Scientists, philosophers, and policymakers disagree about how to define microaggression. Here, we offer a taxonomy of existing definitions, clustering around (a) the psychological motives of perpetrators, (b) the experience of victims, and (c) the functional role of microaggression in oppressive social structures. We consider conceptual and epistemic challenges to each and suggest that progress may come from developing novel hybrid accounts of microaggression, combining empirically tractable features with sensitivity to the testimony of victims.

At first glance, hate speech and microaggressions seem to have little overlap beyond being communicated verbally or in written form. Hate speech seems clearly macro-aggressive: an intentional, obviously harmful act lacking the ambiguity (and plausible deniability) of microaggressions. If we look back at historical discussions of hate speech, however, many of these assumed differences turn out to be points of similarity. The harmfulness of hate speech only became widely acknowledged after a concerted effort by critical race theorists, feminists, and other (...) activists. Before the 1990s, slurs were widely considered socially acceptable behavior: mere jokes that weren’t intended to be harmful. Authors like Richard Delgado, Mari Matsuda, and Charles Lawrence pushed back against this dismissal. In this chapter, I show that their arguments for the serious harmfulness of hate speech prefigure and provide support for current debates about the serious harmfulness of microaggressions. Exploring resonances with the 1980s hate speech debate will allow us to explain why microaggressions fall below the cutoff for legal liability but remain apt targets for moral blame. (shrink)

Microaggressions are seemingly negligible slights that can cause significant damage to frequently targeted members of marginalized groups. Recently, Scott O. Lilienfeld challenged a key platform of the microaggression research project: what’s aggressive about microaggressions? To answer this challenge, Derald Wing Sue, the psychologist who has spearheaded the research on microaggressions, needs to theorize a spectrum of aggression that ranges from intentional assault to unintentional microaggressions. I suggest turning to Bonnie Mann’s “Creepers, Flirts, Heroes and Allies” for inspiration. Building from Mann’s (...) richer theoretical framework will allow Sue to answer Lilienfeld’s objection and defend the legitimacy of the concept, ‘microaggression’. (shrink)

We argue that machine learning algorithms can inflict microaggressions on members of marginalized groups and that recognizing these harms as instances of microaggressions is key to effectively addressing the problem. The concept of microaggression is also illuminated by being studied in algorithmic contexts. We contribute to the microaggression literature by expanding the category of environmental microaggressions and highlighting the unique issues of moral responsibility that arise when we focus on this category. We theorize two kinds of algorithmic microaggression, stereotyping and (...) erasure microaggressions, and argue that corporations are responsible for the microaggressions their algorithms create. As a case study, we look at the problems faced by Google’s autocomplete prediction and at the insufficiency of their solutions. The case study of autocomplete demonstrates our core claim that microaggressions constitute a distinct form of algorithmic bias and that identifying them as such allows us to avoid seeming solutions that recreate the same kinds of harms. Google has a responsibility to make information freely available, without exposing users to degradation. To fulfill its duties to marginalized groups, Google must abandon the fiction of neutral prediction and instead embrace the liberatory power of suggestion. (shrink)

Many theorists have focused on Wittgenstein’s use of examples, but I argue that examples form only half of his method. Rather than continuing the disjointed style of his Cambridge lectures, Wittgenstein returns to the techniques he employed while teaching elementary school. Philosophical Investigations trains the reader as a math class trains a student—‘by means of examples and by exercises’ (§208). Its numbered passages, carefully arranged, provide a series of demonstrations and practice problems. I guide the reader through one such series, (...) demonstrating how the exercises build upon one another and give us ample opportunity to hone our problem-solving skills. Through careful practice, we learn to pass the test Wittgenstein poses when he claims that something is ‘easy to imagine’ (§19). Whereas other critics have viewed the Investigations as merely a diagnosis of our philosophical delusions, I claim that Wittgenstein also writes a prescription for our disease: Do your exercises. (shrink)

The first degree entailment (FDE) family is a group of logics, a many-valued semantics for each system of which is obtained from classical logic by adding to the classical truth-values true and false any subset of {both, neither, indeterminate}, where indeterminate is an infectious value (any formula containing a subformula with the value indeterminate itself has the value indeterminate). In this paper, we see how to extend a version of star semantics for the logics whose many-valued semantics lack indeterminate to (...) star semantics for logics whose many-valued semantics include indeterminate. The equivalence of the many-valued semantics and star semantics is established by way of a soundness and completeness proof. The upshot of the novel semantics in terms of the applied semantics of these logics, and specifically infectiousness, is explored, settling on the idea that infectiousness concerns ineffability. (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)

• 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)

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)

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)

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)

Describes the Sokal hoax and defends it against attacks by postmodernists.

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)

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)

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)

There is a wide range of realist but non-Platonist philosophies of mathematics—naturalist or Aristotelian realisms. Held by Aristotle and Mill, they played little part in twentieth century philosophy of mathematics but have been revived recently. They assimilate mathematics to the rest of science. They hold that mathematics is the science of X, where X is some observable feature of the (physical or other non-abstract) world. Choices for X include quantity, structure, pattern, complexity, relations. The article lays out and compares these (...) options, including their accounts of what X is, the examples supporting each theory, and the reasons for identifying the science of X with (most or all of) mathematics. Some comparison of the options is undertaken, but the main aim is to display the spectrum of viable alternatives to Platonism and nominalism. It is explained how these views answer Frege’s widely accepted argument that arithmetic cannot be about real features of the physical world, and arguments that such mathematical objects as large infinities and perfect geometrical figures cannot be physically realized. (shrink)

Dying is (sometimes) bad for the dier because it prevents her from being the subject of wellbeing she otherwise would (the deprivation account). I argue for this from a (plausible) principle about which futures are bad for a prudential subject (the future-comparison principle). A strengthening of this principle yields that death is not always bad, and that the badness of death does not consist in that it destroys the dier.

Many philosophers of science are ontologically committed to a lush rainforest of special science entities ), but are often reticent about the criteria that determine which entities count as real. On the other hand, the metaphysics literature is much more forthcoming about such criteria, but often links ontological commitment to irreducibility. We argue that the irreducibility criteria are in tension with scientific realism: for example, they would exclude viruses, which are plausibly theoretically reducible and yet play a sufficiently important role (...) in scientific accounts of the world that they should be included in our ontology. In this paper, we show how the inhabitants of the rainforest can be inoculated against the eliminative threat of reduction: by demonstrating that they are emergent. According to our account, emergence involves a screening off condition as well as novelty. We go on to demonstrate that this account of emergence, which is compatible with theoretical reducibility, satisfies common intuitions concerning what should and shouldn't count as real: viruses are emergent, as are trouts and turkeys, but philosophically gerrymandered objects like trout-turkeys do not qualify. (shrink)

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)

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).

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)

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.

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)

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 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.

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)

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)

An essay on the compatibility of Jewish and Muslim aspirations for the Land that argues that a vision of peaceful coexistence to provide a spur to the settling of grievances, but that this vision must respect the deeply felt aspirations of both communities, including in particular those underpinned by religious lore. Existing formulations of the aims of each community are blatantly inconsistent; it is time to attempt to characterise the just and religiously authentic goals of each community in ways that (...) are compatible. I argue that there religious and personal dimensions of the conflict that have been displaced by less deep-seated political goals, but which can be addressed more readily. I outline a tiered constitutional settlement that could address legitimate aspirations by avoiding the anathema of partition. (shrink)

Nearly all defences of the agent-causal theory of free will portray the theory as a distinctively libertarian one — a theory that only libertarians have reason to accept. According to what I call ‘the standard argument for the agent-causal theory of free will’, the reason to embrace agent-causal libertarianism is that libertarians can solve the problem of enhanced control only if they furnish agents with the agent-causal power. In this way it is assumed that there is only reason to accept (...) the agent-causal theory if there is reason to accept libertarianism. I aim to refute this claim. I will argue that the reasons we have for endorsing the agent-causal theory of free will are nonpartisan. The real reason for going agent-causal has nothing to do with determinism or indeterminism, but rather with avoiding reductionism about agency and the self. As we will see, if there is reason for libertarians to accept the agent-causal theory, there is just as much reason for compatibilists to accept it. It is in this sense that I contend that if anyone should be an agent-causalist, then everyone should be an agent-causalist. (shrink)

Journal of Applied Philosophy, EarlyView.

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)

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.

Quantity is the first category that Aristotle lists after substance. It has extraordinary epistemological clarity: "2+2=4" is the model of a self-evident and universally known truth. Continuous quantities such as the ratio of circumference to diameter of a circle are as clearly known as discrete ones. The theory that mathematics was "the science of quantity" was once the leading philosophy of mathematics. The article looks at puzzles in the classification and epistemology of quantity.

Multiple realisation prompts the question: how is it that multiple systems all exhibit the same phenomena despite their different underlying properties? In this paper I develop a framework for addressing that question and argue that multiple realisation can be reductively explained. I illustrate this position by applying the framework to a simple example – the multiple realisation of electrical conductivity. I defend my account by addressing potential objections:contra Polger and Shapiro, Batterman, and Sober, I claim that multiple realisation is commonplace, (...) that it can be reductively explained, but that it requires asui generisreductive explanatory strategy. (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)

It may be a myth that Plato wrote over the entrance to the Academy “Let no-one ignorant of geometry enter here.” But it is a well-chosen motto for his view in the Republic that mathematical training is especially productive of understanding in abstract realms, notably ethics. That view is sound and we should return to it. Ethical theory has been bedevilled by the idea that ethics is fundamentally about actions (right and wrong, rights, duties, virtues, dilemmas and so on). That (...) is an error like the one Plato mentions of thinking mathematics is about actions (of adding, constructing, extracting roots and so on). Mathematics is about eternal relations between universals, such as the ratio of the diagonal of a square to the side. Ethics too is about eternal verities, such as the equal worth of persons and just distributions. Mathematical and ethical verities do both constrain actions, such as the possibility of walking over the seven bridges of Königsberg once and once only or of justly discriminating between races. But they are not themselves about action. In principle, neither mathematical nor ethical verities are subject to historical forces or disagreement among tribes (though they can be better understood as time goes on). Plato is right: immersion in mathematics induces an understanding of the necessities underpinning reality, an understanding that is essential for distinguishing objective ethics from tribal custom. Equality, for example, is an abstract concept which is foundational for both mathematics and ethics. (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.

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.

The late scholastics, from the fourteenth to the seventeenth centuries, contributed to many fields of knowledge other than philosophy. They developed a method of conceptual analysis that was very productive in those disciplines in which theory is relatively more important than empirical results. That includes mathematics, where the scholastics developed the analysis of continuous motion, which fed into the calculus, and the theory of risk and probability. The method came to the fore especially in the social sciences. In legal theory (...) they developed, for example, the ethical analyses of the conditions of validity of contracts, and natural rights theory. In political theory, they introduced constitutionalism and the thought experiment of a “state of nature”. Their contributions to economics included concepts still regarded as basic, such as demand, capital, labour, and scarcity. Faculty psychology and semiotics are other areas of significance. In such disciplines, later developments rely crucially on scholastic concepts and vocabulary. (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)

The Tree of Life has traditionally been understood to represent the history of species lineages. However, recently researchers have suggested that it might be better interpreted as representing the history of cellular lineages, sometimes called the Tree of Cells. This paper examines and evaluates reasons offered against this cellular interpretation of the Tree of Life. It argues that some such reasons are bad reasons, based either on a false attribution of essentialism, on a misunderstanding of the problem of lineage identity, (...) or on a limited view of scientific representation. I suggest that debate about the Tree of Cells and other successors to the traditional Tree of Life should be formulated in terms of the purposes these representations may serve. In pursuing this strategy, we see that the Tree of Cells cannot serve one purpose suggested for it: as an explanation for the hierarchical nature of taxonomy. We then explore whether, instead, the tree may play an important role in the dynamic modeling of evolution. As highly-integrated complex systems, cells may influence which lineage components can successfully transfer into them and how they change once integrated. Only if they do in fact have a substantial role to play in this process might the Tree of Cells have some claim to be the Tree of Life. (shrink)

The abstract Latinate vocabulary of modern English, in which philosophy and science are done, is inherited from medieval scholastic Latin. Words like "nature", "art", "abstract", "probable", "contingent", are not native to English but entered it from scholastic translations around the 15th century. The vocabulary retains much though not all of its medieval meanings.

Antitheodicy objects to all attempts to solve the problem of evil. Its objections are almost all on moral grounds—it argues that the whole project of theodicy is morally offensive. Trying to excuse God’s permission of evil is said to deny the reality of evil, to exhibit gross insensitivity to suffering, and to insult the victims of grave evils. Since antitheodicists urge the avoidance of theodicies for moral reasons, it is desirable to evaluate the moral reasons against theodicies in abstraction from (...) the intellectual reasons for and against them. It is argued that the best known theodicies such as those based on soul-making and free will are guilty of moral faults as alleged. But Leibniz’s best of all possible worlds theory, often thought to be the most morally offensive ‘Panglossian’ theodicy, is morally blameless because it excuses God by the absolute impossibility of his choosing any world better than the present one. Theodicy should not be conceived of as a search for greater goods which may excuse God’s permitting evils. From the divine point of view, creation is an upfront choice between scenarios—in modern parlance, a Trolley problem rather than a Transplant problem. In cases of forced choice among scenarios, it is morally improper to criticize one who chooses the best. (shrink)

John Locke occupies a central place in the contemporary philosophical literature on parental authority, and his child-centered approach has inspired a number of recognizably Lockean theories of parenthood.2 But unlike the best historically informed scholarship on other aspects of Locke's thought, those interested in his account of parental rights have not yet tried to understand its connection to debates of the period or to Locke's broader theory of natural law. In particular, Locke's relation to the seventeenth-century conversation about the role (...) of generation in grounding 'paternal power' is not well-known. Understanding this background is interesting in itself, but more importantly, it can provide us with a .. (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)

Probabilistic inference from frequencies, such as "Most Quakers are pacifists; Nixon is a Quaker, so probably Nixon is a pacifist" suffer from the problem that an individual is typically a member of many "reference classes" (such as Quakers, Republicans, Californians, etc) in which the frequency of the target attribute varies. How to choose the best class or combine the information? The article argues that the problem can be solved by the feature selection methods used in contemporary Big Data science: the (...) correct reference class is that determined by the features relevant to the target, and relevance is measured by correlation (that is, a feature is relevant if it makes a difference to the frequency of the target). (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)