural selection and drift. On the causal interpretation, these models describe the causes of population change. On the statistical interpretation, the models of population dynamics models specify statistical parameters that explain, predict, and quantify changes in population structure, without identifying the causes of those changes. Selection and drift are part of a statistical description of population (...) change; they are not discrete, apportionable causes. Our objective here is to provide a definitive statement of the statistical position, so as to allay some confusions in the current literature. We outline four commitments that are central to statisticalism. They are: 1. Natural Selection is a higher order effect; 2. Trait fitness is primitive; 3. Modern Synthesis (MS)-models are substrate neutral; 4. MS-selection and drift are model-relative. (shrink)

The central point of this essay is to demonstrate the incommensurability of ‘Darwinian fitness’ with the numeric values associated with reproductive rates used in population genetics. While sometimes both are called ‘fitness’, they are distinct concepts coming from distinct explanatory schemes. Further, we try to outline a possible answer to the following question: from the natural properties of organisms and a knowledge of their environment, can we construct an algorithm for a particular kind of organismic life-history pattern that itself will (...) allow us to predict whether a type in the population will increase or decrease relative to other types? 1. Introduction2. Darwinian fitness3. Reproductive fitness and genetical models of evolution4. The models of reproductive fitness4.1 The Standard Viability Model4.2 Frequency-dependent selection4.3 Fertility models4.4 Overlapping generations5. Fitness as outcome5.1 Fitness as actual increase in type5.2 Fitness as expected increase in type5.2.1 Expected increase within a generation5.2.2 Expected increase between generations5.2.3 Postponed reproductive fitness effects6. The book-keeping problem7. Conclusion. (shrink)

Occasions of Identity is an exploration of timeless philosophical issues about persistence, change, time, and sameness. Andre Gallois offers a critical survey of various rival views about the nature of identity and change, and puts forward his own original theory. He supports the idea of occasional identities, arguing that it is coherent and helpful to suppose that things can be identical at one time but distinct at another. Gallois defends this view, demonstrating how it can solve puzzles about persistence dating (...) back to the Ancient Greeks, and investigates the metaphysical consequences of rejecting the necessity and eternity of identities. (shrink)

Le génie de Léonard de Vinci, celui de Michel-Ange ressortent mieux sur le fond révélateur de l’Académie de Careggi, où Marsile Ficin règne en maître, évoquant sinon invoquant Platon. La culture platonicienne entretenue par Ficin - mais Cristoforo Landino ou Ange Politien sont tour à tour convoqués - délimite le contour d’un nouvel ordre artistique dont André Chastel, dans un travail de jeunesse qui engage déjà ses subtiles analyses d’histoire de l’art et des idées, rend raison avec passion. En quelques (...) pages lumineuses, Jean Wirth donne à ce maître livre sa juste place dans une tradition historiographique qu’il a contribué à renouveler. (shrink)

Covering the basics as well as recent research results, this book provides a very readable introduction to the exciting interface of computability and ...

ABSTRACT: In this essay I characterize arguments by analogy, which have an impor- tant role both in philosophical and everyday reasoning. Arguments by analogy are dif- ferent from ordinary inductive or deductive arguments and have their own distinct features. I try to characterize the structure and function of these arguments. It is further discussed that some arguments, which are not explicit arguments by analogy, nevertheless should be interpreted as such and not as inductive or deductive arguments. The result is that (...) a presumed outcome of a philosophical dispute will have to be reconsidered. (shrink)

The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts (...) and methods originating from randomness enrich computability theory.The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory. (shrink)

John McDowell and Bill Brewer famously defend the view that one can only have empirical beliefs if one’s perceptual experiences serve as reasons for such beliefs, where reasons are understood in terms of subject’s reasons. In this paper I show, first, that it is a consequence of the adoption of such a requirement for one to have empirical beliefs that children as old as 3 years of age have to considered as not having genuine empirical beliefs at all. But we (...) have strong reasons to think that 3-year-old children have empirical beliefs, or so I argue. If this is the case, McDowell and Brewer’s requirement for one to have empirical beliefs faces a strong challenge. After showing this, I propose an alternative requirement for one to have empirical beliefs, and argue that it should be favoured over McDowell and Brewer’s requirement. (shrink)

Since it implies a reduction in the quality and the quantity of the natural resources, environmental degradation is a present day problem that requires immediate solutions. This situation is driving firms to undertake an environmental transformation process with the purpose of reducing the negative externalities that come from their economic activities. Within this context, environmental marketing is an emerging business philosophy by which organizations can address sustainability issues. Moreover, environmental marketing and orientation are seen as valuable strategies to improve a (...) firm's competitiveness. However, the literature that has analyzed the link between environmental strategies and firms' results has been inconclusive and contradictory. In this study, we propose and test a model that analyses how the implementation of ecological issues within a firm's marketing strategy and orientation influences organizational results. Data were obtained through a survey sent to Spanish manufacturing firms. The results show that environmental marketing positively affects firms' operational and commercial performance and this improvement will influence their economic results. Moreover, environmental marketing is revealed as an excellent strategy to obtain competitive advantages in costs and in product differentiation. Thus, this study agrees with the researchers who affirm that environmental strategies positively affect firm's competitiveness while reducing environmental impact. (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)

Colexification refers to the phenomenon of multiple meanings sharing one word in a language. Cross‐linguistic lexification patterns have been shown to be largely predictable, as similar concepts are often colexified. We test a recent claim that, beyond this general tendency, communicative needs play an important role in shaping colexification patterns. We approach this question by means of a series of human experiments, using an artificial language communication game paradigm. Our results across four experiments match the previous cross‐linguistic findings: all other (...) things being equal, speakers do prefer to colexify similar concepts. However, we also find evidence supporting the communicative need hypothesis: when faced with a frequent need to distinguish similar pairs of meanings, speakadjust their colexification preferences to maintain communicative efficiency and avoid colexifying those similar meanings which need to be distinguished in communication. This research provides further evidence to support the argument that languages are shaped by the needs and preferences of their speakers. (shrink)

This volume features original essays on the philosophy of love. The essays are organized thematically around the past, present, and future of philosophical thinking about love. In section I, the contributors explore what we can learn from the history of philosophical thinking about love. The chapters cover Ancient Greek thinkers, namely Plato and Aristotle, as well as Kierkegaard's critique of preferential love and Erich Fromm's mystic interpretation of sexual relations. Section II covers current conceptions and practices of love. These chapters (...) explore how love changes over time, the process of falling in love, envy in romantic partnerships, and a new interpretation of grand-parental love. Finally, Section III looks at the future of love. These chapters address technological developments related to love, such as algorithm-driven dating apps and robotic companions, as well as the potential of polyamory as a future romantic ideal. This book will be of interest to researchers and advanced students in moral philosophy and social and political philosophy who are working on issues related to philosophy of love. (shrink)

One of the current debates in philosophy of mind is whether the content of perceptual experiences is conceptual or nonconceptual. The proponents of nonconceptual content, or nonconceptualists, typically support their position by appealing to the so-called Fineness of Grain Argument, which, in rough terms, has as its conclusion that we do not possess concepts for everything we perceive. In his Mind and World, John McDowell tried to give a response to the argument, and show that we do possess concepts for (...) everything we perceive. His response is based on the idea that we have a capacity to recognize all that we perceive. However, a good number of people took this proposal as being empirically false. My aim in this paper is to show that McDowell’s proposal is not only not empirically false, but likely to be empirically true. We do have the capacity to recognize all that we perceive, but such recognition capacity is dependent on information stored in short-term memory, and not in longterm memory, as McDowell’s critics have mistakenly supposed. (shrink)