The puzzle of petitionary prayer: if we ask for the best thing, God was already going to do it, and if we ask for something that's not the best, God's not going to grant our request. In this paper, we give a new solution to the puzzle.

The Condorcet Jury Theorem formalises the “wisdom of crowds”: binary decisions made by majority vote are asymptotically correct as the number of voters tends to infinity. This classical result assumes like-minded, expected utility maximising voters who all share a common prior belief about the right decision. Ellis : 865–895, 2016) shows that when voters have ambiguous prior beliefs—a set of priors—and follow maxmin expected utility, such wisdom requires that voters’ beliefs satisfy a “disjoint posteriors” condition: different private signals lead to (...) posterior sets with disjoint interiors. Both the original theorem and Ellis’s generalisation assume symmetric penalties for wrong decisions. If, as in the jury context, errors attract asymmetric penalties then it is natural to consider voting rules that raise the hurdle for the decision carrying the heavier penalty for error. In a classical model, Feddersen and Pesendorfer :23–35, 1998) have shown that, paradoxically, raising this hurdle may actually increase the likelihood of the more serious error. In particular, crowds are not wise under the unanimity rule: the probability of the more serious error does not vanish as the crowd size tends to infinity. We show that this “Jury Paradox” persists in the presence of ambiguity, whether or not juror beliefs satisfy Ellis’s “disjoint posteriors” condition. We also characterise the strictly mixed equilibria of this model and study their properties. Such equilibria cannot exist in the absence of ambiguity but may exist for arbitrarily large jury size when ambiguity is present. In addition to uninformative strictly mixed equilibria, analogous to those exhibited by Ellis : 865–895, 2016), there may also exist strictly mixed equilibria which are informative about voter signals. (shrink)

Choquet expected utility substitutes capacities for subjective probabilities to explain uncertainty aversion and related phenomena. This paper studies capacities as models of belief. The notions of inner and outer acceptance context are defined. These are shown to be the natural acceptance contexts when belief expansion is described by naïve Bayesian and Dempster–Shafer updating of capacities respectively. We also show that Eichberger and Kelsey's use of Dempster–Shafer updating as a model of belief revision may lead to violations of the AGM axioms (...) for rational belief change. (shrink)

Rather than advance novel strategies for achieving the objectives of conservation, Sandler suggests that we change the goals of conservation itself, emphasizing ecological processes through...

A probability distribution is regular if it does not assign probability zero to any possible event. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson and Benci et al. have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s “isomorphic” events are not in fact isomorphic, but Howson is speaking (...) of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

Recent work has defended “Euclidean” theories of set size, in which Cantor’s Principle (two sets have equally many elements if and only if there is a one-to-one correspondence between them) is abandoned in favor of the Part-Whole Principle (if A is a proper subset of B then A is smaller than B). It has also been suggested that Gödel’s argument for the unique correctness of Cantor’s Principle is inadequate. Here we see from simple examples, not that Euclidean theories of set (...) size are wrong, but that they must be either very weak and narrow or largely arbitrary and misleading. (shrink)

We examine collective decision-making in a jury voting game under the unanimity rule when voters have ambiguous beliefs. Unlike in existing studies (Ellis in Theoretical Economics 11:865–895, 2016; Fabrizi et al., in: AUT Economics Working Paper, 2021; Ryan in Theory and Decision 90:543–577, 2021), the locus of ambiguity is the likelihood function (signal precision) rather than the prior. This significantly alters the properties of symmetric equilibria. While prior ambiguity may induce multiple equilibria (Fabrizi et al., in: AUT Economics Working (...) Paper, 2021; Ryan in Theory and Decision 90:543–577, 2021) we show that, under likelihood ambiguity, there exists a unique non-trivial symmetric responsive equilibrium that takes the same form as in the absence of ambiguity (Feddersen and Pesendorfer in The American Political Science Review 92:23–35, 1998). Moreover, likelihood ambiguity partially offsets the pernicious effects of pivotality on decision quality: the frequency of Type I error (convicting the innocent) is typically lower than in the absence of ambiguity. (shrink)

The ‘Ordinary Language’ philosophy of the early 20th century is widely thought to have failed. It is identified with the broader so-called ‘linguistic turn’, a common criticism of which is captured by Devitt and Sterelny (1999), who quip: “When the naturalistic philosopher points his finger at reality, the linguistic philosopher discusses the finger.” (p 280) The implication is that according to ‘linguistic’ philosophy, we are not to study reality or truth or morality etc, but the meaning of the words ‘reality’, (...) ‘truth’, ‘morality’ etc. Ordinary Language philosophy has fallen so thoroughly into disrepute because it is supposed to advocate that not only are we to study words and meanings rather than the phenomena themselves (which is apparently bad enough), but we must restrict that study to words and meanings as they occur in the language used by the ordinary speaker. A number of preposterous corollaries have been taken to follow from this view. Most seriously, perhaps, and irritatingly, is that any theory which contains ‘non-ordinary’ uses of expressions is thereby ‘meaningless’ or simply false – which is clearly absurd. In this paper I show that this is a completely inaccurate picture of Ordinary Language philosophy. My aim is to correct these persistent misinterpretations, and make possible a more sensible reassessment of the philosophy. (shrink)

It is widely held that agent-neutral consequentialism is incompatible with deontic constraints. Recently, Kieran Setiya has challenged this orthodoxy by presenting a form of agent-neutral consequentialism that he claims can capture deontic constraints. In this reply, we argue against Setiya's proposal by pointing to features of deontic constraints that his account fails to capture.

The rise of populism and nationalism in the West have raised concerns about the fragility of liberal political values, chief among them tolerance. But what alternative social resources exist for cultivating the interpersonal relationships and mutual goodwill necessary for sustainable peace? And how might the lived practices of religious communities carry potential to reinterpret or re-circuit these interpersonal tensions and transform the relationship with the cultural "other" (Fremde) from "foe" (Feind) to "friend" (Freund)? This volume contributes a unique analysis of (...) this shifting discourse by viewing the contemporary socio-political upheaval through the lens of Friedrich Schleiermacher's theology, with a focus on the themes of friendship, interpersonal subjectivity, and sociability as a path beyond mere tolerance. Each of the essays of the volume is written by an internationally recognized scholar in the field, and the volume examines Schleiermacher's novel reflections across multiple social contexts, including North America, Great Britain, western Europe, and South Africa. As these essays demonstrate, the implications of this conversation continue to resound in contemporary religious communities and political discourse. (shrink)

Scholars are increasingly calling for the environmental issues of the industrial agricultural system to be addressed via eventual agroecological system-level transformation. It is critical to identify the barriers to this transition. Drawing from Henke’s theory of “repair,” we explore how farmers participate in the reproduction of the industrial system through “discursive repair,” or arguing for the continuation of the industrial agriculture system. Our empirical case relates to water pollution from nitrogen fertilizer and draws data from a sample of over 150 (...) interviews with row-crop farmers in the midwestern United States. We find that farmers defend this system by denying agriculture’s causal role and proposing the potential for within-system solutions. They perform these defenses by drawing on ideological positions and may be ultimately led to seek system maintenance because they are unable to envision an alternative to the industrial agriculture system. (shrink)

Patient and public involvement (PPI) has gained widespread support in health research and health policy circles, but there is little consensus on the precise meaning or justifications of PPI. We argue that an important step towards clarifying the meaning and justification for PPI is to split apart the familiar acronym and draw a distinction between patient and public involvement. Specifically, we argue that patient involvement should refer to the practice of involving individuals in health research or policy on the basis (...) of their experience with a particular condition, while public involvement should refer to the practice of involving individuals in health policy or research based on their status as members of a relevant population. Analyzing cases from the UK, Australia, and the USA, we show how our proposed distinction can deliver much needed clarity to conversations on PPI, while guiding the development and evaluation of future PPI‐based policies. (shrink)

The Ontology for Biomedical Investigations (OBI) is an ontology that provides terms with precisely defined meanings to describe all aspects of how investigations in the biological and medical domains are conducted. OBI re-uses ontologies that provide a representation of biomedical knowledge from the Open Biological and Biomedical Ontologies (OBO) project and adds the ability to describe how this knowledge was derived. We here describe the state of OBI and several applications that are using it, such as adding semantic expressivity to (...) existing databases, building data entry forms, and enabling interoperability between knowledge resources. OBI covers all phases of the investigation process, such as planning, execution and reporting. It represents information and material entities that participate in these processes, as well as roles and functions. Prior to OBI, it was not possible to use a single internally consistent resource that could be applied to multiple types of experiments for these applications. OBI has made this possible by creating terms for entities involved in biological and medical investigations and by importing parts of other biomedical ontologies such as GO, Chemical Entities of Biological Interest (ChEBI) and Phenotype Attribute and Trait Ontology (PATO) without altering their meaning. OBI is being used in a wide range of projects covering genomics, multi-omics, immunology, and catalogs of services. OBI has also spawned other ontologies (Information Artifact Ontology) and methods for importing parts of ontologies (Minimum information to reference an external ontology term (MIREOT)). The OBI project is an open cross-disciplinary collaborative effort, encompassing multiple research communities from around the globe. To date, OBI has created 2366 classes and 40 relations along with textual and formal definitions. The OBI Consortium maintains a web resource providing details on the people, policies, and issues being addressed in association with OBI. (shrink)

Human cooperation is highly unusual. We live in large groups composed mostly of non-relatives. Evolutionists have proposed a number of explanations for this pattern, including cultural group selection and extensions of more general processes such as reciprocity, kin selection, and multi-level selection acting on genes. Evolutionary processes are consilient; they affect several different empirical domains, such as patterns of behavior and the proximal drivers of that behavior. In this target article, we sketch the evidence from five domains that bear on (...) the explanatory adequacy of cultural group selection and competing hypotheses to explain human cooperation. Does cultural transmission constitute an inheritance system that can evolve in a Darwinian fashion? Are the norms that underpin institutions among the cultural traits so transmitted? Do we observe sufficient variation at the level of groups of considerable size for group selection to be a plausible process? Do human groups compete, and do success and failure in competition depend upon cultural variation? Do we observe adaptations for cooperation in humans that most plausibly arose by cultural group selection? If the answer to one of these questions is “no,” then we must look to other hypotheses. We present evidence, including quantitative evidence, that the answer to all of the questions is “yes” and argue that we must take the cultural group selection hypothesis seriously. If culturally transmitted systems of rules that limit individual deviance organize cooperation in human societies, then it is not clear that any extant alternative to cultural group selection can be a complete explanation. (shrink)

For Ordinary Language philosophy, at issue is the use of the expressions of language, not expressions in and of themselves. So, at issue is not, for example, ordinary versus (say) technical words; nor is it a distinction based on the language used in various areas of discourse, for example academic, technical, scientific, or lay, slang or street discourses – ordinary uses of language occur in all discourses. It is sometimes the case that an expression has distinct uses within distinct discourses, (...) for example, the expression ‘empty space’. This may have both a lay and a scientific use, and both uses may count as ordinary; as long as it is quite clear which discourse is in play, and thus which of the distinct uses of the expression is in play. Though connected, the difference in use of the expression in different discourses signals a difference in the sense with which it is used, on the Ordinary Language view. One use, say the use in physics, in which it refers to a vacuum, is distinct from its lay use, in which it refers rather more flexibly to, say, a room with no objects in it, or an expanse of land with no buildings or trees. However, on this view, one sense of the expression, though more precise than the other, would not do as a replacement of the other term; for the lay use of the term is perfectly adequate for the uses it is put to, and the meaning of the term in physics would not allow speakers to express what they mean in these other contexts. (shrink)

Perceived size is a function of viewing distance, retinal images size, and various contextual cues such as linear perspective and the size and location of neighboring objects. Recently, we demonstrated that illusion magnitudes of classic visual size illusions may be greatly enhanced or reduced by adding dynamic elements. Specifically, a dynamic version of the Ebbinghaus illusion (classically considered a “size contrast” illusion) led to a greatly enhanced illusory effect, whereas a dynamic version of the Corridor illusion (a “size constancy” illusion) (...) led to a greatly diminished illusory effect. Although these differences may arise from the different processes underlying these illusions (size contrast vs. size constancy), the dynamic variants we tested in our previous work also differed in the nature of the dynamic elements; specifically, whereas the Dynamic Ebbinghaus included a moving target and inducers that changed size and position, the Dynamic Corridor only included a moving target on a static background. Here, we explore further dynamic versions of the Ebbinghaus illusion and the Corridor and Ponzo illusions by separately manipulating three types of dynamic elements: target motion, context translation, and dynamic changes in context. Across five experiments examining 21 dynamic illusory configurations, adding target motion or a dynamically changing context separately resulted in little-to-no illusory effect. In contrast, the combination of target motion and a dynamically changing context led to a robust size illusion, consistent with an interactive effect. However, illusory effects that exceeded the matched classic, static illusory configuration were only observed for the dynamic versions of the Ebbinghaus illusion and the Revealed Ponzo illusions, in which the contextual elements changed size. We conclude that the combination of target motion and a dynamically changing context are necessary to produce dynamic size illusions, but that enhancement above and beyond static illusions may be largely specific to size contrast effects. Our results have important implications for the integration of motion signals, a ubiquitous environmental stimulus, in the perception of object size. (shrink)

In late December 1998, Renada Daniel-Patterson's father offered to donate a kidney to his daughter and ignited a controversy in the bioethics community. Renada had been born with only one kidney, which began to fail early in her childhood. At age 6, Renada had to receive dialysis three times a week. She was unable to attend school or venture very far from home. This pattern continued until Renada was 13, when Mr. Patterson called from prison to offer her his kidney. (...) Renada was surprised to hear from her father, who was serving 12 years at California State Prison for burglary and drug convictions. Mr. Patterson was determined to be a compatible donor, and the family proceeded with the transplant operation. As a result of this surgery, Renada was able to live the life of a healthy girl for 2 years. Because the medication to prevent rejection of the transplanted organ made her feel ill and bloated and caused her to develop a hump on her back, Renada gradually began to skip doses. As a result, her donated kidney began to fail. It was under these circumstances that David Patterson offered to donate his second kidney to his daughter in 1998. (shrink)

In a fair, infinite lottery, it is possible to conclude that drawing a number divisible by four is strictly less likely than drawing an even number; and, with apparently equal cogency, that drawing a number divisible by four is equally as likely as drawing an even number.

A probability distribution is regular if no possible event is assigned probability zero. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “isomorphic” events are not in fact isomorphic, but Howson is speaking (...) of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

The ‘between Wars’ period in England in the early twentieth century was extraordinary, philosophically. It was marked by a profusion of new, controversial, and revolutionary ideas. Developments in formal logic, the rise of the method of ‘analysis’, and logical atomism were already changing the face of philosophy in England. From this mix emerged two distinctive views about language and its connection to philosophical methodology: one championing the concept of an ideal language; and one rejecting this and favoring appeal to ordinary (...) language. The origin of both views is to be found in the (earlier and later) work of Ludwig Wittgenstein. In this paper, I will examine the emergence of these views in relation to one another: an ideal language conception represented by A.J. Ayer in his Language, Truth and Logic, and the reaction against this conception in the early phases of ordinary language philosophy, in particular in the work of John Wisdom. (shrink)

There is no uniquely standard concept of an effectively decidable set of real numbers or real n-tuples. Here we consider three notions: decidability up to measure zero [M.W. Parker, Undecidability in Rn: Riddled basins, the KAM tori, and the stability of the solar system, Phil. Sci. 70(2) (2003) 359–382], which we abbreviate d.m.z.; recursive approximability [or r.a.; K.-I. Ko, Complexity Theory of Real Functions, Birkhäuser, Boston, 1991]; and decidability ignoring boundaries [d.i.b.; W.C. Myrvold, The decision problem for entanglement, in: (...) R.S. Cohen et al. (Eds.), Potentiality, Entanglement, and Passion-at-a-Distance: Quantum Mechanical Studies fo Abner Shimony, Vol. 2, Kluwer Academic Publishers, Great Britain, 1997, pp. 177–190]. Unlike some others in the literature, these notions apply not only to certain nice sets, but to general sets in Rn and other appropriate spaces. We consider some motivations for these concepts and the logical relations between them. It has been argued that d.m.z. is especially appropriate for physical applications, and on Rn with the standard measure, it is strictly stronger than r.a. [M.W. Parker, Undecidability in Rn: Riddled basins, the KAM tori, and the stability of the solar system, Phil. Sci. 70(2) (2003) 359–382]. Here we show that this is the only implication that holds among our three decidabilities in that setting. Under arbitrary measures, even this implication fails. Yet for intervals of non-zero length, and more generally, convex sets of non-zero measure, the three concepts are equivalent. (shrink)

We consider an approach to some philosophical problems that I call the Method of Conceptual Articulation: to recognize that a question may lack any determinate answer, and to re-engineer concepts so that the question acquires a definite answer in such a way as to serve the epistemic motivations behind the question. As a case study we examine “Galileo’s Paradox”, that the perfect square numbers seem to be at once as numerous as the whole numbers, by one-to-one correspondence, and yet less (...) numerous, being a proper subset. I argue that Cantor resolved this paradox by a method at least close to that proposed—not by discovering the true nature of cardinal number, but by articulating several useful and appealing extensions of number to the infinite. Galileo was right to suggest that the concept of relative size did not apply to the infinite, for the concept he possessed did not. Nor was Bolzano simply wrong to reject Hume’s Principle (that one-to-one correspondence implies equal number) in the infinitary case, in favor of Euclid’s Common Notion 5 (that the whole is greater than the part), for the concept of cardinal number (in the sense of “number of elements”) was not clearly defined for infinite collections. Order extension theorems now suggest that a theory of cardinality upholding Euclid’s principle instead of Hume’s is possible. Cantor’s refinements of number are not the only ones possible, and they appear to have been shaped by motivations and fruitfulness, for they evolved in discernible stages correlated with emerging applications and results. Galileo, Bolzano, and Cantor shared interests in the particulate analysis of the continuum and in physical applications. Cantor’s concepts proved fruitful for those pursuits. Finally, Gödel was mistaken to claim that Cantor’s concept of cardinality is forced on us; though Gödel gives an intuitively compelling argument, he ignores the fact that Euclid’s Common Notion is also intuitively compelling, and we are therefore forced to make a choice. The success of Cantor’s concept of cardinality lies not in its truth (for concepts are not true or false), nor its uniqueness (for it is not the only extension of number possible), but in its intuitive appeal, and most of all, its usefulness to the understanding. (shrink)

As an application of his Material Theory of Induction, Norton (2018; manuscript) argues that the correct inductive logic for a fair infinite lottery, and also for evaluating eternal inflation multiverse models, is radically different from standard probability theory. This is due to a requirement of label independence. It follows, Norton argues, that finite additivity fails, and any two sets of outcomes with the same cardinality and co-cardinality have the same chance. This makes the logic useless for evaluating multiverse models based (...) on self-locating chances, so Norton claims that we should despair of such attempts. However, his negative results depend on a certain reification of chance, consisting in the treatment of inductive support as the value of a function, a value not itself affected by relabeling. Here we define a purely comparative infinite lottery logic, where there are no primitive chances but only a relation of ‘at most as likely’ and its derivatives. This logic satisfies both label independence and a comparative version of additivity as well as several other desirable properties, and it draws finer distinctions between events than Norton's. Consequently, it yields better advice about choosing between sets of lottery tickets than Norton's, but it does not appear to be any more helpful for evaluating multiverse models. Hence, the limitations of Norton's logic are not entirely due to the failure of additivity, nor to the fact that all infinite, co-infinite sets of outcomes have the same chance, but to a more fundamental problem: We have no well-motivated way of comparing disjoint countably infinite sets. (shrink)

In standard probability theory, probability zero is not the same as impossibility. But many have suggested that only impossible events should have probability zero. This can be arranged if we allow infinitesimal probabilities, but infinitesimals do not solve all of the problems. We will see that regular probabilities are not invariant over rigid transformations, even for simple, bounded, countable, constructive, and disjoint sets. Hence, regular chances cannot be determined by space-time invariant physical laws, and regular credences cannot satisfy seemingly reasonable (...) symmetry principles. Moreover, the examples here are immune to the objections against Williamson’s infinite coin flips. (shrink)

Some have suggested that certain classical physical systems have undecidable long-term behavior, without specifying an appropriate notion of decidability over the reals. We introduce such a notion, decidability in (or d- ) for any measure , which is particularly appropriate for physics and in some ways more intuitive than Ko's (1991) recursive approximability (r.a.). For Lebesgue measure , d- implies r.a. Sets with positive -measure that are sufficiently "riddled" with holes are never d- but are often r.a. This explicates Sommerer (...) and Ott's (1996) claim of uncomputable behavior in a system with riddled basins of attraction. Furthermore, it clarifies speculations that the stability of the solar system (and similar systems) may be undecidable, for the invariant tori established by KAM theory form sets that are not d-. (shrink)

The behavior of some systems is non-computable in a precise new sense. One infamous problem is that of the stability of the solar system: Given the initial positions and velocities of several mutually gravitating bodies, will any eventually collide or be thrown off to infinity? Many have made vague suggestions that this and similar problems are undecidable: no finite procedure can reliably determine whether a given configuration will eventually prove unstable. But taken in the most natural way, this is trivial. (...) The state of a system corresponds to a point in a continuous space, and virtually no set of points in space is strictly decidable. A new, more pragmatic concept is therefore introduced: a set is decidable up to measure zero (d.m.z.) if there is a procedure to decide whether a point is in that set and it only fails on some points that form a set of zero volume. This is motivated by the intuitive correspondence between volume and probability: we can ignore a zero-volume set of states because the state of an arbitrary system almost certainly will not fall in that set. D.m.z. is also closer to the intuition of decidability than other notions in the literature, which are either less strict or apply only to special sets, like closed sets. Certain complicated sets are not d.m.z., most remarkably including the set of known stable orbits for planetary systems (the KAM tori). This suggests that the stability problem is indeed undecidable in the precise sense of d.m.z. Carefully extending decidability concepts from idealized models to actual systems, we see that even deterministic aspects of physical behavior can be undecidable in a clear and significant sense. (shrink)

We examine a case in which non-computable behavior in a model is revealed by computer simulation. This is possible due to differing notions of computability for sets in a continuous space. The argument originally given for the validity of the simulation involves a simpler simulation of the simulation, still further simulations thereof, and a universality conjecture. There are difficulties with that argument, but there are other, heuristic arguments supporting the qualitative results. It is urged, using this example, that absolute validation, (...) while highly desirable, is overvalued. Simulations also provide valuable insights that we cannot yet (if ever) prove. (shrink)

A renewed focus on the role of interpersonal relationships in the cultivation of religious sensibilities is emerging in the study of religion. Matthew Ryan Robinson addresses this question in his study of Friedrich Schleiermacher's notion of "free sociability." In Schleiermacher's ethics, the human person is formed in and consists of intimate, tightly interconnecting relationships with others. Schleiermacher describes this sociability as a natural tendency prompted by experiences of physical and existential limitation that lead one to look to others (...) to complete one's experience. But this experience of incompleteness and orientation to "the completion of humanity" also constitute the fundamental structure of religion in Schleiermacher's theory of religion as orientation to "the universe and the relationship of humanity to it." Thus, Schleiermacher not only presents sociability as basic to human nature, but also as inherently religious - and, potentially, redemptive. What making such a claim means and the implications it raises are central considerations of this study of Schleiermacher's ethics, theory of religion and ecclesiology. (shrink)

Ontological arguments like those of Gödel (1995) and Pruss (2009; 2012) rely on premises that initially seem plausible, but on closer scrutiny are not. The premises have modal import that is required for the arguments but is not immediately grasped on inspection, and which ultimately undermines the simpler logical intuitions that make the premises seem plausible. Furthermore, the notion of necessity that they involve goes unspecified, and yet must go beyond standard varieties of logical necessity. This leaves us little reason (...) to believe the premises, while their implausible existential import gives us good reason not to. (shrink)

With essay deadlines looming for many of our students, Matt Parker relives some of the angst involved in writing philosophy. You’re not alone.

A probability distribution is regular if it does not assign probability zero to any possible event. Williamson argued that we should not require probabilities to be regular, for if we do, certain “isomorphic” physical events must have different probabilities, which is implausible. His remarks suggest an assumption that chances are determined by intrinsic, qualitative circumstances. Weintraub responds that Williamson’s coin flip events differ in their inclusion relations to each other, or the inclusion relations between their times, and this can account (...) for their differences in probability. Haverkamp and Schulz rebut Weintraub, but their rebuttal fails because the events in their example are even less symmetric than Williamson’s. However, Weintraub’s argument also fails, for it ignores the distinction between intrinsic, qualitative differences and relations of time and bare identity. Weintraub could rescue her argument by claiming that the events differ in duration, under a non-standard and problematic conception of duration. However, we can modify Williamson’s example with Special Relativity so that there is no absolute inclusion relation between the times, and neither event has longer duration except relative to certain reference frames. Hence, Weintraub’s responses do not apply unless chance is observer-relative, which is also problematic. Finally, another symmetry argument defeats even the appeal to frame-dependent durations, for there the events have the same finite duration and are entirely disjoint, as are their respective times and places. (shrink)

On the first page of “What is Cantor's Continuum Problem?”, Gödel argues that Cantor's theory of cardinality, where a bijection implies equal number, is in some sense uniquely determined. The argument, involving a thought experiment with sets of physical objects, is initially persuasive, but recent authors have developed alternative theories of cardinality that are consistent with the standard set theory ZFC and have appealing algebraic features that Cantor's powers lack, as well as some promise for applications. Here we diagnose Gödel's (...) argument, showing that it fails in two important ways: Its premises are not sufficiently compelling to discredit countervailing intuitions and pragmatic considerations, nor pluralism, and its final inference, from the superiority of Cantor's theory as applied to sets of changeable physical objects to the unique acceptability of that theory for all sets, is irredeemably invalid. (shrink)

Recent theories of decision making are characterised by a growing emphasis on understanding the cognitive mechanisms that produce decisions. This has seen a growth in methods that allow for the con...

Due to natural selection pressure, certain aspects of memory may have been selected to give humans a survival advantage. Research has demonstrated that processing information for survival relevance leads to better item memory (i.e., the content of information) compared to control conditions. The current study investigates the effects of survival processing on context memory (i.e., memory for peripheral episodic details) and item memory to better understand when the survival processing memory advantage emerges. In this study, participants viewed objects in either (...) a plausible color, for example a red apple, or in an implausible color, such as a green pie. We chose this color plausibility manipulation because color is a detail that conveys information about the fitness of an item. After studying items in either a survival or moving (control) condition, participants made item memory judgments (did you see this item before?), and two context memory judgments: color context (in which color did you see this item?), and source context (in which condition did you see this item?). Results indicated better item memory for materials processed in the survival relative to moving condition. Critically, for color context there was a condition by plausibility interaction, where memory was best for plausibly colored items in the survival processing condition. There was no difference, however, in source context memory between the survival and moving conditions. These results suggest the survival processing memory advantage extends to some contextual details, but only those details that tap into the survival utility of items, such as color. (shrink)