This analysis shows Cantor's diagonal definition in his 1891 paper was not compatible with his horizontal enumeration of the infinite set M. The diagonal sequence was a counterfeit which he used to produce an apparent exclusion of a single sequence to prove the cardinality of M is greater than the cardinality of the set of integers N.

Art, beauty, and the voice of God. And what of beauty?

First, I argue that scientific progress is possible in the absence of increasing verisimilitude in science’s theories. Second, I argue that increasing theoretical verisimilitude is not the central, or primary, dimension of scientific progress. Third, I defend my previous argument that unjustified changes in scientific belief may be progressive. Fourth, I illustrate how false beliefs can promote scientific progress in ways that cannot be explicated by appeal to verisimilitude.

Stanford’s argument against scientific realism focuses on theories, just as many earlier arguments from inconceivability have. However, there are possible arguments against scientific realism involving unconceived (or inconceivable) entities of different types: observations, models, predictions, explanations, methods, instruments, experiments, and values. This paper charts such arguments. In combination, they present the strongest challenge yet to scientific realism.

When do we agree? The answer might once have seemed simple and obvious; we agree that p when we each believe that p. But from a formal epistemological perspective, where degrees of belief are more fundamental than beliefs, this answer is unsatisfactory. On the one hand, there is reason to suppose that it is false; degrees of belief about p might differ when beliefs simpliciter on p do not. On the other hand, even if it is true, it is too (...) vague; for what it is to believe simpliciter ought to be explained in terms of degrees of belief. This paper presents several possible notions of agreement, and corresponding notions of disagreement. It indicates how the findings are fruitful for the epistemology of disagreement, with special reference to the notion of epistemic peerhood. (shrink)

First, I answer the controversial question ’What is scientific realism?’ with extensive reference to the varied accounts of the position in the literature. Second, I provide an overview of the key developments in the debate concerning scientific realism over the past decade. Third, I provide a summary of the other contributions to this special issue.

An important suggestion of objective Bayesians is that the maximum entropy principle can replace a principle which is known to get into paradoxical difficulties: the principle of indifference. No one has previously determined whether the maximum entropy principle is better able to solve Bertrand’s chord paradox than the principle of indifference. In this paper I show that it is not. Additionally, the course of the analysis brings to light a new paradox, a revenge paradox of the chords, that is unique (...) to the maximum entropy principle. (shrink)

What do we do with Judges? This two-edged word? This ambidextrous book? These ambivalent heroes? The Judges were drawing their last fleeting breaths shipwrecked and scattered upon the shores of historical-critical-grammatical-linear-modernist-masculine interpretation. "The narrative is primitive," they said. "The editors have made a mess," they exclaimed. "The conclusion is really an appendix," another said. Then the bible-acrobats jumped in pretending there was no literary carnage while at the same time drawing our eyes away from the literary carnage. "No, no, there (...) is an order to this disorderly book!" "Gideon is a man of faith," they explained. "Gideon is a sham," others retorted. "Long live the king," they cried. "Oh no, the king will bring down the nation," others said. Enter the latest literary critics and the fresh feminist readers to save the day. And save they have. Barry noted the irony. Cheryl called attention to the elaborate, spiraling labyrinth. Phyllis remembered the forgotten. Mieke heralded the incoherence. Deborah the Bee slings Barak with irony. Cowardly Jephthah sacrifices his virgin daughter immediately after he is filled with the spirit. Blind Samson remains stuck in some adolescent, Pinnochio-like stage milling around the same old vices. The Levite, the man of word and sacrifice, lies to the people and dismembers his wife. To beat it all the myopic narrator joins in lock step with the other blind characters stumbling around in the narrative. What manner of text is this? These Judges, these stories, are even more troubling now that we take them seriously. Now what do we do with Judges? The recent scholarship is most promising, but I think we must press forward, or is that backward, or perhaps to another plan. Perhaps Judges hearkens forward to the postmodern. What would Judges look like if we viewed the story through a postmodern lens? Would we see the text in another dimension? Would we let the characters live and breathe as confusing, confounding, intricate characters? Judges speaks to me. These judges, they teach me. How can I ever forget my reading of Judges? For once I found a text reflecting the madness of faith in my maddening world. For once I saw a text like Pablo. I heard the echo of Umberto. I noted the faint murmurings of Jacques. I danced a most joyous jig with Julia. I saw, up ahead, or was that behind me, or over to the side, Martin's flickering candle. Mieke, meet Jael. Barak, meet Barry. Jacques, meet Gideon. Samson, meet Martin. Umberto, meet the narrator or two or three. Pablo, meet the Levite's wife---sorry, she has no name. (shrink)

Schwitzgebel (2001) — henceforth 'S' — offers three examples in order to convince us that there are situations in which individuals are neither accurately describable as believing that p or failing to so believe, but are rather in 'in-between states of belief'. He then argues that there are no 'Bayesian' or representational strategies for explicating these, and proposes a dispositional account. I do not have any fundamental objection to the idea that there might be 'in-between states of belief'. What I (...) shall argue, rather, is that: (I) S does not provide a convincing argument that there really are such states; (II) S does not show, as he claims, that 'in-between states of belief' could not be accounted for in terms of degrees of belief; (III) S’s dispositional account of 'in-between states of belief' is more problematic than the 'degree of belief' alternative. (shrink)

People often act in ways that appear incompatible with their sincere assertions. But how might we explain such cases? On the shifting view, subjects’ degrees of belief may be highly sensitive to changes in context. This paper articulates and refines this view, after defending it against recent criticisms. It details two mechanisms by which degrees of beliefs may shift.

Contemporary naturalism is changing and scientific reductionism is under challenge from those who advocate a more comprehensive outlook. This special issue of Telos, based on the first Telos Australia Symposium held at Swinburne University in Melbourne in February 2014, introduces some of the key questions in the current debates. It also poses the question of whether more satisfactory political and social thought can be produced if scientific reductionism is replaced by a richer and more hermeneutical naturalism, one that takes more (...) account of philosophical anthropology, actual co-involvements of human beings and their environments, and the potential of more naturalistically grounded approaches to culture. (shrink)

Do component forces exist? I argue that the answer lies in the affirmative, on historical and operational grounds.

Hájek has recently presented the following paradox. You are certain that a cable guy will visit you tomorrow between 8 a.m. and 4 p.m. but you have no further information about when. And you agree to a bet on whether he will come in the morning interval (8, 12] or in the afternoon interval (12, 4). At first, you have no reason to prefer one possibility rather than the other. But you soon realise that there will definitely be a future (...) time at which you will (rationally) assign higher probability to an afternoon arrival than a morning one, due to time elapsing. You are also sure there may not be a future time at which you will (rationally) assign a higher probability to a morning arrival than an afternoon one. It would therefore appear that you ought to bet on an afternoon arrival. The paradox is based on the apparent incompatibility of the principle of expected utility and principles of diachronic rationality which are prima facie plausible. Hájek concludes that the latter are false, but doesn't provide a clear diagnosis as to why. We endeavour to further our understanding of the paradox by providing such a diagnosis. (shrink)

First, I identify a methodological thesis associated with scientific realism. This has different variants, but each concerns the reliability of scientific methods in connection with acquiring, or approaching, truth or approximate truth. Second, I show how this thesis bears on what scientists should do when considering new theories that significantly contradict older theories. Third, I explore how vulnerable scientific realism is to a reductio ad absurdum as a result. Finally, I consider which variants of the methodological thesis are the most (...) defensible in light of the earlier findings. (shrink)

Kuhn’s view of science is as follows. Science involves two key phases: normal and extraordinary. In normal science, disciplinary matrices (DMs) are large and pervasive. DMs involve “beliefs, values, techniques, and so on shared by the members of a given community” (Kuhn 1996, 175). “And so on” is regrettably vague, but Kuhn (1977, 1996) mentions three other key elements: symbolic generalizations (such as F=dp/dt), models (such as Bohr’s atomic model), and exemplars. These components of DMs overlap somewhat. For instance, symbolic (...) generalizations may feature in techniques and beliefs, and models may exhibit values. To be a (genuine) scientist, in the normal science phase, is to puzzle solve within the boundaries of the DM. It is to buy into the ruling dogma (Kuhn 1963) and to accept that “failure to achieve a solution discredits only the scientist ... ‘It is a poor carpenter who blames his tools’” (Kuhn 1996, 80). Puzzle solving involves a wide variety of activities, including. (shrink)

Theory of Computation -- Computation by Abstracts Devices.

The work described in this report is motivated by the desire to test the expressive possibilities of action language C+. The Causal Calculator (CCalc) is a system that answers queries about action domains described in a fragment of that language. The Zoo World and the Traffic World have been proposed by Erik Sandewall in his Logic Modelling Workshop—an environment for communicating axiomatizations of action domains of nontrivial size. -/- The Zoo World consists of several cages and the exterior, gates between (...) them, and animals of several species, including humans. Actions in this domain include moving within and between cages, opening and closing gates, and mounting and riding animals. The Traffic World includes vehicles moving continuously between road crossings subject to a number of restrictions, such as speed limits and keeping a fixed safety distance away from other vehicles on the road. We show how to represent the two domains in the input language of CCalc, and how to use CCalc to test these representations. (shrink)

Philosophical work on explanation has focused on the following two topics: theories of explanation, intended to enumerate necessary and sufficient conditions for explanation, and inference to the best explanation as the strongest form of justification for ontological or metaphysical claims. I critically examine the most important philosophical work in both of these areas and defend my own conclusions about the connections between explanation and ontology. I argue that all of our inferences about the nature of the world, in ontology or (...) metaphysics, presuppose criteria for acceptable explanation. I first examine the metaphysics of Plato, Aristotle, and Leibniz, arguing that their metaphysical reasoning was guided by assumptions about the nature of explanation. I also survey some recent work in ontology and find inference to the best explanation offered as the strongest available method of defending existence claims. To conclude this discussion, I offer an original argument for the thesis that all reasoning about existence claims, being nondeductive, presupposes some criteria for acceptable explanations, or a theory of explanation. Carl Hempel and Wesley Salmon have been two of the most influential philosophers offering theories of explanation, and I examine their work with the intention of discovering ontological or metaphysical assumptions shaping their theories of explanation. I argue that Hempel's theory rests on deterministic assumptions, and I argue the Salmon's theory of causality, which he admits supports his theory of explanation, is subject to empiricist criticisms. Theories of explanation typically rest on assumptions about the nature of the world, I argue, and I explain why this is so with an original theory of explanation connecting it to the psychological phenomenon of understanding. We rely on understanding in the identification of explanations, and understanding requires establishing a metaphysical context for an explanandum-event. I end by indicating the possibility of generating vicious justificatory circles through the reciprocal relationship of support between explanation and ontology, and I argue that vicious circles can be avoided only by grounding all ontological reasoning in a fundamental explanatory task of giving order to experience through a system of categories. (shrink)

Judges is about loss: a loss of the individual which leads to a loss of the tribe, and, if circumstances remain unchecked, a loss of the nation.

"Any man-any artist, as Nietzsche or Cezanne would say- climbs the stairway in the tower of his perfection at the cost of a struggle with a deunde-not with an angel, as some have maintained, or with his muse. This fundamental distinction must be kept in mind if the root of a work of art is to be grasped." -Frederico Garcia Lorca.

It has become more common recently for epistemologists to advocate the pragmatic encroachment on knowledge, the claim that the appropriateness ofknowledge ascriptions is dependent on the relevant practical circumstances. Advocacy of practicalism in epistemology has come at the expense of contextualism, the view that knowledge ascriptions are independent of pragmatic factors and depend alternatively on distinctively epistemological, semantic factors with the result that knowledge ascriptions express different knowledge properties on different occasions of use. Overall, my goal here is to defend (...) a particular version of contextualism drawn from work by Peter Ludlow, called ‘standards contextualism.’ My strategy will be to elaborate on this form of contextualism by defending it from various objections raised by the practicalists Jason Stanley, Jeremy Fantl and Matthew McGrath. In showing how standards contextualism can effectively repel these criticisms I hope to establish that standards contextualism is a viable alternative to practicalism. (shrink)

With the appearance of Mircea Eliade's The Sacred and the Profane came the inauguration of theologians and philosophers questioning the preeminence of scholarly attention given to time to the virtual exclusion of space.

Our generation is turning to mentoring as an instrument of God to repair the ruin of our personal losses.

We lose something central to our humanity when we divide our world into neat little packages of sacred and secular.

It is only the story... that saves our progeny from blundering like blind beggars into the spikes of the cactus fence. The story is our escort. Without we are blind. -Chinua Achebe, Anthills of the Savannah.

Aimee did not want to survive; she neither wanted to live nor to die.

We want God to make sense, to be reasonable, to act according to how we think God should act. This kind of thinking, though, is not far from where we live today. If I give money to the church, then God will bless me financially. If I have my “quiet time” in scripture, then God will bless my day. If I raise my children right, then surely they will turn out right. In themselves these actions are good and right; however, (...) we have to ask ourselves, “Do our motives emerge from the desire to give a place to the mystery of faith, or, rather, to conquer mystery?”. (shrink)

"Everything is a pretext for a good dinner.".

It was the summer of 1984, the American dollar was strong, and this was my first venture to Europe. I found her and didn't even know I was searching for her. Mysteriously she crossed my path one day in Rome. I should confess though- at this point in my life, I am an uneasy Protestant.

It is quite fair to say that to the degree language works is also to the degree language does not work.

We live in a world of many odd-shaped pieces, a cosmic jigsaw puzzle that often seems to have been further complicated by cruel fate.

Narcissus has no need of art because his own reflection preoccupies him.

An encyclopedic exploration of the images, symbols, motifs, metaphors, figures of speech and literary patterns of the Bible.

What is the relationship between prophetic vision and vision in terms for a hoped-for future? How might vision for a church or person best be defined today?

"I tried to find out for myself, from the start, when I was a child, what was right and what was wrong-because no one around me could tell me. And now that everything is leaving me I realize I need someone to show me the way and to blame me and praise me, by right not ofp ower but ofa uthority, I need my father." -Albert Camus, The First Man.

Compassion is called out of us when we see situations where there is an obvious absence of something or someone life-giving.

"He who is satisfied has never truly craved. And he who craves for the light of God neglects his ease for ardor." -Rabbi Abraham J. Heschel.

Le but de ce texte est de mettre en évidence les équi­valences entre la façon dont le concept de conatus résout, dans l'Éthique, le problème de l'unité modale complexe. en rendant consis­tant le concept de chose singulière en tant que celle-ci doit être consi­dérée comme un légitime sujet d'attribution d'états, et la façon dont ce même concept dessine le rapport cognitif de l'esprit avec lui-même, rapport par lequel l'esprit se saisit comme sujet de ses états et qui ca­ractérise la notion (...) moderne de subjectivité. Ainsi, en éclairant cet as­pect du concept spinoziste de chose singulière. on comprendra aussi, de façon indirecte, l'une des conditions par lesquelles les choses peuvent, dans la doctrine spinoziste, devenir des objets ou des signes pour la connaissance humaine. (shrink)

Livro-texto de introdução à lógica, com (mais do que) pitadas de filosofia da lógica, produzido como uma versão revista e ampliada do livro Forallx: Calgary. Trata-se da versão de 13 de outubro de 2022. Comentários, críticas, correções e sugestões são muito bem-vindos.

The question I want to explore is whether experience supports an antireductionist ontology of time, that is, whether we should take it to support an ontology that includes a primitive, monadic property of nowness responsible for the special feel of events in the present, and a relation of passage that events instantiate in virtue of literally passing from the future, to the present, and then into the past.

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.

The tripartite account of propositional, fallibilist knowledge that p as justified true belief can become adequate only if it can solve the Gettier Problem. However, the latter can be solved only if the problem of a successful coordination of the resources (at least truth and justification) necessary and sufficient to deliver propositional, fallibilist knowledge that p can be solved. In this paper, the coordination problem is proved to be insolvable by showing that it is equivalent to the ''''coordinated attack'''' problem, (...) which is demonstrably insolvable in epistemic logic. It follows that the tripartite account is not merely inadequate as it stands, as proved by Gettier-type counterexamples, but demonstrably irreparable in principle, so that efforts to improve it can never succeed. (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)

It seems natural to choose whether to have a child by reflecting on what it would be like to actually have a child. I argue that this natural approach fails. If you choose to become a parent, and your choice is based on projections about what you think it would be like for you to have a child, your choice is not rational. If you choose to remain childless, and your choice is based upon projections about what you think it (...) would be like for you to have a child, your choice is not rational. This suggests we should reject our ordinary conception of how to make this life-changing decision, and raises general questions about how to rationally approach important life choices. (shrink)

The genetic modification of pigs as a source of transplantable organs is one of several possible solutions to the chronic organ shortage. This paper describes existing ethical tensions in xenotransplantation (XTx) that argue against pursuing it. Recommendations for lifelong infectious disease surveillance and notification of close contacts of recipients are in tension with the rights of human research subjects. Parental/guardian consent for pediatric xenograft recipients is in tension with a child’s right to an open future. Individual consent to transplant is (...) in tension with public health threats that include zoonotic diseases. XTx amplifies concerns about justice in organ transplantation and could exacerbate existing inequities. The prevention of infectious disease in source animals is in tension with the best practices of animal care and animal welfare, requiring isolation, ethologically inappropriate housing, and invasive reproductive procedures that would severely impact the well-being of intelligent social creatures like pigs. (shrink)

This discussion revises and extends Jonny Anomaly's ‘public goods’ account of public health ethics in light of recent criticism from Richard Dees. Public goods are goods that are both non-rival and non-excludable. What is significant about such goods is that they are not always provided efficiently by the market. Indeed, the state can sometimes realize efficiency gains either by supplying such goods directly or by compelling private purchase. But public goods are not the only goods that the market may fail (...) to provide efficiently. This point to a way of broadening the public goods account of public health to accommodate Dees' counterexamples, without abandoning its distinctive appeal. On the market failures approach to public health ethics, the role of public health is to correct public health-related market failures of all kinds, so far as possible. The underlying moral commitment is to economic efficiency in the sense of Pareto: if we can re-allocate resources in the economy so as to raise the welfare of some without lowering the welfare of any other, we ought to do so. (shrink)