A formal sequent system dealing with Menelaus' configurations is introduced in this paper. The axiomatic sequents of the system stem from 2-cycles of Δ-complexes. The Euclidean and projective interpretations of the sequents are defined and a soundness result is proved. This system is decidable and its provable sequents deliver incidence results. A cyclic operad structure tied to this system is presented by generators and relations.

Given two internal sets X and Y we prove that every Borel function whose graph is a subset of the product X x Y is a member of the least set containing the class of all internal functions and closed with respect to the operations of monotone countable union and intersection. We also prove that any Souslin function can be extended to a Borel function and obtain, as a corollary, a new proof of the recent result of Henson and Ross (...) about the measure preserving property of injective Souslin functions. Further we give a new proof of the fact that injective Borel functions map Borel sets into Borel. A structural result for Souslin graphs all of whose Y-sections are of cardinality n is given. (shrink)

We prove that a Borel subset of the product of two internal setsX andY all of whoseY-sections are ∏ 1 0 (K)(∑ 1 0 (K)) sets is the intersection (union) of a countable sequence of Borel graphs with internalY-sections. As a consequence we prove some standard results about the domains of graphs in the product of two topological spaces all of whose horizontal section are compact (open) sets. A version of classical Vitali-Lusin theorem for those types of graphs is given (...) as well as a new proof (and an extension) of a classical result of Kunugui. (shrink)

We prove that there exists a function f which reduces a given Π1 1 subset P of an internal set X of an ω1-saturated nonstandard universe to the set WF of well-founded trees possessing properties similar to those possessed by the standard part map. We use f to define the Lusin-Sierpinski index of points in X, and prove the basic properties of that index using the classical properties of the Lusin-Sierpinski index. An example of a Π1 1 but not Σ1 (...) 1 set is given. (shrink)

We prove that every countably determined set C is U-meager if and only if every internal subset A of C is U-meager, provided that the cofinality and coinitiality of the cut U are both uncountable. As a consequence we prove that for such cuts a countably determined set C which intersects every U-monad in at most countably many points is U-meager. That complements a similar result in [KL]. We also give some partial solutions to some open problems from [KL]. We (...) prove that the set K = {1,...,H}, where H is an infinite integer, cannot be expressed as a countable union of countably determined sets each of which is U-meager for some cut U with min{cf (U), ci (U)} ≥ ω1. Also, every Borel, Σ1 m or countably determined set C which is U-meager for every cut U is a countable union of Borel, Σ1 m or countably determined sets respectively, which are U-nowhere dense for every cut U. Further, the class of Borel U-meager sets for min{cf(U), ci(U)} ≥ ω1 coincides with the least family of sets containing internal U-meager sets and closed with respect to the operation of countable union and intersection. The same is true if the phrase "U-meager sets" is replaced by "U-meager for every cut U.". (shrink)

We give positive answers to two open questions from [15]. (1) For every set C countably determined over A, if C is Π 0 α (Σ 0 α ) then it must be Π 0 α (Σ 0 α ) over A, and (2) every Borel subset of the product of two internal sets X and Y all of whose vertical sections are Π 0 α (Σ 0 α ) can be represented as an intersection (union) of Borel sets with (...) vertical sections of lower Borel rank. We in fact show that (2) is a consequence of the analogous result in the case when X is a measurable space and Y a complete separable metric space (Polish space) which was proved by A. Louveau and that (1) is equivalent to the property shared by the inverse standard part map in Polish spaces of preserving almost all levels of the Borel hierarchy. (shrink)

Organ transplantation is an accepted therapy for major organ failure, but it depends on the availability of viable organs. Most organs transplanted in the U.S. come from either "brain-dead" or living related donors. Recently organ procurement from patients pronounced dead using cardiopulmonary criteria, so-called "non-heart-beating cadaver donors" (NHBCDs), has been reconsidered. In May 1992, the University of Pittsburgh Medical Center (UPMC) enacted a new, complicated policy for procuring organs from NHBCDs after the elective removal of life support. Seventeen months later (...) only one patient has become a NHBCD. This article describes her case and the results of interviews with the health care team and the patient's family. The case and interviews are discussed in relation to several of the ethical concerns previously raised about the policy, including potential conflicts of interest, the definition of cardiopulmonary death, and a possible net decrease in organ donation. The conclusion is reached that organ procurement from non-heart-beating cadavers is feasible and may be desirable both for the patient's family and the health care providers. (shrink)

Weber’s very important theory on the influence of religion on economic behaviour was tested in the societies which belong to different cultural and religious circles. However, due to various socio-political circumstances, the testing of Weber’s theoretical-methodological framework has been largely neglected in the countries where Orthodox Christianity is dominant. However, the difficulties that arose in Orthodox societies during the post-socialist transformation, as well as the shift from the economic research paradigm to the cultural one on the global level, along with (...) the revival of religion in Eastern Europe as one of the most important institutions of ideological and social life, contributed to the focus of our scientific interest be directed in this direction. The central questions that we tried to answer on this occasion were primarily related to the specifics of the concept of work in Orthodox Christianity and the relationship to the accumulation of capital. (shrink)

In the preceding commentary, Campbell and Weber raise two valid and important issues concerning non-heart-beating organ donation (NHBOD). First, because the procedure links withdrawal of life support and the potential for subsequent organ donation, the desire for organs may create a situation in which care of the dying individual has relatively less importance and the dying may receive suboptimal care. Second, even if concerns about care of the dying were dealt with adequately, there will not be enough non-heart-beating donors to (...) significantly decrease the organ shortage that exists, making the procedure not worth the risk. We agree that attention to the important details of caring for the dying are, and must be, the primary concern of all health care workers caring for those individuals. Ensuring the patients' comfort, dignity, and autonomy, and providing for family and social support are the mainstays of this care. All policies for NHBOD should clearly support and mandate these concepts. Regarding the second concern, we agree that NHBOD is currently rare; however, evidence is increasing that this type of donation has great potential. Continued growth of the practice in this country will depend largely on public acceptance, which we believe will be directly influenced by whether the public perceives that care of the dying is not compromised by this procedure. (shrink)

Kit Fine (2000) breaks with tradition, arguing that, pace Russell (e.g., 1903: 228), relations have neither directions nor converses. He considers two ways to conceive of these new "neutral" relations, positionalism and anti-positionalism, and argues that the latter should be preferred to the former. Cody Gilmore (2013) argues for a generalization of positionalism, slot theory, the view that a property or relation is n-adic if and only if there are exactly n slots in it, and (very roughly) that each slot (...) may be occupied by at most one entity. Slot theory (and with it, positionalism) bears the full brunt of Fine's (2000) symmetric completions and conflicting adicities problems. I fully develop an alternative, plural slot theory (or pocket theory), which avoids these problems, key elements of which are first considered by Yi (1999: 168 ff.). Like the slot theorist, the pocket theorist posits entities (pockets) in properties and relations that can be occupied. But unlike the slot theorist, the pocket theorist denies that at most one entity can occupy any one of them. As a result, she must also deny that the adicity of a property or relation is equal to the number of occupiable entities in it. By abandoning these theses, however, the pocket theorist is able to avoid Fine's problems, resulting in a stronger theory about the internal structure of properties and relations. Pocket theory also avoids a serious drawback of anti-positionalism. (shrink)

Recent highly publicized privacy breaches in health care and genomics research have led many to question whether current standards of data protection are adequate. Improvements in de-identification techniques, combined with pervasive data sharing, have increased the likelihood that external parties can track individuals across multiple databases. This paper focuses on the communication of identifiability risks in the process of obtaining consent for donation and research. Most ethical discussions of identifiability risks have focused on the severity of the risk and how (...) it might be mitigated, and what precisely is at stake in pervasive data sharing. However, there has been little discussion of whether and how to communicate the risk to potential donors. We review the ethical arguments behind favoring different types of risk communication in the consent process, and outline how identifiability concerns can be incorporated into either a detailed or simplified method of communicating risks during the consent process. (shrink)

Affordances are opportunities for action. An appropriately positioned teapot, for example, might afford the act of gripping. Evidence that we perceive affordances in our environment can be found through first-person reflection on our perceptual phenomenology and through third-person theorizing about how subjects select what action to perform. This paper argues for two claims about affordance perception. First, I argue that by experiencing affordances we implicitly experience ourselves as agents with the power to perform the afforded actions. This variety of implicit (...) self-awareness is an important but overlooked aspect of our sense of agency. Second, I argue that among the affordances we experience are affordances for mental action such as attending, imagining, and deliberating. Our awareness of mental affordances helps us to select which mental actions to perform and underwrites our sense of ourselves as mental agents. My case for these two conclusions combines a range of phenomenological and theoretical considerations. (shrink)

The dramatic events of the crisis have reignited debates on the independence of central banks and the scope of their mandates. In this article, I contribute to the normative understanding of these developments by discussing John Rawls’s position in debates of the 1950s and 1960s on the independence of the US Federal Reserve. Rawls’s account of the central bank in his property-owning democracy, Democratic Central Banking (DCB), assigns authority over monetary policy directly to the government and prioritizes low unemployment over (...) price stability. I contrast DCB with Central Bank Independence (CBI), which requires that the central bank is independent of the government and pursues low inflation. I evaluate DCB by asking whether justice as fairness requires democratic control of the central bank and argue that it does not. Instead, so I argue, the choice between DCB and CBI should be justified in terms of the difference principle. By reflecting on central banking in a property-owning democracy, I cast new light on the Rawlsian realistic utopia of a just capitalist society, while also investigating democratic objections to today’s independent central banks. (shrink)

The variety DMM of De Morgan monoids has just four minimal subvarieties. The join-irreducible covers of these atoms in the subvariety lattice of DMM are investigated. One of the two atoms consisting of idempotent algebras has no such cover; the other has just one. The remaining two atoms lack nontrivial idempotent members. They are generated, respectively, by 4-element De Morgan monoids C4 and D4, where C4 is the only nontrivial 0-generated algebra onto which finitely subdirectly irreducible De Morgan monoids may (...) be mapped by noninjective homomorphisms. The homomorphic preimages of C4 within DMM constitute a proper quasivariety, which is shown to have a largest subvariety U. The covers of the variety within U are revealed here. There are just ten of them. In exactly six of these ten varieties, all nontrivial members have C4 as a retract. In the varietal join of those six classes, every subquasivariety is a variety—in fact, every finite subdirectly irreducible algebra is projective. Beyond U, all covers of [or of ] within DMM are discriminator varieties. Of these, we identify infinitely many that are finitely generated, and some that are not. We also prove that there are just 68 minimal quasivarieties of De Morgan monoids. (shrink)

How are love and justice related? Iris Murdoch characterizes the former by drawing on the latter. Love, she maintains, is just attention, which in turn triggers acts of compassion. Arguably, for Murdoch, love is the most important moral activity. By engaging in love, she maintains, moral agents progress on their journey from appearances to reality. Through love, they overcome selfish leanings, acquire a clearer vision of the world and, importantly, other individuals, which in turn enables them to act increasingly well. (...) In this paper, I lay Murdoch’s account of love alongside of Aristotle’s notion of philia. Ultimately, I argue that both Murdochian love and Aristotelian philia are crucial for enabling moral progress. I proceed as follows: First, I introduce Murdoch’s view. I then propose a novel reading of an argument from Aristotle’s Nicomachean Ethics in order to explain what I shall call his necessity claim (NC): philia is necessary to a flourishing life. Along the way, I point out ways in which Murdoch’s and Aristotle’s accounts are mutually illuminating. (shrink)

The standard approach to protecting privacy in healthcare aims to control access to personal information. We cannot regain control of information after it has been shared, so we must restrict access from the start. This ‘control’ conception of privacy conflicts with data-intensive initiatives like precision medicine and learning health systems, as they require patients to give up significant control of their information. Without adequate alternatives to the control-based approach, such data-intensive programmes appear to require a loss of privacy. This paper (...) argues that the control view of privacy is shortsighted and overlooks important ways to protect health information even when widely shared. To prepare for a world where we no longer control our data, we must pursue three alternative strategies: obfuscate health data, penalise the misuse of health data and improve transparency around who shares our data and for what purposes. Prioritising these strategies is necessary when health data are widely shared both within and outside of the health system. (shrink)

Chalmers (2018) considers a wide range of possible responses to the meta-problem of consciousness. Among them is the ignorance hypothesis -- the view that there only appears to be a hard problem because of our inadequate conception of the physical. Although Chalmers quickly dismisses this view, I argue that it has much greater promise than he recognizes. The plausibility of the ignorance hypothesis depends on how exactly one frames the 'problem intuitions' that a solution to the meta-problem must explain. I (...) argue that problem intuitions are hybrid intuitions that encompass one's intuitive take on the phenomenal and one's intuitive take on the physical. The ignorance hypothesis undermines the second half of these hybrid intuitions. I show how the ignorance hypothesis is preferable to the alternatives and attempt to explain why there is such widespread resistance to this promising position. (shrink)

Beskow and Weinfurt (2019) present an excellent and timely discussion of how to respond to evidence that individuals do not fully understand a biobank consent form. We faced similar challenges afte...

Are there universal structures or stages of experience, so-called contemplative landmarks, that unfold during meditative practice? As commonly described in contemplative manuals or handbooks, there is a transition from a form of meditation where the subject must exert continual effort in order for consciousness to remain focused. As Kenneth Rose has recently shown, these manuals, stemming from the Buddhist, Hindu, and Christian traditions, agree that a transition will take place from effortful meditation into a state where attention is fixed or (...) locked in on the meditation object. This article describes the micro-phenomenology of this phenomenon, sometimes called dhyana or access concentration, from the first-person perspective. This study both confirms and refines the traditional account, engaging with certain difficulties involved in establishing a correspondence between traditional, clear-cut, and sometimes contradictory concepts and actual experiences, which can be hard to conceptualize precisely. (shrink)

Sellars (1962) contains some of the most important metaphilosophical reflections from the analytic tradition. He insightfully describes the relationship between philosophy and science, by identifying the philosophical task of integrating the manifest image into the scientific image. But while this description is sound, it is importantly incomplete. Here, I first suggest that a more complete picture shows philosophy in “superposition” in relation to science; philosophy occuplies multiple positions in relation to science, owing to the variegated tasks that philosophers pursue. In (...) the final section, we shall see that our catalogue of philosophical tasks provides means for confronting that obstinate question “How is metaphysics possible?”. (shrink)

It was shown recently that epimorphisms need not be surjective in a variety K of Heyting algebras, but only one counter-example was exhibited in the literature until now. Here, a continuum of such examples is identified, viz. the variety generated by the Rieger-Nishimura lattice, and all of its (locally finite) subvarieties that contain the original counter-example K . It is known that, whenever a variety of Heyting algebras has finite depth, then it has surjective epimorphisms. In contrast, we show that (...) for every integer $n \geq 2$ , the variety of all Heyting algebras of width at most n has a non-surjective epimorphism. Within the so-called Kuznetsov-Gerčiu variety (i.e., the variety generated by finite linear sums of one-generated Heyting algebras), we describe exactly the subvarieties that have surjective epimorphisms. This yields new positive examples, and an alternative proof of epimorphism surjectivity for all varieties of Gödel algebras. The results settle natural questions about Beth-style definability for a range of intermediate logics. (shrink)

There are at least three vaguely atomistic principles that have come up in the literature, two explicitly and one implicitly. First, standard atomism is the claim that everything is composed of atoms, and is very often how atomism is characterized in the literature. Second, superatomism is the claim that parthood is well-founded, which implies that every proper parthood chain terminates, and has been discussed as a stronger alternative to standard atomism. Third, there is a principle that lies between these two (...) theses in terms of its relative strength: strong atomism, the claim that every maximal proper parthood chain terminates. Although strong atomism is equivalent to superatomism in classical extensional mereology, it is strictly weaker than it in strictly weaker systems in which parthood is a partial order. And it is strictly stronger than standard atomism in classical extensional mereology and, given the axiom of choice, in such strictly weaker systems as well. Though strong atomism has not, to my knowledge, been explicitly identified, Shiver appears to have it in mind, though it is unclear whether he recognizes that it is not equivalent to standard atomism in each of the mereologies he considers. I prove these logical relationships which hold amongst these three atomistic principles, and argue that, whether one adopts classical extensional mereology or a system strictly weaker than it in which parthood is a partial order, standard atomism is a more defensible addition to one’s mereology than either of the other two principles, and it should be regarded as the best formulation of the atomistic thesis. (shrink)

Once one accepts that certain things metaphysically depend upon, or are metaphysically explained by, other things, it is natural to begin to wonder whether these chains of dependence or explanation must come to an end. This essay surveys the work that has been done on this issue—the issue of grounding and infinite descent. I frame the discussion around two questions: (1) What is infinite descent of ground? and (2) Is infinite descent of ground possible? In addressing the second question, I (...) will consider a number of arguments that have been made for and against the possibility of infinite descent of ground. When relevant, I connect the discussion to two important views about the way reality can be structured by grounding: metaphysical foundationalism and metaphysical infinitism. (shrink)

Introductory-level undergraduate classes in Logic or Critical Thinking are a staple in the portfolio of many Philosophy programs. A standard approach to these classes is to include teaching and learning activities focused on formal deductive and inductive logic, sometimes accompanied by teaching and learning activities focused on informal fallacies or argument construction. In this article, I discuss a proposal to include an additional element within these classes—namely, teaching and learning activities focused on intellectual virtues. After clarifying the proposal, I identify (...) three reasons in favor of implementing it and I discuss how to implement it, focusing on questions about pedagogical strategies and pedagogical resources. (shrink)

Maureen Donnelly’s (2016) relative positionalism correctly handles any fixed arity relation with any symmetry such a relation can have, yielding the intuitively correct way(s) in which that relation can apply. And it supplies an explanation of what is going on in the world that makes this the case. But it has at least one potential shortcoming — one that its opponents are likely to seize upon: it can only handle relations with fixed arities. It is unable to handle relations with (...) variable arities. I argue that, all else being equal, relative positionalism ought nonetheless to be preferred to its closest competitors — at least to the extent that the explanation it supplies of relational application is plausible — even though those competitors can handle variable arity relations in addition to fixed arity relations. (shrink)

We consider the relation between versions of Ramsey’s Theorem and König’s Infinity Lemma, in the absence of the axiom of choice.

Contingency-theorists have gestured to a series of phenomena such as random mutations or rare Armageddon-like events as that which accounts for evolutionary contingency. These phenomena constitute a class, which may be aptly called the ‘sources of contingency’. In this paper, I offer a probabilistic conception of what it is to be a source of contingency and then examine two major candidates: chance variation and genetic drift, both of which have historically been taken to be ‘chancy’ in a number of different (...) senses. However,contrathe gesturing of contingency-theorists, chance variation and genetic drift are not always strong sources of contingency, as they can be non-chancy in at least one sense that opposes evolutionary contingency. The probabilistic conception offered herein allows for sources of contingency to appropriately vary in strength. To this end, I import Shannon’sinformation entropyas a statistical measure for systematically assessing the strength of a source of contingency, which is part and parcel of identifying sources of contingency. In brief, the higher the entropy, the greater the strength. This is also empirically significant because molecular, mutational, and replicative studies often contain sufficient frequency or probability data to allow for entropies to be calculated. In this way, contingency-theorists can evaluate the strength of a source of contingency in real-world cases. Moreover, the probabilistic conception also makes conceptual room for the converse of sources of contingency: ‘sources of directionality’, which ought to be recognised, as they can interact with genuine sources of contingency in undermining evolutionary contingency. (shrink)

Some contemporary philosophers suggest that we know just by introspection that folk psychological states exist. However, such an "armchair refutation" of eliminativism seems too easy. I first attack two strategems, inspired by Descartes, on how such a refutation might proceed. However, I concede that the Cartesian intuition that we have direct knowledge of representational states is very powerful. The rest of this paper then offers an error theory of how that intuition might really be mistaken. The idea is that introspection (...) does not detect any folk psychological states, but rather detects neural states that dispose us to certain sorts of linguistic behavior. Briefly, rather than detecting a mental appearance of the state-of-affairs that I am sitting near the fire, introspection detects a state disposing me to assert "It appears to me that I am sitting by the fire." The nature of this linguistic-dispositional state is then given a connectionist underpinning, where inputs from introspection lead to such assertive behavior. The Cartesian certainty we feel in self-ascribing such appearances is also explained. Even though I do not endorse such an error theory outright, I suggest that its tenability is enough to undercut introspection arguments against eliminativism. (shrink)