“Free Will” is a philosophical term of art for a particular sort of capacity of rational agents to choose a course of action from among various alternatives. Which sort is the free will sort is what all the fuss is about. (And what a fuss it has been: philosophers have debated this question for over two millenia, and just about every major philosopher has had something to say about it.) Most philosophers suppose that the concept of free will is very (...) closely connected to the concept of moral responsibility. Acting with free will, on such views, is just to satisfy the metaphysical requirement on being responsible for one's action. (Clearly, there will also be epistemic conditions on responsibility as well, such as being aware—or failing that, being culpably unaware—of relevant alternatives to one's action and of the alternatives' moral significance.) But the significance of free will is not exhausted by its connection to moral responsibility. Free will also appears to be a condition on desert for one's accomplishments (why sustained effort and creative work are praiseworthy); on the autonomy and dignity of persons; and on the value we accord to love and friendship. (See Kane 1996, 81ff. and Clarke 2003, Ch.1.). (shrink)

What role have experiments played, and should they play, in physics? How does one come to believe rationally in experimental results? The Neglect of Experiment attempts to provide answers to both of these questions. Professor Franklin's approach combines the detailed study of four episodes in the history of twentieth century physics with an examination of some of the philosophical issues involved. The episodes are the discovery of parity nonconservation in the 1950s; the nondiscovery of parity nonconservation in the 1930s, when (...) the results of experiments indicated, at least in retrospect, the symmetry violation, but the significance of those results was not realized; the discovery and acceptance of CP symmetry; and Millikan's oil-drop experiment. Franklin examines the various roles that experiment plays, including its role in deciding between competing theories, confirming theories, and calling fo new theories. The author argues that one can provide a philosophical justification for these roles. He contends that if experiment plays such important roles, then one must have good reason to believe in experimental results. He then deals with deveral problems concerning such reslults, including the epistemology of experiment, how one comes to believe rationally in experimental results, the question of the influence of theoretical presuppositions on results, and the problem of scientific fruad. This original and important contribution to the study of the philosophy of experimental science is an outgrowth of many years of research. Franklin brings to this work more than a decade of experience as an experimental high-energy physicist, along with his significant contributions to the history and philosophy of science. (shrink)

In this book, Christopher Evan Franklin develops and defends a novel version of event-causal libertarianism. This view is a combination of libertarianism--the view that humans sometimes act freely and that those actions are the causal upshots of nondeterministic processes--and agency reductionism--the view that the causal role of the agent in exercises of free will is exhausted by the causal role of mental states and events (e.g., desires and beliefs) involving the agent. Franklin boldly counteracts a dominant theory that has similar (...) aims, put forth by well-known philosopher Robert Kane. -/- Many philosophers contend that event-causal libertarians have no advantage over compatibilists when it comes to securing a distinctively valuable kind of freedom and responsibility. To Franklin, this position is mistaken. Assuming agency reductionism is true, event-causal libertarians need only adopt the most plausible compatibilist theory and add indeterminism at the proper juncture in the genesis of human action. The result is minimal event-causal libertarianism: a model of free will with the metaphysical simplicity of compatibilism and the intuitive power of libertarianism. And yet a worry remains: toward the end of the book, Franklin reconsiders his assumption of agency reductionism, arguing that this picture faces a hitherto unsolved problem. This problem, however, has nothing to do with indeterminism or determinism, or even libertarianism or compatibilism, but with how to understand the nature of the self and its role in the genesis of action. Crucially, if this problem proves unsolvable, then not only is event-causal libertarianism untenable, so also is event-causal compatibilism. (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)

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)

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)

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)

In this paper I seek to defend libertarianism about free will and moral responsibility against two well-known arguments: the luck argument and the Mind argument. Both of these arguments purport to show that indeterminism is incompatible with the degree of control necessary for free will and moral responsibility. I begin the discussion by elaborating these arguments, clarifying important features of my preferred version of libertarianism—features that will be central to an adequate response to the arguments—and showing why a strategy of (...) reconciliation (often referred to as “deliberative libertarianism”) will not work. I then consider four formulations of the luck argument and find them all wanting. This discussion will place us in a favorable position to understand why the Mind argument also fails. (shrink)

In Experiment, Right or Wrong, Allan Franklin continues his investigation of the history and philosophy of experiment presented in his previous book, The Neglect of Experiment. Using a combination of case studies and philosophical readings of those studies, Franklin again addresses two important questions: (1) What role does and should experiment play in the choice between competing theories and in the confirmation or refutation of theories and hypotheses? (2) How do we come to believe reasonably in experimental results? Experiment, Right (...) or Wrong makes a significant contribution to an important area in contemporary history and philosophy of science. Philosophers and historians of science, physicists, and advanced students in these areas will find much of interest in this engaging study. (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.

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)

Scientific realists don’t standardly discriminate between, say, biology and fundamental physics when deciding whether the evidence and explanatory power warrant the inclusion of new entities in our ontology. As such, scientific realists are committed to a lush rainforest of special science kinds (Ross, 2000). Viruses certainly inhabit this rainforest – their explanatory power is overwhelming – but viruses’ properties can be explained from the bottom up: reductive explanations involving amino acids are generally available. However, reduction has often been taken to (...) lead to a metaphysical downgrading, so how can viruses keep their place in the rainforest? 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 trout and turkeys, but philosophically gerrymandered objects like trout-turkeys do not qualify. (shrink)

In many diagrams one seems to perceive necessity – one sees not only that something is so, but that it must be so. That conflicts with a certain empiricism largely taken for granted in contemporary philosophy, which believes perception is not capable of such feats. The reason for this belief is often thought well-summarized in Hume's maxim: ‘there are no necessary connections between distinct existences’. It is also thought that even if there were such necessities, perception is too passive or (...) localized a faculty to register them. We defend the perception of necessity against such Humeanism, drawing on examples from mathematics. (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)

Specifically, Allan Franklin is concerned with two problems in the use of experimental results in science: selectivity of data or analysis procedures and the resolution of discordant results.

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)

A crucial question for libertarians about free will and moral responsibility concerns how their accounts secure more control than compatibilism. This problem is particularly exasperating for event-causal libertarianism, as it seems that the only difference between these accounts and compatibilism is that the former require indeterminism. But how can indeterminism, a mere negative condition, enhance control? This worry has led many to conclude that the only viable form of libertarianism is agent-causal libertarianism. In this paper I show that this conclusion (...) is premature. I explain how event-causal libertarianism secures more control than compatibilism by offering a novel argument for incompatibilism. Part of the reason my solution has gone unnoticed is that it is often mistakenly assumed that an agent's control is wholly exhausted by the agent's powers and abilities. I argue, however, that control is constituted not just by what we have the ability to do, but also by what we have the opportunity to do. And it is by furnishing agents with new opportunities that event-causal libertarianism secures enhanced control. In order to defend this claim, I provide an analysis of opportunities and construct a novel incompatibilist argument to show that the opportunity to do otherwise is incompatible with determinism. (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)

A familiar feature of our moral responsibility practices are pleas: considerations, such as “That was an accident”, or “I didn’t know what else to do”, that attempt to get agents accused of wrongdoing off the hook. But why do these pleas have the normative force they do in fact have? Why does physical constraint excuse one from responsibility, while forgetfulness or laziness does not? I begin by laying out R. Jay Wallace’s (Responsibility and the moral sentiments, 1994 ) theory of (...) the normative force of excuses and exemptions. For each category of plea, Wallace offers a single governing moral principle that explains their normative force. The principle he identifies as governing excuses is the Principle of No Blameworthiness without Fault: an agent is blameworthy only if he has done something wrong. The principle he identifies as governing exemptions is the Principle of Reasonableness: an agent is morally accountable only if he is normatively competent. I argue that Wallace’s theory of exemptions is sound, but that his account of the normative force of excuses is problematic, in that it fails to explain the full range of excuses we offer in our practices, especially the excuses of addiction and extreme stress. I then develop a novel account of the normative force of excuses, which employs what I call the “Principle of Reasonable Opportunity,” that can explain the full range of excuses we offer and that is deeply unified with Wallace’s theory of the normative force of exemptions. An important implication of the theory I develop is that moral responsibility requires free will. (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)

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.

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)

The logical interpretation of probability, or "objective Bayesianism'' – the theory that (some) probabilities are strictly logical degrees of partial implication – is defended. The main argument against it is that it requires the assignment of prior probabilities, and that any attempt to determine them by symmetry via a "principle of insufficient reason" inevitably leads to paradox. Three replies are advanced: that priors are imprecise or of little weight, so that disagreement about them does not matter, within limits; that it (...) is possible to distinguish reasonable from unreasonable priors on logical grounds; and that in real cases disagreement about priors can usually be explained by differences in the background information. It is argued also that proponents of alternative conceptions of probability, such as frequentists, Bayesians and Popperians, are unable to avoid committing themselves to the basic principles of logical probability. (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)

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 Fermat's Last Theorem and the Riemann Hypothesis, have had to be considered in terms of the evidence for and against them. It is argued here that it is not adequate to describe the relation of evidence to hypothesis as `subjective', `heuristic' or (...) `pragmatic', but that there must be an element of what it is rational to believe on the evidence, that is, of non-deductive logic. (shrink)

Seemingly one of the most prominent issues that divide theorists about free will and moral responsibility concerns whether the ability to do otherwise is necessary for freedom and responsibility. I defend two claims in this paper. First, that this appearance is illusory: everyone thinks an ability to do otherwise is necessary for freedom and responsibility. The central issue is not whether the ability to do otherwise is necessary for freedom and responsibility but which abilities to do otherwise are necessary. Second, (...) I argue that we cannot determine which abilities are necessary until we have determined the nature and justification of moral responsibility. Thus, theorizing about moral responsibility ought to take pride of place in theorizing about free will. (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)

Recently, there has been a resurgence of interest in general, comprehensive models of human cognition. Such models aim to explain higher-order cognitive faculties, such as deliberation and planning. Given a computational representation, the validity of these models can be tested in computer simulations such as software agents or embodied robots. The push to implement computational models of this kind has created the field of artificial general intelligence (AGI). Moral decision making is arguably one of the most challenging tasks for computational (...) approaches to higher-order cognition. The need for increasingly autonomous artificial agents to factor moral considerations into their choices and actions has given rise to another new field of inquiry variously known as Machine Morality, Machine Ethics, Roboethics, or Friendly AI. In this study, we discuss how LIDA, an AGI model of human cognition, can be adapted to model both affective and rational features of moral decision making. Using the LIDA model, we will demonstrate how moral decisions can be made in many domains using the same mechanisms that enable general decision making. Comprehensive models of human cognition typically aim for compatibility with recent research in the cognitive and neural sciences. Global workspace theory, proposed by the neuropsychologist Bernard Baars (1988), is a highly regarded model of human cognition that is currently being computationally instantiated in several software implementations. LIDA (Franklin, Baars, Ramamurthy, & Ventura, 2005) is one such computational implementation. LIDA is both a set of computational tools and an underlying model of human cognition, which provides mechanisms that are capable of explaining how an agent’s selection of its next action arises from bottom-up collection of sensory data and top-down processes for making sense of its current situation. We will describe how the LIDA model helps integrate emotions into the human decision-making process, and we will elucidate a process whereby an agent can work through an ethical problem to reach a solution that takes account of ethically relevant factors. (shrink)

Event-causal libertarians maintain that an agent’s freely bringing about a choice is reducible to states and events involving him bringing about the choice. Agent-causal libertarians demur, arguing that free will requires that the agent be irreducibly causally involved. Derk Pereboom and Meghan Griffith have defended agent-causal libertarianism on this score, arguing that since on event-causal libertarianism an agent’s contribution to his choice is exhausted by the causal role of states and events involving him, and since these states and events leave (...) it open which decision he will make, he does not settle which decision occurs, and thus “disappears.” My aim is to explain why this argument fails. In particular, I demonstrate that event-causal libertarians can dismantle the argument by enriching the reductive base in their analysis of free will to include a state that plays the functional role of the self-determining agent and with which the agent is identified. (shrink)

This book provides the reader with a detailed and captivating account of the story where, for the first time, physicists ventured into proposing a new force of nature beyond the four known ones - the electromagnetic, weak and strong forces, and gravitation - based entirely on the reanalysis of existing experimental data. Back in 1986, Ephraim Fischbach, Sam Aronson, Carrick Talmadge and their collaborators proposed a modification of Newton's Law of universal gravitation. Underlying this proposal were three tantalizing pieces of (...) evidence: 1) an energy dependence of the CP (particle-antiparticle and reflection symmetry) parameters, 2) differences between the measurements of G, the universal gravitational constant, in laboratories and in mineshafts, and 3) a reanalysis of the Eötvos experiment, which had previously been used to show that the gravitational mass of an object and its inertia mass were equal to approximately one part in a billion. The reanalysis revealed that, contrary to Galileo's position, the force of gravity was in fact very slightly different for different substances. The resulting Fifth Force hypothesis included this composition dependence and also added a small distance dependence to the inverse-square gravitational force. Over the next four years numerous experiments were performed to test the hypothesis. By 1990 there was overwhelming evidence that the Fifth Force, as initially proposed, did not exist. This book discusses how the Fifth Force hypothesis came to be proposed and how it went on to become a showcase of discovery, pursuit and justification in modern physics, prior to its demise. In this new and significantly expanded edition, the material from the first edition is complemented by two essays, one containing Fischbach's personal reminiscences of the proposal, and a second on the ongoing history and impact of the Fifth Force hypothesis from 1990 to the present. <. (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)

The debate over whether Frankfurt-style cases are counterexamples to the principle of alternative possibilities has taken an interesting turn in recent years. Frankfurt originally envisaged his attack as an attempting to show that PAP is false—that the ability to do otherwise is not necessary for moral responsibility. To many this attack has failed. But Frankfurtians have not conceded defeat. Neo-Frankfurtians, as I will call them, argue that the upshot of Frankfurt-style cases is not that PAP is false, but that it (...) is explanatorily irrelevant. Derk Pereboom and David Hunt’s buffer cases are tailor made to establish this conclusion. In this paper I come to the aid of PAP, showing that buffer cases provide no reason for doubting either its truth or relevance with respect to explaining an agent’s moral responsibility. (shrink)

We study arithmetic and hyperarithmetic degrees of categoricity. We extend a result of E. Fokina, I. Kalimullin, and R. Miller to show that for every computable ordinal $\alpha$, $\mathbf{0}^{}$ is the degree of categoricity of some computable structure $\mathcal{A}$. We show additionally that for $\alpha$ a computable successor ordinal, every degree $2$-c.e. in and above $\mathbf{0}^{}$ is a degree of categoricity. We further prove that every degree of categoricity is hyperarithmetic and show that the index set of structures with degrees (...) of categoricity is $\Pi_{1}^{1}$-complete. (shrink)

In 1947 Donald Cary Williams claimed in The Ground of Induction to have solved the Humean problem of induction, by means of an adaptation of reasoning first advanced by Bernoulli in 1713. Later on David Stove defended and improved upon Williams’ argument in The Rational- ity of Induction (1986). We call this proposed solution of induction the ‘Williams-Stove sampling thesis’. There has been no lack of objections raised to the sampling thesis, and it has not been widely accepted. In our (...) opinion, though, none of these objections has the slightest force, and, moreover, the sampling thesis is undoubtedly true. What we will argue in this paper is that one particular objection that has been raised on numerous occasions is misguided. This concerns the randomness of the sample on which the inductive extrapolation is based. (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)

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 currently leading cognitive theory of consciousness, Global Workspace Theory,1,2 postulates that the primary functions of consciousness include a global broadcast serving to recruit internal resources with which to deal with the current situation and to modulate several types of learning. In addition, conscious experiences present current conditions and problems to a "self" system, an executive interpreter that is identifiable with brain structures like the frontal lobes and precuneus.1Be it human, animal or artificial, an autonomous agent3 is said to be (...) functionally conscious if its control structure (mind) implements Global Workspace Theory and the LIDA Cognitive Cycle, which includes unconscious memory and control functions needed to integrate the conscious component of the system. We would therefore consider humans, many animals4 and even some virtual or robotic agents5,6 to be functionally conscious. Such entities may approach phenomenal consciousness, as found in human and other biological brains, as additional brain-like features are added.Here we argue that adding mechanisms to produce a stable, coherent perceptual field7 in a LIDA controlled mobile robot might provide a small but significant step toward phenomenal consciousness in machines.>8 We also propose that implementing several of the various notions of self in such a LIDA controlled robot may well prove another step toward phenomenal consciousness in machines. (shrink)

Theory-ladenness is the view that observation cannot function in an unbiased way in the testing of theories because observational judgments are affected by the theoretical beliefs of the observer. Its more radical cousin, incommensurability, argues that because there is no theory-neutral language, paradigms, or worldviews, cannot be compared because in different paradigms the meaning of observational terms is different, even when the word used is the same. There are both philosophical and practical components to these problems. I argue, using a (...) procedurally-defined, theory-neutral experiment that paradigms are indeed commensurable. The practical problems of theory ladenness include experimental design, failure to interpret observations correctly, possible experimenter bias, and difficulties in data acquisition. I suggest that there are methods to deal with these problems, although sometimes they cannot be dealt with completely. I believe that the philosophical problems of theory-ladenness have been solved, although the practical problems remain. (shrink)

While the consequences of mathematically-based software, algorithms and strategies have become ever wider and better appreciated, ethical reflection on mathematics has remained primitive. We review the somewhat disconnected suggestions of commentators in recent decades with a view to piecing together a coherent approach to ethics in mathematics. Calls for a Hippocratic Oath for mathematicians are examined and it is concluded that while lessons can be learned from the medical profession, the relation of mathematicians to those affected by their work is (...) significantly different. There is something to be learned also from the codes of conduct of cognate but professionalised quantitative disciplines such as engineering and accountancy, as well as from legal principles bearing on professional work. We conclude with recommendations that professional societies in mathematics should sponsor an (international) code of ethics, institutional mission statements for mathematicians and syllabuses of ethics courses for incorporation into mathematics degrees. (shrink)

Calibration, the use of a surrogate signal to standardize an instrument, is an important strategy for the establishment of the validity of an experimental result. In this paper, I present several examples, typical of physics experiments, that illustrate the adequacy of the surrogate. In addition, I discuss several episodes in which the question of calibration is both difficult to answer and of paramount importance. These episodes include early attempts to detect gravity waves, the question of the existence of a 17–keV (...) neutrino, and the question of the existence of a Fifth Force in gravity. I argue that in these more complex cases, the adequacy of calibration, in an extended sense, was both considered and established. (shrink)