This chapter argues that the distinction between ambitious and modest transcendental arguments, developed and deployed by various authors in the wake of Stroud’s influential critique of transcendental reasoning, may be pointless when applied to transcendental arguments from performative inconsistency that have moral statements as their conclusions. If moral truth is assertorically constrained, then any modest moral transcendental argument from performative inconsistency can be converted into an ambitious moral transcendental argument. The chapter provides an account of performative inconsistency and suggests an (...) alternative to the widespread reading of transcendental conditionals in terms of an ‘if-then’-sentences whose antecedents express a proposition to the effect that some x is possible and whose consequents express a statement to the effect that some y is actual. (shrink)

This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counterarguments for various proposed solutions (“the revenge of the Liar”). This solution complements the classical procedure of determining the truth values of sentences by its own failure and, when the procedure fails, through an appropriate semantic shift allows us to express the failure in a classical two-valued language. (...) Formally speaking, the solution is a language with one meaning of symbols and two valuations of the truth values of sentences. The primary valuation is a classical valuation that is partial in the presence of the truth predicate. It enables us to determine the classical truth value of a sentence or leads to the failure of that determination. The language with the primary valuation is precisely the largest intrinsic fixed point of the strong Kleene three-valued semantics (LIFPSK3). The semantic shift that allows us to express the failure of the primary valuation is precisely the classical closure of LIFPSK3: it extends LIFPSK3 to a classical language in parts where LIFPSK3 is undetermined. Thus, this article provides an argumentation, which has not been present in contemporary debates so far, for the choice of LIFPSK3 and its classical closure as the right model for the truth predicate. In the end, an erroneous critique of Kripke-Feferman axiomatic theory of truth, which is present in contemporary literature, is pointed out. (shrink)

In this article I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us, all directions are the same to us and all units of length we use to create geometric figures are the same to us. On the other hand, through the process of algebraic simplification, this system of axioms directly provides the Weyl’s (...) system of axioms for Euclidean geometry. The system of axioms, together with its a priori interpretation, offers new views to philosophy and pedagogy of mathematics: it supports the thesis that Euclidean geometry is a priori, it supports the thesis that in modern mathematics the Weyl’s system of axioms is dominant to the Euclid’s system because it reflects the a priori underlying symmetries, it gives a new and promising approach to learn geometry which, through the Weyl’s system of axioms, leads from the essential geometric symmetry principles of the mathematical nature directly to modern mathematics. (shrink)

Chile experimenta un periodo de readecuaciones en materia social. La demanda ciudadana por una mayor igualdad y seguridad social se refleja en el debate público sobre dimensiones distributivas como el salario mínimo. Como un intento de dar respuestas a estos requerimientos, el gobierno democrático ha implementado reformas en el campo educativo, en materia laboral y previsional. El presente artículo se propone contribuir a una caracterización institucional de la política social chilena y un análisis de la dinámica distributiva. Para el logro (...) de este objetivo, se recurre a los estudios especializados sobre los Estados de bienestar adaptando estas aportaciones a la configuración que evidencian las políticas sociales en el contexto nacional. Más adelante, se presentan algunos indicadores sociales vinculados con el tratamiento de la desigualdad y la pobreza, comparando las medidas distributivas con las utilizadas en los países de la OCDE. (shrink)

en este trabajo, tutorizado por el Dr. Juan José Padial Benticuaga, Paloma García Briones y María Benítez Hidalgo analizan dos vías distintas y opuestas en las que puede derivar la crisis de los valores: el nihilismo y el auge de la importancia de la afección subjetiva.

¿Se puede pensar la verdad desde trascendentales antropológicos? Sí, se puede, y el resultado es una verdad que inspira, que refiere a un buscar no meramente lógico, sino libre, donde lo que se encuentra moviliza en lugar de extasiar en la contemplación sosegada; una verdad que no es fin, sino inicio. La inspiración es un momento propiamente significativo y caracterizador de la verdad: la verdad es esencialmente inspiración cuando se la observa en su ser algo propiamente humano.

Castro-Gómez, Santiago. Revoluciones sin sujeto. Slavoj Žižek y la crítica del historicismo posmoderno. Ciudad de México: Akal, 2015. 400 pp.

La presente obra indaga sobre la tenue línea divisoria entre los discursos de lo que hemos llamado filosofía y literatura. Cuestión de frontera, de imagen no siempre visible, en este libro se sostiene la idea de la casi identificación entre las funciones cognoscitivas, estéticas, referenciales y de cierta aplicabilidad. Del poder de los discursos de la filosofía y la literatura. La última consecuencia del giro lingüístico del pensamiento, y de nuestros hábitos culturales alrededor de la enorme profusión de textos filosófico-literarios (...) o literario-filosóficos, se interpreta así como la posible, acaso provocada, disolución de los géneros discursivos. Un lenguaje que se distingue por su continuidad, contingencia y siempre problemática referencialidad, es lo que el autor pone en juego al querer leer como casos paradigmáticos de esta disolución discursiva a Borges, Cortázar, R. Arenas o Kafka, pero también a Nietzsche, Foucault, Derrida o Deleuze. (shrink)

In this handbook, I put into practice my philosophical views on children's mathematics. The handbook contains brief instructions and examples of mathematical activities. In the INSTRUCTIONS section, instructions are given on how, and in part why that way, to help preschool children in their mathematical development. In the ACTIVITIES section, there are examples of activities through which the child develops her mathematical abilities.

Resumen Al momento de comparar dos obras disímiles en términos de lo que aquí llamaremos el gesto lingüístico, pero similares en cuanto a su comprensión fundamental del decir respecto de su función, se vuelve clara la necesidad de expandir la metódica de acceso a tal fenómeno e incluir el momento analítico clave del ánimo del lenguaje. El presente análisis tiene como meta lograr tal expansión, desde el punto de partida ontológico que se propone en Ser y tiempo, para llevarlo hasta (...) un puerto -en apariencia- tan disímil como es la obra literaria de Roberto Bolaño.When comparing two works, that are dissimilar in terms of what we will call here the linguistic gesture, but similar in terms of their fundamental understanding of the concept with respect to its function, the need to expand the access to such phenomena becomes clear, and to also include the key analytical moment of the mood of the language. The purpose of this analysis is to achieve expansion, from the proposed ontological starting point in Being and time, to take it to a port -apparently- as different as the literary work of Roberto Bolaño. (shrink)

Boris Kment takes a new approach to the study of modality that emphasises the origin of modal notions in everyday thought. He argues that the concepts of necessity and possibility originate in counterfactual reasoning, which allows us to investigate explanatory connections. Contrary to accepted views, explanation is more fundamental than modality.

Se examinan las diversas modalidades de la nada como casos de pérdida del sentido y falta de consumación del conocimiento: la nada como noúmeno y su relación con el fenómeno, así como la conexión trascendental de ambos. Aunque la nada pone en jaque al concepto de sentido, este se encuentra supuesto antes de todo tipo de pregunta por el ser, y se constituye en el trasfondo de las condiciones trascendentales que posibilitan el conocimiento.

This paper analyzes the historical context and systematic importance of Kant's hypothetical use of reason. It does so by investigating the role of hypotheses in Kant's philosophy of science. We first situate Kant’s account of hypotheses in the context of eighteenth-century German philosophy of science, focusing on the works of Wolff, Meier, and Crusius. We contrast different conceptions of hypotheses of these authors and elucidate the different theories of probability informing them. We then adopt a more systematic perspective to discuss (...) Kant's idea that scientific hypotheses must articulate real possibilities. We argue that Kant's views on the intelligibility of scientific hypotheses constitute a valuable perspective on scientific understanding and the constraints it imposes on scientific rationality. (shrink)

Se examinan las diversas modalidades de la nada como casos de pérdida del sentido y falta de consumación del conocimiento: la nada como noúmeno y su relación con el fenómeno, así como la conexión trascendental de ambos. Aunque la nada pone en jaque al concepto de sentido, este se encuentra supuesto antes de todo tipo de pregunta por el ser, y se constituye en el trasfondo de las condiciones trascendentales que posibilitan el conocimiento. Various modes of non-being are examined as (...) cases of loss of sense and as a lack of consummation of knowledge: non-being as noumena and its relationship with the phenomena, as well as the transcendental connection between them. Although non-being makes the concept of sense doubtful, it is presupposed before any kind of question regarding being and it is constituted in the background which belongs to the transcendental conditions which make knowledge possible. (shrink)

I propose a general alethic theory of epistemic risk according to which the riskiness of an agent’s credence function encodes her relative sensitivity to different types of graded error. After motivating and mathematically developing this approach, I show that the epistemic risk function is a scaled reflection of expected inaccuracy. This duality between risk and information enables us to explore the relationship between attitudes to epistemic risk, the choice of scoring rules in epistemic utility theory, and the selection of priors (...) in Bayesian epistemology more generally. (shrink)

We further investigate a divisibility relation on the set of BN ultrafilters on the set of natural numbers. We single out prime ultrafilters (divisible only by 1 and themselves) and establish a hierarchy in which a position of every ultrafilter depends on the set of prime ultrafilters it is divisible by. We also construct ultrafilters with many immediate successors in this hierarchy and find positions of products of ultrafilters.

Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial interpretation of the corresponding language. It follows from the analysis that (i) mathematical objects do not exist in the external world: they are our internally imagined objects, some of which, at least approximately, we can realize or represent; (ii) mathematical truths are not (...) truths about the external world but specifications (formulations) of mathematical conceptions; (iii) mathematics is first and foremost our imagined tool by which, with certain assumptions about its applicability, we explore nature and synthesize our rational cognition of it. (shrink)

While there are satisfactory answers to the question “How should we teach children mathematics?”, there are no satisfactory answers to the question “What mathematics should we teach children?”. This paper provides an answer to the last question for preschool children (early childhood), although the answer is also applicable to older children. This answer, together with an appropriate methodology on how to teach mathematics, gives a clear conception of the place of mathematics in the children’s world and our role in helping (...) children develop their mathematical abilities. Briefly, children’s mathematics consists of the world of children’s internal activities that they eventually purposefully organize in order to understand and control the outside world and organize their overall activities in it. We need to support a child in mathematical activities that she does spontaneously and in which she shows interest, and we need to teach her mathematics that she is interested in developing through these activities. In doing so, we must be fully aware that the child’s mathematics is part of the child’s world of internal activities and is not outside of it. We help the child develop mathematical abilities by developing them in the context of her world and not outside of it. From the point of view of this conception, the standards established today are limiting and too focused on numbers and geometric figures: these topics are too prominent and elaborated, and other mathematical contents are subordinated to them. Adhering to the standards, we drastically limit the mathematics of the child’s world, hamper the correct mathematical development of a child, and we can turn her away from mathematics. (shrink)

We continue the research of an extension of the divisibility relation to the Stone‐Čech compactification. First we prove that ultrafilters we call prime actually possess the algebraic property of primality. Several questions concerning the connection between divisibilities in and nonstandard extensions of are answered, providing a few more equivalent conditions for divisibility in. Results on uncountable chains in are proved and used in a construction of a well‐ordered chain of maximal cardinality. Probably the most interesting result is the existence of (...) a chain of type in. Finally, we consider ultrafilters without divisors in and among them find the greatest class. (shrink)

We construct and study structures imitating the field of complex numbers with exponentiation. We give a natural, albeit non first-order, axiomatisation for the corresponding class of structures and prove that the class has a unique model in every uncountable cardinality. This gives grounds to conjecture that the unique model of cardinality continuum is isomorphic to the field of complex numbers with exponentiation.

In this paper we develop a general theory of algorithmic fairness. Drawing on Johnson King and Babic’s work on moral encroachment, on Gary Becker’s work on labor market discrimination, and on Strawson’s idea of resentment and indignation as responses to violations of the demand for goodwill toward oneself and others, we locate attitudes to fairness in an agent’s utility function. In particular, we first argue that fairness is a matter of a decision-maker’s relative concern for the plight of people from (...) different groups, rather than of the outcomes produced for different groups. We then show how an agent’s preferences, including in particular their attitudes to error, give rise to their decision thresholds. Tying these points together, we argue that the agent’s relative degrees of concern for different groups manifest in a difference in decision thresholds applied to these groups. (shrink)

We continue the exploration of various aspects of divisibility of ultrafilters, adding one more relation to the picture: multiplicative finite embeddability. We show that it lies between divisibility relations \ and \. The set of its minimal elements proves to be very rich, and the \-hierarchy is used to get a better intuition of this richness. We find the place of the set of \-maximal ultrafilters among some known families of ultrafilters. Finally, we introduce new notions of largeness of subsets (...) of \, and compare it to other such notions, important for infinite combinatorics and topological dynamics. (shrink)

The essential role of language in rational cognition is analysed. The approach is functional: only the results of the connection between language, reality, and thinking are considered. Scientific language is analysed as an extension and improvement of everyday language. The analysis gives a uniform view of language and rational cognition. The consequences for the nature of ontology, truth, logic, thinking, scientific theories, and mathematics are derived.