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)
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.
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)
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)
It is said that Europe finds itself today in a post-christian situa-tion. Further, there are many who advocate abandoning monotheism in order to get back to prechristian polytheism in the hope that the plurality of gods would favour a democratic tolerance in a pluralistic world. In this article the author firstly asks if European Christians have not gone back to adoring idols and to attempting to distinguish between them in the new forms of devotion to possessiveness, to power and to (...) pleasure. He then goes on to ask about the possibilities of pro-claiming the God of Jesus Christ. The third and the fourth part of the article point out several forms of necessary witness to God in contemporary society, with special reference made to European society in the conclusion. (shrink)
Misuse or misunderstanding of medication information is a common and costly problem in the U.S. The risks of misunderstanding medication information are compounded for the large and growing population of individuals with limited English proficiency that often lacks access to this information in their own language. This paper examines practices related to translation of medication information in the European Union that may serve as a model for future U.S. policy efforts to improve the quality and availability of medication information for (...) individuals with limited English proficiency. (shrink)
Este trabajo se ocupa de algunas ideas éticas del filósofo latinoamericano Andrés Bello (1781-1865), en especial de su “teoría de los sentimientos morales”. En la polémica del siglo XIX entre el llamado racionalismo ético (representado por Théodore Jouffroy) y el utilitarismo (Bentham), Bello adopta una postura intermedia, que pudiera calificarse de “hedonismo moderado” o de “eudemonismo”. Sus puntos de vista sobre la motivación moral o la manera en que la razón y el sentimiento se entrelazan para formar nuestras creencias (...) morales, se revelan como muy próximos a las doctrinas de Aristóteles y de algunos autores contemporáneos. (shrink)
Se busca rastrear la imagen que Platón tiene de Heráclito y articularla con la estructura argumentativa del Cratilo, para comprender las necesidades textuales a las que responde la doctrina del flujo perpetuo, es decir, la discusión sobre la corrección (ὀρθότης) del nombre. Gracias a la inclusión del testimonio heraclíteo, resulta posible rastrear la presunta consolidación de la tesis sobre los nombres primarios y los secundarios como el eje de la separación entre dos planos de realidad (uno estable y uno móvil) (...) y de la teoría de las Ideas -es decir, como la base de la epistemología platónica presente en los diálogos de madurez-. The article seeks to trace the image Plato has of Heraclitus and connect it with the argumentative structure of the Cratylus in order to understand the textual needs that give rise to the doctrine of perpetual flux, that is, the discussion regarding the correctness (ὀρθότης) of names. The inclusion of Heraclitus's testimony makes it possible to trace the alleged consolidation of the thesis regarding primary and secondary names as the axis of separation between two levels of reality (one stable, the other, changing) and the theory of Ideas -that is, as the basis of Plato's epistemology as set forth in the late dialogues-. (shrink)
Upshot: This is a book for thoughtful science and mathematics teachers and curriculum developers and educational philosophers. Quale helps us to challenge pernicious received “truths‘ and offers us intriguing perspectives, valuable discourse ventures and practical paedagogic strategies to engage the youth of today who are turning away from science in droves, to their and our cost.