“The Ethics of Infection Challenges in Primates,” by Anne Barnhill, Steven Joffe, and Franklin Miller, is an exceptionally timely contribution to the literature on animal research ethics. Animal research has long been both a source of high hopes and a cause for moral concern. When it comes to infection challenge studies with nonhuman primates, neither the hope—to save thousands of human lives from such diseases as Ebola and Marburg—nor the concern—the conviction that primates deserve especially strong protections—could be (...) much higher. Coming just a few years after the National Institutes of Health adopted the Institute of Medicine's recommendations regarding chimpanzees, Barnhill and colleagues attempt to nudge the clarification and specification—one might say the evolution—of NHP research ethics and regulation. They assert that NHP challenge studies “are not justified by marginal gains in human safety or by efficacy gains that are unlikely to translate directly into saving human lives or preventing morbidity.” How, in turn, is their standard—which, although stringent, does permit causing NHPs to suffer and die for human benefit—to be justified? (shrink)

Walter Sinnott-Armstrong and Franklin G Miller recently argued that the wrongness of killing is best explained by the harm that comes to the victim, and that ‘total disability’ best explains the nature of this harm. Hence, killing patients who are already totally disabled is not wrong. I maintain that their notion of total disability is ambiguous and that they beg the question with respect to whether there are abilities left over that remain relevant for the goods of personhood (...) and human worth. If these goods remain, then something more is lost in death than in ‘total disability,’ and their explanation of what makes killing wrong comes up short. But if total disability is equivalent with death, then their argument is an interesting one. (shrink)

Space exploration and the search for a better understanding of life have never been entirely separate from one another. This is not simply a matter of policy, a decision by political administrations to combine the two. Rather, it is a matter of the ways in which both draw upon the same scientific culture and upon overlapping societal influences. Some of the latter are the political influences of particular times and particular places, others are of a far broader nature. Progress in (...) one field has tended to be combined with advances in the other. It is a familiar point that, in the very year that NASA was founded, i.e. 1958, the American molecular biologist Joshua Lederberg won a Nobel Prize for his discovery that bacteria can exchange genetic material (a process now known as ‘bacterial conjugation’). This, in turn, was only six years after the classicMiller-Urey experiment to replicate the production of some of the chemical precursors of life. And the Miller-Urey experiment, in turn, overlapped in time with the work of Watson, Crick and Rosalind Franklin in England, on the structure of DNA. Major breakthroughs came in both fields (activity in space and research into life) within the same time-frame, and drew upon at least some of the same background influences and interests. When Lederberg went on to work with NASA on the early programs to look for life on Mars, the progression was, in an everyday sense, natural. Interest in space and interest in life went together. They have always tended to do so. (shrink)

Temporal dynamists argue that we should believe that there exists temporal passage because there being passage is the best explanation for the presence of our temporal phenomenology. Some non-dynamists have countered that the presence of passage makes no difference to our temporal phenomenology, and consequently that temporal phenomenology cannot be evidence that there is passage. This paper attempts to bolster this non-dynamist response by offering new arguments for the claim that the presence of passage makes no difference to our phenomenology.

The interventionist account of causal explanation, in the version presented by Jim Woodward, has been recently claimed capable of buttressing the widely felt—though poorly understood—hunch that high-level, relatively abstract explanations, of the sort provided by sciences like biology, psychology and economics, are in some cases explanatorily optimal. It is the aim of this paper to show that this is mistaken. Due to a lack of effective constraints on the causal variables at the heart of the interventionist causal-explanatory scheme, as presently (...) formulated it is either unable to prefer high-level explanations to low, or systematically overshoots, recommending explanations at so high of a level as to be virtually vacuous. (shrink)

Philosophers of experiment have acknowledged that experiments are often more than mere hypothesis-tests, once thought to be an experiment's exclusive calling. Drawing on examples from contemporary biology, I make an additional amendment to our understanding of experiment by examining the way that `wide' instrumentation can, for reasons of efficiency, lead scientists away from traditional hypothesis-directed methods of experimentation and towards exploratory methods.

In What Science Knows, the Australian philosopher and mathematician James Franklin explains in captivating and straightforward prose how science works its magic. It offers a semipopular introduction to an objective Bayesian/logical probabilist account of scientific reasoning, arguing that inductive reasoning is logically justified (though actually existing science sometimes falls short). Its account of mathematics is Aristotelian realist.

Transcript of an Interview on the podcast: Irreverend: Faith and Current Affairs.

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)

How were reliable predictions made before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? The book examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates. Also included are the problem of induction before Hume, design arguments for (...) the existence of God, and theories on how to evaluate scientific and historical hypotheses. It is explained how Pascal and Fermat's work on chance arose out of legal thought on aleatory contracts. The book interprets pre-Pascalian unquantified probability in a generally objective Bayesian or logical probabilist sense. (shrink)

What is it about a person's becoming an adult that makes it generally inappropriate to treat that person paternalistically any longer? The Standard View holds that a mere difference in age or stage of life cannot in itself be morally relevant, but only matters insofar as it is correlated with the development of capacities for mature practical reasoning. This paper defends the contrary view: two people can have all the same general psychological attributes and yet the mere fact that one (...) person is at the beginning of a life and another in the middle of one can justify treating the younger person more paternalistically than the older one. Recognising the moral relevance of age, moreover, is crucial if one is to accommodate both the liberal moral ideal of respect for autonomy and our demanding educational aims, given that these otherwise come into conflict with one another. (shrink)

Philosophical discussions of species have focused on multicellular, sexual animals and have often neglected to consider unicellular organisms like bacteria. This article begins to fill this gap by considering what species concepts, if any, apply neatly to the bacterial world. First, I argue that the biological species concept cannot be applied to bacteria because of the variable rates of genetic transfer between populations, depending in part on which gene type is prioritized. Second, I present a critique of phylogenetic bacterial species, (...) arguing that phylogenetic bacterial classification requires a questionable metaphysical commitment to the existence of essential genes. I conclude by considering how microbiologists have dealt with these biological complexities by using more pragmatic and not exclusively evolutionary accounts of species. I argue that this pragmatism is not borne of laziness but rather of the substantial conceptual problems in classifying bacteria based on any evolutionary standard. (shrink)

Just before the Scientific Revolution, there was a "Mathematical Revolution", heavily based on geometrical and machine diagrams. The "faculty of imagination" (now called scientific visualization) was developed to allow 3D understanding of planetary motion, human anatomy and the workings of machines. 1543 saw the publication of the heavily geometrical work of Copernicus and Vesalius, as well as the first Italian translation of Euclid.

It has been a common assumption that words are substances that instantiate or have properties. In this paper, I question the assumption that our ontology of words requires posting substances by outlining a bundle theory of words, wherein words are bundles of various sorts of properties (such as semantic, phonetic, orthographic, and grammatical properties). I argue that this view can better account for certain phenomena than substance theories, is ontologically more parsimonious, and coheres with claims in linguistics.

This paper argues for a particular view about in what metaphysical equivalence consists: namely, that any two metaphysical theories are metaphysically equivalent if and only if those theories are strongly hyperintensionally equivalent. It is consistent with this characterisation that said theories are weakly hyperintensionally distinct, thus affording us the resources to model the content of propositional attitudes directed towards metaphysically equivalent theories in such a way that non-ideal agents can bear different propositional attitudes towards metaphysically equivalent theories.

Dispostions, such as solubility, cannot be reduced to categorical properties, such as molecular structure, without some element of dipositionaity remaining. Democritus did not reduce all properties to the geometry of atoms - he had to retain the rigidity of the atoms, that is, their disposition not to change shape when a force is applied. So dispositions-not-to, like rigidity, cannot be eliminated. Neither can dispositions-to, like solubility.

Explains Aristotle's views on the possibility of continuous variation between biological species. While the Porphyrean/Linnean classification of species by a tree suggests species are distributed discretely, Aristotle admitted continuous variation between species among lower life forms.

The winning entry in David Stove's Competition to Find the Worst Argument in the World was: “We can know things only as they are related to us/insofar as they fall under our conceptual schemes, etc., so, we cannot know things as they are in themselves.” That argument underpins many recent relativisms, including postmodernism, post-Kuhnian sociological philosophy of science, cultural relativism, sociobiological versions of ethical relativism, and so on. All such arguments have the same form as ‘We have eyes, therefore we (...) cannot see’, and are equally invalid. (shrink)

This paper has three main sections. The first section provides a general characterisation of presentism, eternalism and growing blockism. It presents a pair of core, defining claims that jointly capture each of these three views. This makes clear the respects in which the different views agree, and the respects in which they disagree, about the nature of time. The second section takes these characterisations and considers whether we really do have three distinct views, or whether defenders of these views are (...) somehow talking past one another when they claim to disagree. The third section looks at the key objections to each view and considers some of the replies that can be made to those objections. The paper concludes by offering some thoughts about how future research might help us resolve the debate between defenders of these three views. (shrink)

The imperviousness of mathematical truth to anti-objectivist attacks has always heartened those who defend objectivism in other areas, such as ethics. It is argued that the parallel between mathematics and ethics is close and does support objectivist theories of ethics. The parallel depends on the foundational role of equality in both disciplines. Despite obvious differences in their subject matter, mathematics and ethics share a status as pure forms of knowledge, distinct from empirical sciences. A pure understanding of principles is possible (...) because of the simplicity of the notion of equality, despite the different origins of our understanding of equality of objects in general and of the equality of the ethical worth of persons. (shrink)

Metaphysics is supposed to tell us about the metaphysical nature of our world: under what conditions composition occurs; how objects persist through time; whether properties are universals or tropes. It is near orthodoxy that whichever of these sorts of metaphysical claims is true is necessarily true. This paper looks at the debate between that orthodox view and a recently emerging view that claims like these are contingent, by focusing on the metaphysical debate between monists and pluralists about concrete particulars. This (...) paper argues that we should be contingentists about monism and pluralism, and it defends contingentism against some necessitarian objections by offering an epistemology of contingent metaphysical claims. (shrink)

The classical arguments for scepticism about the external world are defended, especially the symmetry argument: that there is no reason to prefer the realist hypothesis to, say, the deceitful demon hypothesis. This argument is defended against the various standard objections, such as that the demon hypothesis is only a bare possibility, does not lead to pragmatic success, lacks coherence or simplicity, is ad hoc or parasitic, makes impossible demands for certainty, or contravenes some basic standards for a conceptual or linguistic (...) scheme. Since the conclusion of the sceptical argument is not true, it is concluded that one can only escape the force of the argument through some large premise, such as an aptitude of the intellect for truth, if necessary divinely supported. (shrink)

People increasingly form beliefs based on information gained from automatically filtered Internet ‎sources such as search engines. However, the workings of such sources are often opaque, preventing ‎subjects from knowing whether the information provided is biased or incomplete. Users’ reliance on ‎Internet technologies whose modes of operation are concealed from them raises serious concerns about ‎the justificatory status of the beliefs they end up forming. Yet it is unclear how to address these concerns ‎within standard theories of knowledge and justification. (...) To shed light on the problem, we introduce a ‎novel conceptual framework that clarifies the relations between justified belief, epistemic responsibility, ‎action, and the technological resources available to a subject. We argue that justified belief is subject to ‎certain epistemic responsibilities that accompany the subject’s particular decision-taking circumstances, ‎and that one typical responsibility is to ascertain, so far as one can, whether the information upon which ‎the judgment will rest is biased or incomplete. What this responsibility comprises is partly determined by ‎the inquiry-enabling technologies available to the subject. We argue that a subject’s beliefs that are ‎formed based on Internet-filtered information are less justified than they would be if she either knew how ‎filtering worked or relied on additional sources, and that the subject may have the epistemic ‎responsibility to take measures to enhance the justificatory status of such beliefs.‎. (shrink)

Scientific consensus is widely deferred to in public debates as a social indicator of the existence of knowledge. However, it is far from clear that such deference to consensus is always justified. The existence of agreement in a community of researchers is a contingent fact, and researchers may reach a consensus for all kinds of reasons, such as fighting a common foe or sharing a common bias. Scientific consensus, by itself, does not necessarily indicate the existence of shared knowledge among (...) the members of the consensus community. I address the question of under what conditions it is likely that a consensus is in fact knowledge based. I argue that a consensus is likely to be knowledge based when knowledge is the best explanation of the consensus, and I identify three conditions—social calibration, apparent consilience of evidence, and social diversity, for knowledge being the best explanation of a consensus. (shrink)

I develop the foundation for cosmopolitan care, an underexplored variety of moral cosmopolitanism. I begin by offering a characterization of contemporary cosmopolitanism from the justice tradition. Rather than discussing the political, economic or cultural aspects of cosmopolitanism, I instead address its moral dimensions. I then employ a feminist philosophical perspective to provide a critical evaluation of the moral foundations of cosmopolitan justice, with an eye toward demonstrating the need for an alternative account of moral cosmopolitanism as cosmopolitan care. After providing (...) an explanation of how care ethics in connection with Kantian ethics generates a duty to care, I consider one main feature of cosmopolitan care, namely the theory of obligation it endorses. In developing this account, I place special emphasis on the practical ramifications of the theory by using it to analyze gender violence in conflict zones. (shrink)

The natural name theory, recently discussed by Johnson (2018), is proposed as an explanation of pure quotation where the quoted term(s) refers to a linguistic object such as in the sentence ‘In the above, ‘bank’ is ambiguous’. After outlining the theory, I raise a problem for the natural name theory. I argue that positing a resemblance relation between the name and the linguistic object it names does not allow us to rule out cases where the natural name fails to resemble (...) the linguistic object it names. I argue that to avoid this problem, we can combine the natural name theory with a type-realist metaphysics of language, and hold that the name is natural because the name is an instance of the kind that it names. I conclude by reflecting on the importance of the metaphysics of language for questions in the philosophy of language. (shrink)

A collection of articles on the the principles of social justice from an Australian Catholic perspective. Contents: Forward (Archbishop Philip Wilson), Introduction (James Franklin), The right to life (James Franklin), The right to serve and worship God in public and private (John Sharpe), The right to religious formation (Richard Rymarz), The right to personal liberty under just law (Michael Casey), The right to equal protection of just law regardless of sex, nationality, colour or creed (Sam Gregg), The right (...) to freedom of expression (Damian Grace), The right to choose and freely maintain a state of life, married or single, lay or religious (Marita Winters), The right to education (Anthony Cleary), The right to petition government for the redress of grievances (Paul Russell), The right to a nationality (Andrew Hamilton), The right to have access to the means of livelihood, by migration when necessary (Brenda Hubber), The right of association and peaceful assembly (Michael Hogan), The right to work and choose one's occupation (Ian Blandthorn), The right to personal ownership, use and disposal of property subject to the right of others (Brian Coman), The right to a living wage (Garrick Small), The right to collective bargaining (Keith Harvey), The right to associate by industries and professions to obtain economic justice (Henrik Jurisevic), The right to assistance from society, if necessary from the State, in distress of persons and family (Catherine Althaus), Afterword (James Franklin). (shrink)

• It would be a moral disgrace for God (if he existed) to allow the many evils in the world, in the same way it would be for a parent to allow a nursery to be infested with criminals who abused the children. • There is a contradiction in asserting all three of the propositions: God is perfectly good; God is perfectly powerful; evil exists (since if God wanted to remove the evils and could, he would). • The religious believer (...) has no hope of getting away with excuses that evil is not as bad as it seems, or that it is all a result of free will, and so on. Piper avoids mentioning the best solution so far put forward to the problem of evil. It is Leibniz’s theory that God does not create a better world because there isn’t one — that is, that (contrary to appearances) if one part of the world were improved, the ramifications would result in it being worse elsewhere, and worse overall. It is a “bump in the carpet” theory: push evil down here, and it pops up over there. Leibniz put it by saying this is the “Best of All Possible Worlds”. That phrase was a public relations disaster for his theory, suggesting as it does that everything is perfectly fine as it is. He does not mean that, but only that designing worlds is a lot harder than it looks, and determining the amount of evil in the best one is no easy matter. Though humour is hardly appropriate to the subject matter, the point of Leibniz’s idea is contained in the old joke, “An optimist is someone who thinks this is the best of all possible worlds, and a pessimist thinks.. (shrink)

Some courses achieve existence, some have to create Professional Issues and Ethics in existence thrust upon them. It is normally Mathematics; but if you don’t do it, we will a struggle to create a course on the ethical be.” I accepted. or social aspects of science or mathematics. The gift of a greenfield site and a bull- This is the story of one that was forced to dozer is a happy occasion, undoubtedly. But exist by an unusual confluence of outside (...) cirwhat to do next? It seemed to me I should cumstances. ensure the course satisfied these require- In the mid 1990s, the University of New ments: South Wales instituted a policy that all its • It should look good to students, to staff. (shrink)

Recent work in personal identity has emphasized the importance of various conventions, or ‘person-directed practices’ in the determination of personal identity. An interesting question arises as to whether we should think that there are any entities that have, in some interesting sense, conventional identity conditions. We think that the best way to understand such work about practices and conventions is the strongest and most radical. If these considerations are correct, persons are, on our view, conventional constructs: they are in part (...) constituted by certain conventions. A person exists only if the relevant conventions exist. A person will be a conscious being of a certain kind combined with a set of conventions. Some of those conventions are encoded in the being itself, so requiring the conventions to exist is requiring the conscious being to be organized in a particular way. In most cases the conventions in question are settled. There is no dispute about what the conventions are, and thus no dispute about which events a person can survive. These are cases where we take the conventions so much for granted, that it is easy to forget that they are there, and that they are necessary constituents of persons. Sometimes though, conventions are not settled. Sometimes there is a dispute about what the conventions should be, and thus a dispute about what events a person can survive. These are the traditional puzzle cases of personal identity. That it appears that conventions play a part in determining persons’ persistence conditions only in these puzzle cases is explained by the fact that only in these cases are the conventions unsettled. Settled or not though, conventions are necessary constituents of persons. (shrink)

El objetivo de este artículo es presentar una demostración de un teorema clásico sobre álgebras booleanas y ordenes parciales de relevancia actual en teoría de conjuntos, como por ejemplo, para aplicaciones del método de construcción de modelos llamado “forcing” (con álgebras booleanas completas o con órdenes parciales). El teorema que se prueba es el siguiente: “Todo orden parcial se puede extender a una única álgebra booleana completa (salvo isomorfismo)”. Donde extender significa “sumergir densamente”. Tal demostración se realiza utilizando cortaduras de (...) Dedekind siguiendo el texto “Set Theory” de Jech, y otras ideas propias del autor de este artículo. Adicionalmente, se formulan algunas versiones débiles del axioma de elección relacionadas con las álgebras booleanas, las cuales son también de gran importancia para la investigación en teoría de conjuntos y teoría de modelos, pues estas son poderosas técnicas de construcción de modelos, como por ejemplo, el teorema de compacidad (permite construir modelos no estándar, etc) y el teorema del ultrafiltro, que permite construir ultraproductos (pueden ser usados para investigar problemas de cardinales grandes, etc). Se presentan algunas referencias de problemas abiertos sobre el tema. -/- The objective of this paper is to present a demonstration of a classical theorem on boolean algebras and partial orders of current relevance in set theory, as for example, for applications of model construction method called forcing" (with boolean algebras complete or with partial orders). The theorem to be proved is as follows: Any partial order can be extended to a single complete boolean algebra (up to isomorphism)". Where to extend means embed densely". Such a demonstration is done using Dedekind's cuts following the text Set Theory" of Jech, and other ideas of the author of this article. In addition, some weak versions of the axiom of choice related to boolean algebras are formulated, which are also of great importance for the research in set theory and model theory, since this are powerful model construction techniques, such as the compactness theorem (allows the construction of non-standard models, etc.) and the ultralter theorem, which allows the construction of ultraproducts (can be used to investigate problems of large cardinals, etc). Some references of open problems on the subject are presented. (shrink)

It is possible to wholly exist at multiple spatial locations at the same time. At least, if time travel is possible and objects endure, then such must be the case. To accommodate this possibility requires the introduction of a spatial analog of either relativising properties to times—relativising properties to spatial locations—or of relativising the manner of instantiation to times—relativising the manner of instantiation to spatial locations. It has been suggested, however, that introducing irreducibly spatially relativised or spatially adverbialised properties presents (...) some difficulties for the endurantist. I will consider an objection according to which embracing such spatially relativised properties could lead us to reject mereology altogether in favour of a metaphysics according to which objects are wholly present at every space-time point at which they exist. I argue that although such a view is coherent, there are some good reasons to reject it. Moreover, I argue that the endurantist can introduce spatially relativised or adverbialised properties without conceding that objects lack spatial parts. Such a strategy has the additional advantage that it allows the endurantist not only to explain time travel, but also to reconcile our competing intuitions about cases of fission. (shrink)

Stove's article, 'So you think you are a Darwinian?'[ 1] was essentially an advertisement for his book, Darwinian Fairytales.[ 2] The central argument of the book is that Darwin's theory, in both Darwin's and recent sociobiological versions, asserts many things about the human and other species that are known to be false, but protects itself from refutation by its logical complexity. A great number of ad hoc devices, he claims, are used to protect the theory. If co operation is observed (...) where the theory predicts competition, then competition is referred to the time of the cavemen, or is reinterpreted as competition between some hidden entities like genes or abstract entities like populations. In a characteristic sally, Stove writes of the sociobiologists' oscillation on the meaning of kin altruism: Any discussion of altruism with an inclusive fitness theorist is, in fact, exactly like dealing with a pair of balloons connected by a tube, one balloon being the belief that kin altruism is an illusion, the other being the belief that kin altruism is caused by shared genes. If a critic puts pressure on the illusion balloon - perhaps by ridiculing the selfish theory of human nature - air is forced into the causal balloon. There is then an increased production of earnest causal explanations of why we love our children, why hymenopteran workers look after their sisters, etc., etc. Then, if the critic puts pressure on the causal balloon - perhaps about the weakness of sibling altruism compared with parental, or the absence of sibling altruism in bacteria - then the illusion balloon is forced to expand. There will now be an increased production of cynical scurrilities about parents manipulating their babies for their own advantage, and vice versa, and in general, about the Hobbesian bad times that are had by all. In this way critical pressure, applied to the theory of inclusive fitness at one point, can always be easily absorbed at another point, and the theory as a whole is never endangered.[ 3] Now, it is uncontroversial to assert that Darwinism is a logically complex theory, and that its relation to empirical evidence is distant and multi faceted. One does not directly observe chance genetic variations leading to the development of new species, or even continuous variations in the fossil record, but must rely on subtle arguments to the best explanation, scaling up from varieties to species, and so on.. (shrink)

I argue that Schaffer’s recent defence of Spinozan Monism—the thesis that the cosmos is the only substance, or the only fundamental and integrated thing— fails to establish that the universe is uniquely fundamental. In addition, Schaffer’s own defence of his thesis offers the pluralist about fundamentality a model for responding to Schaffer’s criticism of pluralism.

"Does torture work?" is a factual rather than ethical or legal question. But legal and ethical discussions of torture should be informed by knowledge of the answer to the factual question of the reliability of torture as an interrogation technique. The question as to whether torture works should be asked before that of its legal admissibility—if it is not useful to interrogators, there is no point considering its legality in court.

We study the acceleration and collisions of rigid bodies in special relativity. After a brief historical review, we give a physical definition of the term ‘rigid body’ in relativistic straight line motion. We show that the definition of ‘rigid body’ in relativity differs from the usual classical definition, so there is no difficulty in dealing with rigid bodies in relativistic motion. We then describe The motion of a rigid body undergoing constant acceleration to a given velocity.The acceleration of a rigid (...) body due to an applied impulse.Collisions between rigid bodies. (shrink)

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)

This paper presents the strongest version of a non-perdurantist four-dimensionalism: a theory according to which persisting objects are four-dimensionally extended in space-time, but not in virtue of having maximal temporal parts. The aims of considering such a view are twofold. First, to evaluate whether such an account could provide a plausible middle ground between the two main competitor accounts of persistence: three-dimensionalism and perdurantist four-dimensionalism. Second, to see what light such a theory sheds on the debate between these two competitor (...) theories. I conclude that despite prima facie reasons to suppose that non-perdurantist four-dimensionalism might be a credible alternative to either other account of persistence, ultimately the view is unsuccessful. The reasons for its failure illuminate the sometimes stagnant debate between three-dimensionalists and perdurantists, providing new reasons to prefer a perdurantist metaphysics. (shrink)

A consensus in a scientific community is often used as a resource for making informed public-policy decisions and deciding between rival expert testimonies in legal trials. This paper contains a social-epistemic analysis of the high-profile Bendectin drug controversy, which was decided in the courtroom inter alia by deference to a scientific consensus about the safety of Bendectin. Drawing on my previously developed account of knowledge-based consensus, I argue that the consensus in this case was not knowledge based, hence courts’ deference (...) to it was not epistemically justified. I draw sceptical lessons from this analysis regarding the value of scientific consensus as a desirable and reliable means of resolving scientific controversies in public life. (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)

Comparative valuation of different policy interventions often requires interpersonal comparability of benefit. In the field of health economics, the metric commonly used for such comparison, quality adjusted life years (QALYs) gained, has been criticized for failing to respect the equality of all persons’ intrinsic worth, including particularly those with disabilities. A methodology is proposed that interprets ‘full quality of life’ as the best health prospect that is achievable for the particular individual within the relevant budget constraint. This calibration is challenging (...) both conceptually and operationally as it shifts dramatically when technology or budget developments alter what can be achieved for incapacitated individuals. The proposal nevertheless ensures that the maximal achievable satisfaction of one person’s preferences can carry no more intrinsic value than that of another. This approach, which can be applied to other domains of social valuation, thus prevents implicit discrimination against the elderly and those with irremediable incapacities. (shrink)

If Tahiti suggested to theorists comfortably at home in Europe thoughts of noble savages without clothes, those who paid for and went on voyages there were in pursuit of a quite opposite human ideal. Cook's voyage to observe the transit of Venus in 1769 symbolises the eighteenth century's commitment to numbers and accuracy, and its willingness to spend a lot of public money on acquiring them. The state supported the organisation of quantitative researches, employing surveyors and collecting statistics to..

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)

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)

The objective of this document is to present three introductory notes on set theory: The first note presents an overview of this discipline from its origins to the present, in the second note some considerations are made about the evaluation of reasoning applying the first-order Logic and Löwenheim's theorems, Church Indecidibility, Completeness and Incompleteness of Gödel, it is known that the axiomatic theories of most commonly used sets are written in a specific first-order language, that is, they are developed within (...) the framework of first-order logic, so this note is relevant; and the third note refers to the presence of mathematical platonism in the axioms of ZFC and in the axioms of "complete ordered field", it is known that the last axioms mentioned characterize (except isomorphism) the real number system and are currently used to develop the real Analysis in the context of set theory. It is hoped that this article will be of pedagogical utility for students interested in set theory and in the philosophy of mathematics (that are beginning in the subject). (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)

Endurantism is not inconsistent with the theory of special relativity, or so I shall argue. Endurantism is not committed to presentism, and thus not committed to a metaphysics that is at least prima facie inconsistent with special relativity. Nor is special relativity inconsistent with the idea that objects are wholly present at a time just if all of their parts co-exist at that time. For the endurantist notion of co-existence in terms of which “wholly present” is defined, is not, I (...) will argue, a notion according to which co-existence is transitive. Although an absence of absolute simultaneity presents some problems for the endurantist claim that objects are wholly present whenever they exist, there are a number of ways that the endurantist can respond to this difficulty. Thus, I conclude, considerations pertaining to the theory of special relativity certainly do not rule out endurantism as a metaphysics of persistence. (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)