Blaming (construed broadly to include both blaming-attitudes and blaming-actions) is a puzzling phenomenon. Even when we grant that someone is blameworthy, we can still sensibly wonder whether we ought to blame him. We sometimes choose to forgive and show mercy, even when it is not asked for. We are naturally led to wonder why we shouldn’t always do this. Wouldn’t it be a better to wholly reject the punitive practices of blame, especially in light of their often undesirable effects, and (...) embrace an ethic of unrelenting forgiveness and mercy? In this paper I seek to address these questions by offering an account of blame that provides a rationale for thinking that to wholly forswear blaming blameworthy agents would be deeply mistaken. This is because, as I will argue, blaming is a way of valuing, it is “a mode of valuation.” I will argue that among the minimal standards of respect generated by valuable objects, notably persons, is the requirement to redress disvalue with blame. It is not just that blame is something additional we are required to do in properly valuing, but rather blame is part of what that it is to properly value. Blaming, given the existence of blameworthy agents, is mode of valuation required by the standards of minimal respect. To forswear blame would be to fail value what we ought to value. (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)

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)

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)

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.

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)

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.

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)

Is a human more conscious than an octopus? In the science of consciousness, it’s oftentimes assumed that some creatures (or mental states) are more conscious than others. But in recent years, a number of philosophers have argued that the notion of degrees of consciousness is conceptually confused. This paper (1) argues that the most prominent objections to degrees of consciousness are unsustainable, (2) examines the semantics of ‘more conscious than’ expressions, (3) develops an analysis of what it is for a (...) degreed property to count as degrees of consciousness, and (4) applies the analysis to various theories of consciousness. I argue that whether consciousness comes in degrees ultimately depends on which theory of consciousness turns out to be correct. But I also argue that most theories of consciousness entail that consciousness comes in degrees. (shrink)

Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...) or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case. (shrink)

Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as the Riemann hypothesis, have had to be considered in terms of the evidence for and against them. In recent decades, massive increases in computer power have permitted the gathering of huge amounts of numerical evidence, both for conjectures in pure mathematics and (...) for the behavior of complex applied mathematical models and statistical algorithms. Mathematics has therefore become (among other things) an experimental science (though that has not diminished the importance of proof in the traditional style). We examine how the evaluation of evidence for conjectures works in mathematical practice. We explain the (objective) Bayesian view of probability, which gives a theoretical framework for unifying evidence evaluation in science and law as well as in mathematics. Numerical evidence in mathematics is related to the problem of induction; the occurrence of straightforward inductive reasoning in the purely logical material of pure mathematics casts light on the nature of induction as well as of mathematical reasoning. (shrink)

This paper develops a theory of analog representation. We first argue that the mark of the analog is to be found in the nature of a representational system’s interpretation function, rather than in its vehicles or contents alone. We then develop the rulebound structure theory of analog representation, according to which analog systems are those that use interpretive rules to map syntactic structural features onto semantic structural features. The theory involves three degree-theoretic measures that capture three independent ways in which (...) a system can be more or less analog. We explain how our theory improves upon prior accounts of analog representation, provides plausible diagnoses for novel challenge cases, extends to hybrid systems that are partially analog and partially symbolic, and accounts for some of the advantages and disadvantages of representing analogically versus symbolically. (shrink)

The objective Bayesian view of proof (or logical probability, or evidential support) is explained and defended: that the relation of evidence to hypothesis (in legal trials, science etc) is a strictly logical one, comparable to deductive logic. This view is distinguished from the thesis, which had some popularity in law in the 1980s, that legal evidence ought to be evaluated using numerical probabilities and formulas. While numbers are not always useful, a central role is played in uncertain reasoning by the (...) ‘proportional syllogism’, or argument from frequencies, such as ‘nearly all aeroplane flights arrive safely, so my flight is very likely to arrive safely’. Such arguments raise the ‘problem of the reference class’, arising from the fact that an individual case may be a member of many different classes in which frequencies differ. For example, if 15 per cent of swans are black and 60 per cent of fauna in the zoo is black, what should I think about the likelihood of a swan in the zoo being black? The nature of the problem is explained, and legal cases where it arises are given. It is explained how recent work in data mining on the relevance of features for prediction provides a solution to the reference class problem. (shrink)

A polemical account of Australian philosophy up to 2003, emphasising its unique aspects (such as commitment to realism) and the connections between philosophers' views and their lives. Topics include early idealism, the dominance of John Anderson in Sydney, the Orr case, Catholic scholasticism, Melbourne Wittgensteinianism, philosophy of science, the Sydney disturbances of the 1970s, Francofeminism, environmental philosophy, the philosophy of law and Mabo, ethics and Peter Singer. Realist theories especially praised are David Armstrong's on universals, David Stove's on logical probability (...) and the ethical realism of Rai Gaita and Catholic philosophers. In addition to strict philosophy, the book treats non-religious moral traditions to train virtue, such as Freemasonry, civics education and the Greek and Roman classics. (shrink)

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.

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)

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.

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)

Einstein, like most philosophers, thought that there cannot be mathematical truths which are both necessary and about reality. The article argues against this, starting with prima facie examples such as "It is impossible to tile my bathroom floor with regular pentagonal tiles." Replies are given to objections based on the supposedly purely logical or hypothetical nature of mathematics.

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)

This paper examines the idea of "objective phenomenology," or a way of understanding the phenomenal character of conscious experiences that doesn’t require one to have had the kinds of experiences under consideration. My central thesis is that structural facts about experience—facts that characterize purely how conscious experiences are structured—are objective phenomenal facts. I begin by precisifying the idea of objective phenomenology and diagnosing what makes any given phenomenal fact subjective. Then I defend the view that structural facts about experience are (...) objective. I also argue that structural facts about experience, despite being objective, nevertheless still give rise to an explanatory gap. (shrink)

Throughout history, almost all mathematicians, physicists and philosophers have been of the opinion that space and time are infinitely divisible. That is, it is usually believed that space and time do not consist of atoms, but that any piece of space and time of non-zero size, however small, can itself be divided into still smaller parts. This assumption is included in geometry, as in Euclid, and also in the Euclidean and non- Euclidean geometries used in modern physics. Of the few (...) who have denied that space and time are infinitely divisible, the most notable are the ancient atomists, and Berkeley and Hume. All of these assert not only that space and time might be atomic, but that they must be. Infinite divisibility is, they say, impossible on purely conceptual grounds. (shrink)

Conscious experiences are characterized by mental qualities, such as those involved in seeing red, feeling pain, or smelling cinnamon. The standard framework for modeling mental qualities represents them via points in geometrical spaces, where distances between points inversely correspond to degrees of phenomenal similarity. This paper argues that the standard framework is structurally inadequate and develops a new framework that is more powerful and flexible. The core problem for the standard framework is that it cannot capture precision structure: for example, (...) consider the phenomenal contrast between seeing an object as crimson in foveal vision versus merely as red in peripheral vision. The solution I favor is to model mental qualities using regions, rather than points. I explain how this seemingly simple formal innovation not only provides a natural way of modeling precision, but also yields a variety of further theoretical fruits: it enables us to formulate novel hypotheses about the space and structures of mental qualities, formally differentiate two dimensions of phenomenal similarity, generate a quantitative model of the phenomenal sorites, and define a measure of discriminatory grain. A noteworthy consequence is that the structure of the mental qualities of conscious experiences is fundamentally different from the structure of the perceptible qualities of external objects. (shrink)

Some philosophers think that life is worth living not merely because of the goods and the bads within it, but also because life itself is good. I explain how this idea can be formalized by associating each version of such of a view with a function from length of life to the value generated by life itself. Then I argue that every version of the view that life itself is good faces some version of the following dilemma: either (1) good (...) human lives are worse than very long lives wholly devoid of pleasure, desire-satisfaction, knowledge, or any other goods, or (2) very short lives containing nothing but suffering are worth living. Since neither result is plausible, we ought to reject the view that life itself is good. On the view I favor, any given life may be worth living because of the goods that it contains, but life itself is neutral. (shrink)

Moti Mizrahi (2013) presents some novel counterexamples to Hypothetical Syllogism (HS) for indicative conditionals. I show that they are not compelling as they neglect the complicated ways in which conditionals and modals interact. I then briefly outline why HS should nevertheless be rejected.

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)

Even where willingness-to-pay as a measure of welfare impact is adjusted for diminishing marginal utility, welfare economics is shown to favour policies that add to the life expectancy or that enhance the quality of life of persons who are already better-off. I propose an alternative, Equal Respect methodology, under an axiomatic claim that at the point of decision the prospective life years of all individuals are of equal intrinsic social value. This justifies equal valuation of risk mitigation across all persons; (...) similarly, all appraised impacts should be scaled to accord equal respect to difficult but no-less-valuable lives. (shrink)

Collection of articles on themes of Australian Catholic philosophy and history. Articles of philosophical interest include 'Catholic thought and Catholic Action: Dr Paddy Ryan MSC' (on the scholastic philosopher and anti-Communist), 'Catholic schooldays with philosophy', 'Traditional Catholic philosophy: baby and bathwater', 'Secular versus Catholic conceptions of values in Australian education', 'Accountancy as computational casuistics', 'The Mabo High Court and natural law values', and 'Stove, Hume and Enlightenment'.

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)

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)

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)

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 .

A response to a declaration in 'Le Monde', 'Luttons efficacement contre les théories du complot' by Gérald Bronner, Véronique Campion-Vincent, Sylvain Delouvée, Sebastian Dieguez, Karen Douglas, Nicolas Gauvrit, Anthony Lantian, and Pascal Wagner-Egger, published on June the 6th, 2016.

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)

Many philosophers accept both of the following claims: (1) consciousness matters morally, and (2) species membership doesn’t matter morally. In other words, many reject speciesism but accept what we might call 'sentientism'. But do the reasons against speciesism yield analogous reasons against sentientism, just as the reasons against racism and sexism are thought to yield analogous reasons against speciesism? This paper argues that speciesism is disanalogous to sentientism (as well as racism and sexism). I make a case for the following (...) asymmetry: (a) some non-humans clearly have interests, but (b) no non-conscious entities clearly have interests. This asymmetry, I argue, renders sentientism resistant to the standard argument against speciesism. (shrink)

An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and (...) are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge. (shrink)

Both realist and anti-realist accounts of natural kinds possess prima facie virtues: realists can straightforwardly make sense of the apparent objectivity of the natural kinds, and anti-realists, their knowability. This paper formulates a properly anti-realist account designed to capture both merits. In particular, it recommends understanding natural kinds as ‘categorical bottlenecks,’ those categories that not only best serve us, with our idiosyncratic aims and cognitive capacities, but also those of a wide range of alternative agents. By endorsing an ultimately subjective (...) categorical principle, this view sidesteps epistemological difficulties facing realist views. Yet, it nevertheless identifies natural kinds that are fairly, though not completely, stance-independent or objective. (shrink)

Andrew McGonigal presents some interesting data concerning truth in serial fictions.1 Such data has been taken by McGonigal, Cameron and Caplan to motivate some form of contextualism or relativism. I argue, however, that many of these approaches are problematic, and that all are under-motivated as the data can be explained in a standard invariantist semantic framework given some independently plausible principles.

A number of philosophers argue that the moral value of national identity is sufficient to justify at least a prima facie right of a national community to create its own independent, sovereign state. In the literature, this argument is commonly referred to as the identity argument. In this paper, I consider whether the identity argument successfully proves that a national group is entitled to a state of its own. To do so, I first explain three important steps in the argument (...) and then consider whether they lead to the desired conclusion. My examination reveals that the identity argument relies on the Optimal Protection Principle; however, this principle does not apply to the case of a national community. As a result, the identity argument fails to justify even a prima facie right of a national community to establish its own state. (shrink)

Are a material object, such as a statue, and its constituting matter, the clay, parts of one another? One wouldn't have thought so, and yet a number of philosophers have argued that they are. I review the arguments for this surprising claim showing how they all fail. I then consider two arguments against the view concluding that there are both pre-theoretical and theoretical considerations for denying that the statue and the clay are mutual parts.

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)

Allen Buchanan proposes a methodological framework with which theorists may evaluate different theories of secession, including the National Self-Determination theory. An important claim he makes is, because the right to secede is inherently institutional, any adequate theory of secession must include, as an integral part, an analysis of institutional morality. Because the National Self-Determination theory blatantly lacks such an analysis, Buchanan concludes that this theory is inherently flawed. In this paper, I consider Buchanan’s framework and the responses from supporters of (...) national self-determination theory. I try to clarify the confusion shared by both parties. I conclude that, although Buchanan’s theory of institutional morality is sound, his critiques of the national self-determination theory fails. (shrink)

Epistemic injustices are wrongs that agents can suffer in their capacity as knowers. In this article, I offer a conceptualisation of a phenomenon I call anticipatory epistemic injustice, which I claim is a distinct and particularly pernicious type of epistemic injustice worthy of independent analysis. I take anticipatory epistemic injustice to consist in the wrongs that agents can suffer as a result of anticipated challenges in their process of taking up testimony-sharing opportunities. I distinguish my account from paradigmatic cases of (...) epistemic injustice, such as Miranda Fricker’s concepts of testimonial injustice and hermeneutical injustice; additionally, I differentiate my view from Kristie Dotson’s account of testimonial smothering. I argue, ultimately, that anticipatory epistemic injustice is a useful addition to our current taxonomy of epistemic injustices, as it has promising explanatory potential for a range of non-standard cases of epistemic injustice. (shrink)

Recent discussions of emergence in physics have focussed on the use of limiting relations, and often particularly on singular or asymptotic limits. We discuss a putative example of emergence that does not fit into this narrative: the case of phonons. These quasi-particles have some claim to be emergent, not least because the way in which they relate to the underlying crystal is almost precisely analogous to the way in which quantum particles relate to the underlying quantum field theory. But there (...) is no need to take a limit when moving from a crystal lattice based description to the phonon description. Not only does this demonstrate that we can have emergence without limits, but also provides a way of understanding cases that do involve limits. (shrink)

I defend the thesis that legal standards of proof are reducible to thresholds of probability. Many have rejected this thesis because it seems to entail that defendants can be found liable solely on the basis of statistical evidence. I argue that this inference is invalid. I do so by developing a view, called Legal Causalism, that combines Thomson's (1986) causal analysis of evidence with recent work in formal theories of causal inference. On this view, legal standards of proof can be (...) reduced to probabilities, but deriving these probabilities involves more than just statistics. (shrink)

Whether or not quantum physics can account for molecular structure is a matter of considerable controversy. Three of the problems raised in this regard are the problems of molecular structure. We argue that these problems are just special cases of the measurement problem of quantum mechanics: insofar as the measurement problem is solved, the problems of molecular structure are resolved as well. In addition, we explore one consequence of our argument: that claims about the reduction or emergence of molecular structure (...) cannot be settled independently of the choice of a particular resolution to the measurement problem. Specifically, we consider how three standard putative solutions to the measurement problem inform our under- standing of a molecule in isolation, as well as of chemistry’s relation to quantum physics. (shrink)

Are counterfactuals with true antecedents and consequents automatically true? That is, is Conjunction Conditionalization: if (X & Y), then (X > Y) valid? Stalnaker and Lewis think so, but many others disagree. We note here that the extant arguments for Conjunction Conditionalization are unpersuasive, before presenting a family of more compelling arguments. These arguments rely on some standard theorems of the logic of counterfactuals as well as a plausible and popular semantic claim about certain semifactuals. Denying Conjunction Conditionalization, then, requires (...) rejecting other aspects of the standard logic of counterfactuals, or else our intuitive picture of semifactuals. (shrink)

It is commonly claimed that the universality of critical phenomena is explained through particular applications of the renormalization group. This article has three aims: to clarify the structure of the explanation of universality, to discuss the physics of such RG explanations, and to examine the extent to which universality is thus explained. The derivation of critical exponents proceeds via a real-space or a field-theoretic approach to the RG. Building on work by Mainwood, this article argues that these approaches ought to (...) be distinguished: while the field-theoretic approach explains universality, the real-space approach fails to provide an adequate explanation. (shrink)

La siguiente ponencia-taller tiene por finalidad explicar cómo podría aplicarse el Método de George Polya para resolver problemas (matemáticos) en el contexto de la Lógica Matemática, especialmente en la lógica Matemática elemental (la lógica de primer orden con identidad). Es una propuesta pedagógica experimental (además de las ya existentes) que tal vez pueda ser útil para la enseñanza de la lógica matemática en ciencias o en humanidades. Dicha ponencia se presentó (vía web) con motivo de la celebración del Día Mundial (...) de Lógica 2022 en dos ocasiones: En la Universidad Central de Venezuela (Venezuela) y en la Universidad Mayor de San Andrés (Logic & Analytics Group - La Paz y La Sociedad Científica de Filosofía de la UMSA, Bolivia). Es un proyecto pedagógico en construcción. (shrink)