This paper considers the potential of impasses within cinematic assemblages and the pedagogy of cinema to expand the possible horizons of Black queer youth. Black queerness in film provides pedagogical tools for exploring the limits of the category of queer. Both Barry Jenkins’s Moonlight and Dee Rees’s Pariah counter uncritical narratives of pathology, and are research data in their explorations of affective dimensions of gender, sexuality, race, poverty, and love through moving-images and sound. After situating the context of Moonlight, Pariah, (...) and modern-day America within readings of antiblackness and heteronormativity, we explore the pedagogical work of affect and the impasse in film to make worlds differently. Through reading the impasses within Moonlight and Pariah with these concepts, we re/view how isolation, vulnerability, Blackness, and queer feeling entangle toward investment in the possible, but largely unimaginable, futures in a moment overwhelmed by queerphobia and antiblackness. In so doing, the pedagogy of cinema employed maps our collective potential to remake our moment. (shrink)

This paper critiques the new mechanistic explanatory program on grounds that, even when applied to the kinds of examples that it was originally designed to treat, it does not distinguish correct explanations from those that blunder. First, I offer a systematization of the explanatory account, one according to which explanations are mechanistic models that satisfy three desiderata: they must 1) represent causal relations, 2) describe the proper parts, and 3) depict the system at the right ‘level.’ Second, I argue that (...) even the most developed attempts to fulfill these desiderata fall short by failing to appropriately constrain explanatorily apt mechanistic models. -/- *This paper used to be called "The Emperor's New Mechanisms". (shrink)

The universality of critical phenomena is best explained by appeal to the Renormalisation Group (RG). Batterman and Morrison, among others, have claimed that this explanation is irreducible. I argue that the RG account is reducible, but that the higher-level explanation ought not to be eliminated. I demonstrate that the key assumption on which the explanation relies – the scale invariance of critical systems – can be explained in lower-level terms; however, we should not replace the RG explanation with a bottom-up (...) account, rather we should acknowledge that the explanation appeals to dependencies which may be traced down to lower levels. (shrink)

A problem for Aristotelian realist accounts of universals (neither Platonist nor nominalist) is the status of those universals that happen not to be realised in the physical (or any other) world. They perhaps include uninstantiated shades of blue and huge infinite cardinals. Should they be altogether excluded (as in D.M. Armstrong's theory of universals) or accorded some sort of reality? Surely truths about ratios are true even of ratios that are too big to be instantiated - what is the truthmaker (...) of such truths? It is argued that Aristotelianism can answer the question, but only a semi-Platonist form of it. (shrink)

This paper sketches a causal account of scientific explanation designed to sustain the judgment that high-level, detail-sparse explanations—particularly those offered in biology—can be at least as explanatorily valuable as lower-level counterparts. The motivating idea is that complete explanations maximize causal economy: they cite those aspects of an event’s causal run-up that offer the biggest-bang-for-your-buck, by costing less (in virtue of being abstract) and delivering more (in virtue making the event stable or robust).

Though biologists identify individuals as ‘male’ or ‘female’ across a broad range of animal species, the particular traits exhibited by males and females can vary tremendously. This diversity has led some to conclude that cross-animal sexes (males, or females, of whatever animal species) have “little or no explanatory power” (Dupré 1986: 447) and, thus, are not natural kinds in any traditional sense. This essay will explore considerations for and against this conclusion, ultimately arguing that the animal sexes, properly understood, are (...) “historical explanatory kinds”: groupings that can be scientifically significant even while their members differ radically in their current properties and particular histories. Whether this makes them full-fledged natural kinds is a question I take up at the very end. (shrink)

The modern Everett interpretation of quantum mechanics describes an emergent multiverse. The goal of this paper is to provide a perspicuous characterisation of how the multiverse emerges making use of a recent account of (weak) ontological emergence. This will be cashed out with a case study that identifies decoherence as the mechanism for emergence. The greater metaphysical clarity enables the rebuttal of critiques due to Baker (2007) and Dawid and Th\'ebault (2015) that cast the emergent multiverse ontology as incoherent; responses (...) are also offered to challenges to the Everettian approach from Maudlin (2010) and Monton (2013). (shrink)

The global/local contrast is ubiquitous in mathematics. This paper explains it with straightforward examples. It is possible to build a circular staircase that is rising at any point (locally) but impossible to build one that rises at all points and comes back to where it started (a global restriction). Differential equations describe the local structure of a process; their solution describes the global structure that results. The interplay between global and local structure is one of the great themes of mathematics, (...) but rarely discussed explicitly. (shrink)

Fifty years of effort in artificial intelligence (AI) and the formalization of legal reasoning have produced both successes and failures. Considerable success in organizing and displaying evidence and its interrelationships has been accompanied by failure to achieve the original ambition of AI as applied to law: fully automated legal decision-making. The obstacles to formalizing legal reasoning have proved to be the same ones that make the formalization of commonsense reasoning so difficult, and are most evident where legal reasoning has to (...) meld with the vast web of ordinary human knowledge of the world. Underlying many of the problems is the mismatch between the discreteness of symbol manipulation and the continuous nature of imprecise natural language, of degrees of similarity and analogy, and of probabilities. (shrink)

A point charge accelerating under the influence of an external force emits electromagnetic radiation that reduces the increase in its mechanical energy. This causes a reduction in the particle's acceleration. We derive the decrease in acceleration due to radiation reaction for a particle accelerating parallel to its velocity, and show that it has a negligible effect.

The journey of the Wycliffe Global Alliance is an example of how some paradigm shifts are influencing leading in mission. Since Christianity is both an agent and product of globalization, its beliefs have spread from one source to another, crossing religious, linguistic and cultural contexts. As a result, there are polycentric or multiple centres of influence since Christianity has homes within a diversity of contexts. This carries with it various implications including how partnering in mission needs to be deconceptualized through (...) greater emphasis on friendship. In order for this to happen as a missiological principle, third spaces may need to be created. Viewed against the backdrop of church and mission agency leadership, structures may be ‘stuck in the Industrial Era’. Therefore, the stage is set for exploring how these and other themes influence leadership in God’s mission. (shrink)

When a company raises its share price by sacking workers or polluting the environment, it is avoiding paying real costs. Accountancy, which quantifies certain rights, needs to combine with applied ethics to create a "computational casuistics" or "moral accountancy", which quantifies the rights and obligations of individuals and companies. Such quantification has proved successful already in environmental accounting, in health care allocation and in evaluating compensation payments. It is argued that many rights are measurable with sufficient accuracy to make them (...) credible and legally actionable. (shrink)

We show that every countable ideal of degrees that are low for isomorphism is contained in a principal ideal of degrees that are low for isomorphism by adapting an exact pair construction. We further show that within the hyperimmune free degrees, lowness for isomorphism is entirely independent of computable traceability.

El objetivo principal de este artículo es presentar la demostración directa del Teorema de compacidad de la Lógica de primer orden (Gama tiene un modelo si y sólo si cada subconjunto finito de Gama tiene un modelo) que se realiza utilizando el Método de construcción de modelos llamado "Ultraproductos" que, a su vez, usa "Ultrafiltros". Actualmente es más común demostrar el Teorema de compacidad como un corolario del Teorema de completitud de Gödel y usar el método de reducción al absurdo (...) para probarlo. Sin embargo, vale la pena estudiar también esta prueba directa que usa Ultraproductos porque dicha técnica tiene importantes aplicaciones en investigaciones contemporáneas de matemáticas, por ejemplo en la Teoría de conjuntos y en el Análisis. Al final del artículo se realiza un breve comentario sobre Compacidad, Ultraproductos, Cardinales grandes y Modelos no estándar. (shrink)

Ultrafilters are very important mathematical objects in mathematical research [6, 22, 23]. There are a wide variety of classical theorems in various branches of mathematics where ultrafilters are applied in their proof, and other classical theorems that deal directly with ultrafilters. The objective of this article is to contribute (in a divulgative way) to ultrafilter research by describing the demonstrations of some such theorems related (uniquely or in combination) to topology, Measure Theory, algebra, combinatorial infinite, set theory and first-order logic, (...) also formulating some updated open problems of set theory that refer to non-principal ultrafilters on N, the Mathias’s model and the Solovay’s model. -/- Resumen: Los ultrafiltros son objetos matemáticos muy importantes en la investigación matemática [6, 22, 23]. Existen una gran variedad de teoremas clásicos en diversas ramas de la matemática donde se aplican ultrafiltros en su demostración, y otros teoremas clásicos que tratan directamente sobre ultrafiltros. El objetivo de este artículo es contribuir (de una manera divulgativa) con la investigación sobre ultrafiltros describiendo las demostraciones de algunos de tales teoremas relacionados (de manera única o combinada) con topología, teoría de la medida, álgebra, combinatoria infinita, teoría de conjuntos y lógica de primer orden, formulando además algunos problemas abiertos actuales de la teoría de conjuntos que se refieren a ultrafiltros no principales sobre N, al Modelo de Mathias y al Modelo de Solovay. (shrink)

Para matemáticos interesados en problemas de fundamentos, lógico-matemáticos y filósofos de la matemática, el axioma de elección es centro obligado de reflexión, pues ha sido considerado esencial en el debate dentro de las posiciones consideradas clásicas en filosofía de la matemática (intuicionismo, formalismo, logicismo, platonismo), pero también ha tenido una presencia fundamental para el desarrollo de la matemática y metamatemática contemporánea. Desde una posición que privilegia el quehacer matemático, nos proponemos mostrar los aportes que ha tenido el axioma en varias (...) áreas fundamentales de la matemática, su aplicación en la lógica de primer orden, así como una breve descripción de las pruebas de consistencia relativa debidas a Gödel y Cohen, las cuales establecieron su independencia del sistema axiomático Zermelo-Fraenkel (ZF). Con todo lo anterior mostraremos cómo el quehacer matemático contemporáneo se adscribe al platonismo matemático en los términos de Bernays y Ferreirós. Revisaremos también los argumentos de Zermelo y Cantor para permitir el uso de asunciones en la matemática, los cuales se acercan a los planteamientos de la investigación científica y esbozan relaciones con la filosofía de la práctica matemática. Finalmente, justificamos el uso del axioma de elección en la contemporaneidad, abogando por unas relaciones de equidad entre la matemática y la filosofía, presentando además su plena vigencia, a través de la referencia a algunos problemas abiertos en la actualidad que vinculan el axioma de elección con la teoría de Ramsey. (shrink)

En este artículo se presentan dos demostraciones del teorema de interpolación: Una para la lógica proposicional y otra para la lógica de primer orden. Ambas se realizan en el contexto de la teoría de modelos. El teorema de interpolación afirma que si A y B son fórmulas, donde A no es una contradicción, B no es válida, y B es una consecuencia lógica de A, entonces existe una fórmula C que esta escrita en el lenguaje común al de A y (...) de B, tal que C es una consecuencia lógica de A y B es una consecuencia lógica de C. El teorema de interpolación fue demostrado por primera vez para la lógica de primer orden por William Craig en 1957, y desde entonces se ha investigado la posibilidad de generalizarlo o aplicarlo. Dicho teorema tiene generalizaciones o aplicaciones en teoría de la demostración, teoría de modelos abstracta, ciencias de la computación, lógica modal, lógica intuicionista, etc. Se presentan ejemplos de aplicaciones o generalizaciones de la propiedad de interpolación relacionados con lógicas infinitarias, cuantificadores generalizados, segundo orden, no clásicas, abstractas, etc. También se ofrecen referencias de problemas abiertos sobre interpolación en el contexto de la teoría de modelos abstracta. (shrink)

En este artículo realizamos una reconstrucción del Programa original de Hilbert antes del surgimiento de los teoremas limitativos de la tercera década del siglo pasado. Para tal reconstrucción empezaremos por mostrar lo que Torretti llama los primeros titubeos formales de Hilbert, es decir, la defensa por el método axiomático como enfoque fundamentante. Seguidamente, mostraremos como estos titubeos formales se establecen como un verdadero programa de investigación lógico-matemático y como dentro de dicho programa la inquietud por la decidibilidad de los problemas (...) matemáticos y en específico la decidibilidad de la Lógica de primer orden cobra peso. Luego pasamos a analizar como la inquietud por la decibilidad toma lugar dentro del pensamiento filosófico-matemático de Hilbert presentándose como uno de los grandes problemas a los cuales la metamatemática debe encontrar una solución, esto lo hacemos mostrando un contraste con autores, como John von Neumann y Roberto Torretti, quienes de alguna u otra manera no interpretan el problema de la decidibilidad de la Lógica de primer orden como un problema de peso dentro del programa original de Hilbert. Finalmente argumentamos que el resultado meta-teórico de Church puede entenderse como una refutación del optimismo intelectual que permea a todo el programa original de Hilbert. (shrink)

El estudio de los "cardinales grandes" es uno de los principales temas de investigación de la teoría de conjuntos y de la teoría de modelos que ha contribuido con el desarrollo de dichas disciplinas. Existe una gran variedad de tales cardinales, por ejemplo cardinales inaccesibles, débilmente compactos, Ramsey, medibles, supercompactos, etc. Tres valiosos teoremas clásicos sobre cardinales medibles son los siguientes: (i) compacidad débil, (ii) Si κ es un cardinal medible, entonces κ es un cardinal inaccesible y existen κ cardinales (...) inaccesibles menores que κ , y (iii) Si existe un cardinal medible, entonces el axioma de constructibilidad (V=L) es falso. El objetivo de este artículo es presentar una demostración de cada uno de estos tres teoremas en el contexto de la teoría de modelos usando ideas del texto de Chang y Keisler (Model Theory). Tales demostraciones tienen en común el uso del método de construcción de modelos llamado ultraproductos, de lógicas infinitarias o fragmentos de la lógica de segundo orden, y del axioma de elección. Cardinales grandes y/o ultraproductos son importantes en teoría de conjuntos, teoría de modelos, análisis matemático, teoría de la medida, probabilidades, topología, análisis funcional, física, teoría de números, finanzas, etc. (shrink)

We study several perfect set properties of the Baire space which follow from the Ramsey property ω→(ω) ω . In particular we present some independence results which complete the picture of how these perfect set properties relate to each other.

Resumen: En la actualidad uno de los libros más usados para dar lógica elemental es el de Irving Copi y Carl Cohen (Introducción a la lógica, 2001), allí se presentan unas reglas para decidir la validez de los silogismos categóricos de forma estándar. Pero en tal texto ni en ninguno que nosotros conozcamos se ofrece una fundamentación de las mismas. Es decir, una demostración de que ellas son realmente una condición necesaria y suficiente de la validez de un silogismo categórico (...) de forma estándar, lo único que hemos leído es su motivación como condición necesaria. El objetivo de este trabajo es ofrecer una fundamentación de las mismas usando la noción de conjunto (o clase) y la técnica de diagramas de Venn, un concepto y una técnica que están expuestos en los principales textos de lógica elemental, incluyendo el referido anteriormente. -/- Abstract: Currently, one of the most widely used textbooks in elementary logic is the one by Irving Copi and Carl Cohen (Introduction to Logic, 2001). They offer rules for deciding the validity of standard categorical syllogisms. But neither that textbook, nor any other we know of, provides the foundations of these rules; that is to say, the demonstration that they are a necessary and sufficient condition for the validity of a standard categorical syllogism. We have only found motivations for the necessary condition. The main goal of this work is to provide a foundation of these rules using the notion of set as well as Venn diagrams, a concept and a technique exposed in the main textbooks of logic, including the aforementioned. (shrink)

Habermas and Apel commonly defend a form of universal moral theory that is also postmetaphysical. Still, they differ with respect to both the character and the justification of a universal moral principle. Habermas denies and Apel asserts that this principle is a transcendental condition of life practice or human activity as such, and each criticizes the claims of the other. This paper argues that each is correct in his criticism of the other and, therefore, both are wrong. The contention between (...) them cannot be resolved within the post metaphysical conviction they have in common, and the reasons for this conclusion imply that a universal moral principle cannot be redeemed independently of metaphysics. (shrink)

This article’s objetive is to present four application examples of Herbrand’s theorem to decide the validity of reasoning on first order language, in accordance whit Church’s Undecidability’s theorem. Also, to tell which is the principal problem around it. The logical resolution calculus will be worked on this article, which is a method used in artificial intelligence.

El objetivo de este trabajo es presentar en un solo cuerpo tres maneras de relativizar (o generalizar) el concepto de conjunto constructible de Gödel que no suelen aparecer juntas en la literatura especializada y que son importantes en la Teoría de Conjuntos, por ejemplo para resolver problemas de consistencia o independencia. Presentamos algunos modelos resultantes de las diferentes formas de relativizar el concepto de constructibilidad, sus propiedades básicas y algunas formas débiles del Axioma de Elección válidas o no válidas en (...) ellas. (shrink)

The late twentieth century saw two long-term trends in popular thinking about ethics. One was an increase in relativist opinions, with the “generation of the Sixties” spearheading a general libertarianism, an insistence on toleration of diverse moral views (for “Who is to say what is right? – it’s only your opinion.”) The other trend was an increasing insistence on rights – the gross violations of rights in the killing fields of the mid-century prompted immense efforts in defence of the “inalienable” (...) rights of the victims of dictators, of oppressed peoples, of refugees. The obvious incompatibility of those ethical stances, one anti-objectivist, the other objectivist in the extreme, proved no obstacle to their both being held passionately, often by the same people. (shrink)

¿Qué ha pasado con el problema del cardinal del continuo después de Gödel (1938) y Cohen (1964)? Intentos de responder esta pregunta pueden encontrarse en los artículos de José Alfredo Amor (1946-2011), "El Problema del continuo después de Cohen (1964-2004)", de Carlos Di Prisco , "Are we closer to a solution of the continuum problem", y de Joan Bagaria, "Natural axioms of set and the continuum problem" , que se pueden encontrar en la biblioteca digital de mi blog de Lógica (...) Matemática y Fundamentos de la Matemática (ver). También en la entrada "The Continuum Hypothesis" de la web de Enciclopedia de Filosofía de la Universidad de Stanford existe información importante y actualizada al respecto. En esta breve nota se comenta sobre el tema de una manera divulgativa. (shrink)

The objective of this article is to present an original proof of the following theorem: Thereis a generic extension of the Solovay’s model L(R) where there is a linear order of P(N)/fin that extends to the partial order (P(N)/f in), ≤*). Linear orders of P(N)/fin are important because, among other reasons, they allow constructing non-measurable sets, moreover they are applied in Ramsey's Theory .

Do people hold robots responsible for their actions? While Clark and Fischer present a useful framework for interpreting social robots, we argue that they fail to account for people's willingness to assign responsibility to robots in certain contexts, such as when a robot performs actions not predictable by its user or programmer.

En el ámbito de la lógica matemática existe un problema sobre la relación lógica entre dos versiones débiles del Axioma de elección (AE) que no se ha podido resolver desde el año 2000 (aproximadamente). Tales versiones están relacionadas con ultrafiltros no principales y con Propiedades Ramsey (Bernstein, Polarizada, Subretículo, Ramsey, Ordinales flotantes, etc). La primera versión débil del AE es la siguiente (A): “Existen ultrafiltros no principales sobre el conjunto de los números naturales (ℕ)”. Y la segunda versión débil del (...) AE es la siguiente (B): “Existen ultraflitros sobre ℕ”. Se sabe que A implica B, pero se desconoce si B implica A. Di Prisco y Henle conjeturan en los artículos ([1], [2]) que esto no ocurre, es decir, conjeturan que B no implica A, en otras palabras, conjeturan que A es más fuerte estrictamente que B, que A es independiente de B, pero esto no se ha podido demostrar todavía aunque se ha intentado hacer desde hace aproximadamente 21 años. Una descripción detallada de este problema abierto puede encontrarse en esta ponencia (dictada en el marco del Día Mundial de la Lógica 14-01-2022) y en el artículo [3]. [1] C. Di Prisco y H. Henle. “Doughnuts, Floating Ordinals, Square Brackets, and Ultraflitters”. Journal of Symbolic Logic 65 (2000) 462-473. [2] C. Di Prisco y H. Henle. “Partitions of the reals and choice”. En “Models, algebras and proofs”. X. Caicedo y C.M. Montenegro. Eds. Lecture Notes in Pure and Appl. Math, 203, Marcel Dekker, 1999. [3] F. Galindo. “Tópicos de ultrafiltros”. Divulgaciones Matemáticas. Vol. 21, No 1-2, 2020. (shrink)

El objetivo de este artículo es presentar dos tópicos de Lógica matemática y sus fundamentos: El primer tópico es una actualización de la demostración de Alonzo Church del Teorema de completitud de Gödel para la Lógica de primer orden, la cual aparece en su texto "Introduction to Mathematical Logic" (1956) y usa el procedimientos efectivos de Forma normal prenexa y Forma normal de Skolem; y el segundo tópico es una demostración de que la propiedad de partición (tipo Ramsey) del espacio (...) topológico de Baire llamada "Propiedad de partición polarizada" es falsa en el Modelo Básico de Cohen. (shrink)

The teaching of the Aquinas Academy in its first thirty years was based on the scholastic philosophy of Thomas Aquinas, then regarded as the official philosophy of the Catholic Church. That philosophy has not been so much heard of in the last thirty years, but it has a strong presence below the surface. Its natural law theory of ethics, especially, still informs Vatican pronouncements on moral topics such as contraception and euthanasia. It has also been important in Australia in the (...) High Court’s deliberations on the Mabo case. It is argued that some officially-sanctioned deductions on particular cases have not been correct, but that any attempt to do without a natural law foundation of ethics would throw out the baby with the bathwater. The sense of the basic objective worth of persons that is the centre of natural law ethics is essential to any ethics better than a simple “might is right” approach. (shrink)

In this paper I argue, using two case studies of episodes from recent physics against the contingency view advocated by social constructionists. In this view, physics, or science in general, is, in Ian Hacking’s words, not determined by anything. Much of the previous discussion has centered on examples of scientific success. In this paper I argue that experimental evidence and reasoned and critical discussion played the crucial role in the refutation of a previously strongly believed hypothesis, and in the decision (...) that a proposed new elementary particle did not exist, leaving no reasonable doubt. I suggest that the argument against contingency does not require the absence of all possible doubt, but rather the absence of reasonable doubt.Keywords: Contingency; Refutation; 17-keV neutrino; Parity nonconservation. (shrink)

Brains, unlike artificial neural nets, use symbols to summarise and reason about perceptual input. But unlike symbolic AI, they “ground” the symbols in the data: the symbols have meaning in terms of data, not just meaning imposed by the outside user. If neural nets could be made to grow their own symbols in the way that brains do, there would be a good prospect of combining neural networks and symbolic AI, in such a way as to combine the good features (...) of each. The article argues the cluster analysis provides algorithms to perform the task, and that any solution to the task must be a form of cluster analysis. (shrink)

In the target article, Baars has offered both a theory of consciousness and a strategy for scientifically testing the theory. This commentary is intended as an addendum. I'd like to suggest implementing global workspace agents as both an additional strategy toward scientific testing, and as a means of fleshing out the theory.

Uses connectionism (neural networks) to extract the "gist" of a story in order to represent a context going forward for the disambiguation of incoming words as a text is processed.

Though there is no international government, there are many international regimes that enact binding regulations on particular matters. They include the Basel II regime in banking, IFRS in accountancy, the FIRST computer incident response system, the WHO’s system for containing global epidemics and many others. They form in effect a very powerful international public sector based on technical expertise. Unlike the public services of nation states, they are almost free of accountability to any democratically elected body or to any legal (...) system. Although by and large they have acted for good, the dangers of long-term unaccountability are illustrated by the travesties of justice perpetrated by the International Labour Organisation Administrative Tribunal. (shrink)

methods that have shown promise for improving extreme risk analysis, particularly for assessing the risks of invasive pests and pathogens associated with international trade. We describe the legally inspired regulatory regime for banks, where these methods have been brought to bear on extreme ‘operational risks’. We argue that an ‘advocacy model’ similar to that used in the Basel II compliance regime for bank operational risks and to a lesser extent in biosecurity import risk analyses is ideal for permitting the diversity (...) of relevant evidence about invasive species to be presented and soundly evaluated. We recommend that the process be enhanced in ways that enable invasion ecology to make more explicit use of the methods found successful.. (shrink)

Both philosophical and practical analyses of global justice issues have been vitiated by two errors: a too-high emphasis on the supposed duties of collectives to act, and a too-low emphasis on the analysis of causes and risks. Concentrating instead on the duties of individual actors and analysing what they can really achieve reconfigures the field. It diverts attention from individual problems such as poverty or refugees or questions on what states should do. Instead it shows that there are different duties (...) for political leaders, intelligence operatives, opinion leaders and citizens in devising, urging and implementing such plans as transfers of aid with accountability, military interventions in rogue states and limited intakes of refugees. With collectivist excuses for inaction such as sovereignty out of the way, it is possible to take a cautiously optimistic view of the possibility of forceful and morally responsible interventions in the range of major global problems. (shrink)

Australian women who are university graduates have fewer children than non-graduates. In most cases this appears to be the result of circumstantial pressures not preference. Long years of study fill the most fertile years of women students and new graduates need further time to establish their careers. The chance of medical infertility increases with age so, for some, this means that childbearing is not postponed but ruled out. Graduates who do make the transition from university to professional work find that (...) working hours are long and that professional occupations are now both highly demanding and insecure. Women who take time off to care for young children must depend on one insecure income (their partner’s) rather than two, and their return to work is uncertain. These difficulties of time, money and insecurity are compounded by problems in finding a suitable partner. They are magnified by the enduring tendency of women to marry up. Thus it can be more difficult for women graduates to find husbands than it is for women who are non-graduates. (shrink)

Church's Undecidability Theorem is one of the meta-theoretical results of the mid-third decade of the last century, which along with other limiting theorems such as those of Gödel and Tarski have generated endless reflections and analyzes, both within the framework of the formal sciences, that is, mathematics, logic and theoretical computation, as well as outside them, especially the philosophy of mathematics, philosophy of logic and philosophy of mind. We propose, as a general purpose of this article, to formulate Church's Undecidability (...) Theorem and present the main ideas of its demonstration. In order to carry out the first objective, we need to introduce and explain the notions of recursive function and numbering used by Gödel, which will allow to formally and rigorously enunciate Church's Theorem. After we enunciate Church's Theorem of Unspeakability in a formal and rigorous manner, we will present the main ideas of the proof of Church's Undecidability Theorem for First Order Logic, which uses Robinson's axiomatic system for arithmetic and four facts about himself: In Robinson's system for arithmetic recursive functions are representable Robinson's system is undecidable, The number of axioms proper to the Robinson system is finite and The logical calculation of the Robinson system is equal to the calculation of the first-order logic. (shrink)

My dissertation develops a novel theory of free will and moral responsibility, Strawsonian libertarianism, which combines Strawsonianism about the concept of moral responsibility with event-causal libertarianism concerning its conditions of application. I construct this theory in light of and response to the three main objections to libertarianism: the moral shallowness objection, the intelligibility objection, and the empirical plausibility objection.The moral shallowness objection contends that libertarianism seems plausible only in the absence of a robust understanding of the nature of moral responsibility. (...) P.F. Strawson's work is the fount of this objection. In response I argue, surprisingly, that Strawson's account of the nature of responsibility, according to which the essence of responsibility is defined in terms of the reactive attitudes (such as gratitude and resentment), actually leads to libertarianism about its conditions of application. In defense of this contention I offer a theory of the normative force of excuse which shows that moral responsibility requires that agents have free will. I then construct the No Opportunity Argument which demonstrates that free will, and thus moral responsibility, is incompatible with determinism.In the remainder of the dissertation I develop and defend this account of moral responsibility against the intelligibility and empirical objections, both of which focus on my contention that indeterminism is necessary for freedom and responsibility. The intelligibility objection contends that libertarians cannot provide an intelligible account of freedom and responsibility because indeterminism is either (at best) irrelevant or (at worst) inimical to control. I respond to these objections by showing that if we locate indeterminism at the moment of free choice, libertarianism can explain both why indeterminism does not diminish control and also how it is relevant to enhancing it.Finally, I turn to the empirical plausibility objection which contends that libertarianism is scientifically implausible. This objection centers on my contention that humans must be indeterministic systems in order to be free and responsible. I argue that my commitment to neuronal indeterminism fares well in light of current physical and neurobiological findings and, therefore, that Strawsonian libertarianism is not as scientifically demanding as many have thought. (shrink)

Cognition, writ broadly to include motivation and emotion, is best conceived of as control structure for autonomous agents . Autonomous agents are situated in a environment. They both sense and act on that environment, over time, so as to effect subsequent sensing. Examples of such agents include humans, animals, some mobile robots, some artificial life creatures (who "live" in a simulated environment on a computer) and some software agents (who "live" in a file system, a database, or on a network). (...) Their actions are in pursuit of their own agendas, as designed in by their maker or programmer, or as evolved and shaped by culture. Each such agent employs some control mechanism whose continual duty is to select the next action. The term "cognition," in its broad sense, refers to the workings of such control mechanisms. (shrink)