The inflation of Type I error rates is thought to be one of the causes of the replication crisis. Questionable research practices such as p-hacking are thought to inflate Type I error rates above their nominal level, leading to unexpectedly high levels of false positives in the literature and, consequently, unexpectedly low replication rates. In this article, I offer an alternative view. I argue that questionable and other research practices do not usually inflate relevant Type I error rates. I begin (...) with an introduction to Type I error rates that distinguishes them from theoretical errors. I then illustrate my argument with respect to model misspecification, multiple testing, selective inference, forking paths, exploratory analyses, p-hacking, optional stopping, double dipping, and HARKing. In each case, I demonstrate that relevant Type I error rates are not usually inflated above their nominal level, and in the rare cases that they are, the inflation is easily identified and resolved. I conclude that the replication crisis may be explained, at least in part, by researchers’ misinterpretation of statistical errors and their underestimation of theoretical errors. (shrink)

Kerr coined the term ‘HARKing’ to refer to the practice of ‘hypothesizing after the results are known’. This questionable research practice has received increased attention in recent years because it is thought to have contributed to low replication rates in science. The present article discusses the concept of HARKing from a philosophical standpoint and then undertakes a critical review of Kerr’s twelve potential costs of HARKing. It is argued that these potential costs are either misconceived, misattributed to HARKing, lacking evidence, (...) or that they do not take into account pre- and post-publication peer review and public availability to research materials and data. It is concluded that it is premature to conclude that HARKing has led to low replication rates. (shrink)

The replication crisis has caused researchers to distinguish between exact replications, which duplicate all aspects of a study that could potentially affect the results, and direct replications, which duplicate only those aspects of the study that are thought to be theoretically essential to reproduce the original effect. The replication crisis has also prompted researchers to think more carefully about the possibility of making Type I errors when rejecting null hypotheses. In this context, the present article considers the utility of two (...) types of Type I error probability: the Neyman–Pearson long run Type I error rate and the Fisherian sample-specific Type I error probability. It is argued that the Neyman–Pearson Type I error rate is inapplicable in social science because it refers to a long run of exact replications, and social science deals with irreversible units that make exact replications impossible. Instead, the Fisherian sample-specific Type I error probability is recommended as a more meaningful way to conceptualize false positive results in social science because it can be applied to each sample-specific decision about rejecting the same substantive null hypothesis in a series of direct replications. It is concluded that the replication crisis may be partly due to researchers’ unrealistic expectations about replicability based on their consideration of the Neyman–Pearson Type I error rate across a long run of exact replications. (shrink)

Scientists often adjust their significance threshold during null hypothesis significance testing in order to take into account multiple testing and multiple comparisons. This alpha adjustment has become particularly relevant in the context of the replication crisis in science. The present article considers the conditions in which this alpha adjustment is appropriate and the conditions in which it is inappropriate. A distinction is drawn between three types of multiple testing: disjunction testing, conjunction testing, and individual testing. It is argued that alpha (...) adjustment is only appropriate in the case of disjunction testing, in which at least one test result must be significant in order to reject the associated joint null hypothesis. Alpha adjustment is inappropriate in the case of conjunction testing, in which all relevant results must be significant in order to reject the joint null hypothesis. Alpha adjustment is also inappropriate in the case of individual testing, in which each individual result must be significant in order to reject each associated individual null hypothesis. The conditions under which each of these three types of multiple testing is warranted are examined. It is concluded that researchers should not automatically assume that alpha adjustment is necessary during multiple testing. Illustrations are provided in relation to joint studywise hypotheses and joint multiway ANOVAwise hypotheses. (shrink)

Several researchers have recently argued that p values lose their meaning in exploratory analyses due to an unknown inflation of the alpha level (e.g., Nosek & Lakens, 2014; Wagenmakers, 2016). For this argument to be tenable, the familywise error rate must be defined in relation to the number of hypotheses that are tested in the same study or article. Under this conceptualization, the familywise error rate is usually unknowable in exploratory analyses because it is usually unclear how many hypotheses have (...) been tested on a spontaneous basis and then omitted from the final research report. In the present article, I argue that it is inappropriate to conceptualize the familywise error rate in relation to the number of hypotheses that are tested. Instead, it is more appropriate to conceptualize familywise error in relation to the number of different tests that are conducted on the same null hypothesis in the same study. Under this conceptualization, alpha level adjustments in exploratory analyses are (a) less necessary and (b) objectively verifiable. As a result, p values do not lose their meaning in exploratory analyses. (shrink)

Fisher criticised the Neyman-Pearson approach to hypothesis testing by arguing that it relies on the assumption of “repeated sampling from the same population.” The present article considers the responses to this criticism provided by Pearson and Neyman. Pearson interpreted alpha levels in relation to imaginary replications of the original test. This interpretation is appropriate when test users are sure that their replications will be equivalent to one another. However, by definition, scientific researchers do not possess sufficient knowledge about the relevant (...) and irrelevant aspects of their tests and populations to be sure that their replications will be equivalent to one another. Pearson also interpreted the alpha level as a personal rule that guides researchers’ behavior during hypothesis testing. However, this interpretation fails to acknowledge that the same researcher may use different alpha levels in different testing situations. Addressing this problem, Neyman proposed that the average alpha level adopted by a particular researcher can be viewed as an indicator of that researcher’s typical Type I error rate. Researchers’ average alpha levels may be informative from a metascientific perspective. However, they are not useful from a scientific perspective. Scientists are more concerned with the error rates of specific tests of specific hypotheses, rather than the error rates of their colleagues. It is concluded that neither Neyman nor Pearson adequately rebutted Fisher’s “repeated sampling” criticism. Fisher’s significance testing approach is briefly considered as an alternative to the Neyman-Pearson approach. (shrink)

We present some techniques in c.c.c. forcing, and apply them to prove consistency results concerning the isomorphism and embeddability relations on the family of ℵ 1 -dense sets of real numbers. In this direction we continue the work of Baumgartner [2] who proved the axiom BA stating that every two ℵ 1 -dense subsets of R are isomorphic, is consistent. We e.g. prove Con). Let K H , be the set of order types of ℵ 1 -dense homogeneous subsets of (...) R with the relation of embeddability. We prove that for every finite model L , : Con iff L is a distributive lattice. We prove that it is consistent that the Magidor-Malitz language is not countably compact. We deal with the consistency of certain topological partition theorems. E.g. We prove that MA is consistent with the axiom OCA which says: “If X is a second countable space of power ℵ 1 , and { U 0 ,\h.;, U n−1 } is a cover of D ▪ X x X -} x,x> ¦ x ϵ X } consisting of symmetric open sets, then X can be partitioned into { X i \brvbar; i ϵ ω } such that for every i ϵ ω there is l such that D ⊇ U l ”. We also prove that MA+OCA [xrArr] 2 ℵ 0 = ℵ 2. (shrink)

Hypothesizing after the results are known, or HARKing, occurs when researchers check their research results and then add or remove hypotheses on the basis of those results without acknowledging this process in their research report (Kerr, 1998). In the present article, I discuss three forms of HARKing: (1) using current results to construct post hoc hypotheses that are then reported as if they were a priori hypotheses; (2) retrieving hypotheses from a post hoc literature search and reporting them as a (...) priori hypotheses; and (3) failing to report a priori hypotheses that are unsupported by the current results. These three types of HARKing are often characterized as being bad for science and a potential cause of the current replication crisis. In the present article, I use insights from the philosophy of science to present a more nuanced view. Specifically, I identify the conditions under which each of these three types of HARKing is most and least likely to be bad for science. I conclude with a brief discussion about the ethics of each type of HARKing. (shrink)

Although death by neurologic criteria is legally recognized throughout the United States, state laws and clinical practice vary concerning three key issues: the medical standards used to determine death by neurologic criteria, management of family objections before determination of death by neurologic criteria, and management of religious objections to declaration of death by neurologic criteria. The American Academy of Neurology and other medical stakeholder organizations involved in the determination of death by neurologic criteria have undertaken concerted action to address variation (...) in clinical practice in order to ensure the integrity of brain death determination. To complement this effort, state policymakers must revise legislation on the use of neurologic criteria to declare death. We review the legal history and current laws regarding neurologic criteria to declare death and offer proposed revisions to the Uniform Determination of Death Act and the rationale for these recommendations. (shrink)

In this article, our aim is to take a step towards a full understanding of the notion of paraconsistency in the context of metainferential logics. Following the work initiated by Barrio et al. [2018], we will consider a metainferential logic to be paraconsistent whenever the metainferential version of Explosion is invalid. However, our contribution consists in modifying the definition of meta-Explosion by extending the standard framework and introducing a negation for inferences and metainferences. From this new perspective, Tarskian paraconsistent logics (...) such as LP will not turn out to be metainferentially paraconsistent, in contrast to, for instance, non-transitive logics like ST. Finally, we will end up by defining a logic which is metainferentially paraconsistent at every level, and discussing whether this logic is uniform through translations. (shrink)

Gelman and Loken (2013, 2014) proposed that when researchers base their statistical analyses on the idiosyncratic characteristics of a specific sample (e.g., a nonlinear transformation of a variable because it is skewed), they open up alternative analysis paths in potential replications of their study that are based on different samples (i.e., no transformation of the variable because it is not skewed). These alternative analysis paths count as additional (multiple) tests and, consequently, they increase the probability of making a Type I (...) error during hypothesis testing. The present article considers this forking paths problem and evaluates four potential solutions that might be used in psychology and other fields: (a) adjusting the prespecified alpha level, (b) preregistration, (c) sensitivity analyses, and (d) abandoning the Neyman-Pearson approach. It is concluded that although preregistration and sensitivity analyses are effective solutions to p-hacking, they are ineffective against result-neutral forking paths, such as those caused by transforming data. Conversely, although adjusting the alpha level cannot address p-hacking, it can be effective for result-neutral forking paths. Finally, abandoning the Neyman-Pearson approach represents a further solution to the forking paths problem. (shrink)

Preregistration has been proposed as a useful method for making a publicly verifiable distinction between confirmatory hypothesis tests, which involve planned tests of ante hoc hypotheses, and exploratory hypothesis tests, which involve unplanned tests of post hoc hypotheses. This distinction is thought to be important because it has been proposed that confirmatory hypothesis tests provide more compelling results (less uncertain, less tentative, less open to bias) than exploratory hypothesis tests. In this article, we challenge this proposition and argue that there (...) are several advantages of exploratory hypothesis tests that can make their results more compelling than those of confirmatory hypothesis tests. We also consider some potential disadvantages of exploratory hypothesis tests and conclude that their advantages can outweigh the disadvantages. We conclude that exploratory hypothesis tests avoid researcher commitment and researcher prophecy biases, reduce the probability of data fraud, are more appropriate in the context of unplanned deviations, facilitate inference to the best explanation, and allow peer reviewers to make additional contributions at the data analysis stage. In contrast, confirmatory hypothesis tests may lead to an inappropriate level of confidence in research conclusions, less appropriate analyses in the context of unplanned deviations, and greater bias and errors in theoretical inferences. (shrink)

During multiple testing, researchers often adjust their alpha level to control the familywise error rate for a statistical inference about a joint union alternative hypothesis (e.g., “H1,1 or H1,2”). However, in some cases, they do not make this inference. Instead, they make separate inferences about each of the individual hypotheses that comprise the joint hypothesis (e.g., H1,1 and H1,2). For example, a researcher might use a Bonferroni correction to adjust their alpha level from the conventional level of 0.050 to 0.025 (...) when testing H1,1 and H1,2, find a significant result for H1,1 (p < 0.025) and not for H1,2 (p > .0.025), and so claim support for H1,1 and not for H1,2. However, these separate individual inferences do not require an alpha adjustment. Only a statistical inference about the union alternative hypothesis “H1,1 or H1,2” requires an alpha adjustment because it is based on “at least one” significant result among the two tests, and so it refers to the familywise error rate. Hence, an inconsistent correction occurs when a researcher corrects their alpha level during multiple testing but does not make an inference about a union alternative hypothesis. In the present article, I discuss this inconsistent correction problem, including its reduction in statistical power for tests of individual hypotheses and its potential causes vis-à-vis error rate confusions and the alpha adjustment ritual. I also provide three illustrations of inconsistent corrections from recent psychology studies. I conclude that inconsistent corrections represent a symptom of statisticism, and I call for a more nuanced inference-based approach to multiple testing corrections. (shrink)

A number of philosophers defend naturalistic moral realism by appeal to an externalist semantics for moral predicates. The application of semantic externalism to moral predicates has been attacked by Terence Horgan and Mark Timmons in a series of papers that make use of their “ Moral Twin Earth ” thought experiment. In response, several defenders of naturalistic moral realism have claimed that the Moral Twin Earth thought experiment is misleading and yields distorted and inaccurate semantic intuitions. If they are right, (...) the intuitions generated by Moral Twin Earth cannot be appealed to in arguments against externalist moral semantics. The most developed case against the Moral Twin Earth argument that follows this strategy is found in a paper by Stephen Laurence, Eric Margolis and Angus Dawson. Here I argue that their attack on the Moral Twin Earth thought experiment fails. Laurence, Margolis and Dawson have not shown that we have reason to distrust the semantic intuitions it generates. (shrink)

Popper’s (1983, 2002) philosophy of science has enjoyed something of a renaissance in the wake of the replication crisis, offering a philosophical basis for the ensuing science reform movement. However, adherence to Popper’s approach may also be at least partly responsible for the sense of “crisis” that has developed following multiple unexpected replication failures. In this article, I contrast Popper’s approach with Lakatos’ (1978) approach and a related approach called naïve methodological falsificationism (NMF; Lakatos, 1978). The Popperian approach is powerful (...) because it is based on logical refutation, but its theories are noncausal and, therefore, lacking in scientific value. In contrast, the Lakatosian approach considers causal theories, but it concedes that these theories are not logically refutable. Finally, the NMF approach subjects Lakatosian causal theories to Popperian logical refutations. However, its approach of temporarily accepting a ceteris paribus clause during theory testing may be viewed as scientifically inappropriate, epistemically inconsistent, and “completely redundant” (Lakatos, 1978, p. 40). I conclude that the replication “crisis” makes the most sense in the context of the Popperian and NMF approaches because it is only in these two approaches that replication failures represent logical refutations of theories. In contrast, replication failures are less problematic in the Lakatosian approach because they do not logically refute theories. Indeed, in the Lakatosian approach, replication failures can be legitimately ignored or used to motivate theory development. (shrink)

Metascientists have studied questionable research practices in science. The present article considers the parallel concept of questionable metascience practices (QMPs). A QMP is a research practice, assumption, or perspective that has been questioned by several commentators as being potentially problematic for metascience and/or the science reform movement. The present article reviews ten QMPs that relate to criticism, replication, bias, generalization, and the characterization of science. Specifically, the following QMPs are considered: (1) rejecting or ignoring self-criticism; (2) a fast ‘n’ bropen (...) scientific criticism style; (3) overplaying the role of replication in science; (4) assuming a replication rate is “too low” without specifying an “acceptable” rate; (5) an unacknowledged metabias towards explaining the replication crisis in terms of researcher bias; (6) assuming that researcher bias can be reduced; (7) devaluing exploratory results as being more “tentative” than confirmatory results; (8) presuming that questionable research practices are problematic research practices; (9) focusing on knowledge accumulation; and (10) focusing on specific scientific methods. It is stressed that only some metascientists engage in some QMPs some of the time, and that these QMPs may not always be problematic. Research is required to estimate the prevalence and impact of QMPs. In the meantime, QMPs should be viewed as invitations to ask questions about how we go about doing better metascience. (shrink)

Environmental ethicists have been arguing for decades that swift action to protect our natural environment is morally paramount, and that our concern for the environment should go beyond its importance for human welfare. It might be thought that the widespread acceptance of moral anti-realism would undermine the aims of environmental ethicists. One reason is that recent empirical studies purport to show that moral realists are more likely to act on the basis of their ethical convictions than anti-realists. In addition, it (...) is sometimes argued that only moral realists can countenance the claim that nature is intrinsically valuable. Against this, we argue that the acceptance of moral anti-realism is no threat to the environmentalist cause. We argue, further, that the acceptance of moral realism is potentially an obstacle to delivering on a third core environmental ethicist demand: namely, that successful action on climate change and environmental destruction requires us to change some of our commonly-held ethical views and to achieve a workable consensus. (shrink)

Recently it has been shown that transformations of Heisenberg-picture operators are the causal mechanism which allows Bell-theorem-violating correlations at a distance to coexist with locality in the Everett interpretation of quantum mechanics. A calculation to first order in perturbation theory of the generation of EPRB entanglement in nonrelativistic fermionic field theory in the Heisenberg picture illustrates that the same mechanism leads to correlations without nonlocality in quantum field theory as well. An explicit transformation is given to a representation in which (...) initial-condition information is transferred from the state vector to the field operators, making the locality of the theory manifest. (shrink)

THEOREM 1. (⋄ ℵ 1 ) If B is an infinite Boolean algebra (BA), then there is B 1 such that $|\operatorname{Aut} (B_1)| \leq B_1| = \aleph_1$ and $\langle B_1, \operatorname{Aut} (B_1)\rangle \equiv \langle B, \operatorname{Aut}(B)\rangle$ . THEOREM 2. (⋄ ℵ 1 ) There is a countably compact logic stronger than first-order logic even on finite models. This partially answers a question of H. Friedman. These theorems appear in §§ 1 and 2. THEOREM 3. (a) (⋄ ℵ 1 ) If (...) B is an atomic ℵ 1 -saturated infinite BA, ψ ε L ω 1ω and $\langle B, \operatorname{Aut} (B)\rangle \models\psi$ then there is B 1 such that $|\operatorname{Aut}(B_1)| \leq |B_1| = \aleph_1$ and $\langle B_1, \operatorname{Aut}(B_1)\rangle\models\psi$ . In particular if B is 1-homogeneous so is B 1 . (b) (a) holds for B = P(ω) even if we assume only CH. (shrink)

We prove that the logics of Magidor-Malitz and their generalization by Rubin are distinct even for PC classes. Let $M \models Q^nx_1 \cdots x_n \varphi(x_1 \cdots x_n)$ mean that there is an uncountable subset A of |M| such that for every $a_1, \ldots, a_n \in A, M \models \varphi\lbrack a_1, \ldots, a_n\rbrack$ . Theorem 1.1 (Shelah) $(\diamond_{\aleph_1})$ . For every n ∈ ω the class $K_{n + 1} = \{\langle A, R\rangle \mid \langle A, R\rangle \models \neg Q^{n + 1} (...) x_1 \cdots x_{n + 1} R(x_1, \ldots, x_{n + 1})\}$ is not an ℵ 0 -PC-class in the logic L n , obtained by closing first order logic under Q 1 , ..., Q n . I.e. for no countable L n -theory T, is K n + 1 the class of reducts of the models of T. Theorem 1.2 (Rubin) $(\diamond_{\aleph_1}).^3$ . Let $M \models Q^E x y\varphi(x, y)$ mean that there is $A \subseteq |M|$ such that $E_{A, \varphi} = \{\langle a, b \rangle \mid a, b \in A$ and $M \models \varphi\lbrack a, b\rbrack\}$ is an equivalence relation on A with uncountably many equivalence classes, and such that each equivalence class is uncountable. Let $K^E = \{\langle A, R\rangle\mid \langle A, R\rangle\models \neg Q^Exy R(x, y)\}$ . Then K E is not an ℵ 0 -PC-class in the logic gotten by closing first order logic under the set of quantifiers {Q n ∣ n ∈ ω} which were defined in Theorem 1.1. (shrink)

A metainference is usually understood as a pair consisting of a collection of inferences, called premises, and a single inference, called conclusion. In the last few years, much attention has been paid to the study of metainferences—and, in particular, to the question of what are the valid metainferences of a given logic. So far, however, this study has been done in quite a poor language. Our usual sequent calculi have no way to represent, e.g. negations, disjunctions or conjunctions of inferences. (...) In this paper we tackle this expressive issue. We assume some background sentential language as given and define what we call an inferential language, that is, a language whose atomic formulas are inferences. We provide a model-theoretic characterization of validity for this language—relative to some given characterization of validity for the background sentential language—and provide a proof-theoretic analysis of validity. We argue that our novel language has fruitful philosophical applications. Lastly, we generalize some of our definitions and results to arbitrary metainferential levels. (shrink)

According to Michael Devitt, the primary work of a rigidity distinction for kind terms is to distinguish non-descriptional predicates from descriptional predicates. The standard conception of rigidity fails to do this work when it is extended to kind terms. Against the standard conception, Devitt defends rigid application: a predicate is a rigid applier iff, if it applies to an object in one world, it applies to that object in every world in which it exists. Devitt maintains that rigid application does (...) the job of identifying nondescriptional predicates perfectly. I argue that Devitt is wrong about this. When we examine more closely alternative theories about the identity and persistence conditions of those entities to which mass terms apply, we find no plausible theory that has the result that a term is rigid iff it is non-descriptional. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:An Exposition of The Divine Names, The Book of Blessed Dionysius by Thomas AquinasMichael J. Rubin, Elizabeth C. Shaw, and Staff*AQUINAS, Thomas. An Exposition of The Divine Names, The Book of Blessed Dionysius. Translated and edited with an introduction by Michael A. Augros. Merrimack, N.H.: Thomas More College Press, 2021. xxv + 549 pp. Cloth, $65.00The profound influence that Pseudo-Dionysius had on Aquinas’s thought, especially in his metaphysics (...) of participation and his apophatic theology, has been known for some time now, thanks to the excellent work of such scholars as Fran O’Rourke. One would therefore think that Aquinas’s Exposition of the Divine Names (his only commentary on the works of Pseudo-Dionysius) would have been translated a lot sooner. This delay is assuredly due not just to the difficulty of translating this work but also to a certain embarrassment felt by Thomists over Aquinas’s sincere belief that the “Dionysius” who wrote the Divine Names was the Areopagite whose conversion at the teaching of St. Paul is mentioned in the Acts of the Apostles. That the author calling himself “Dionysius” was in fact a theologian writing in the fifth or sixth centuries has been well established by modern scholarship. Hence, Thomists may have felt tempted to discount or at least pass over the influence of this author on Aquinas since it is discomfiting to think that the Church’s greatest theologian accorded such authority to an imposter.Michael Augros tackles these concerns head-on in the excellent introduction to his new translation of the Divine Names commentary. First, Augros points out that in past centuries a pseudonym was usually not an act of forgery but, rather, a way of concealing the author’s identity, which an early Christian theologian might well decide to do either out of humility or out of a desire “to avoid provoking certain prejudices” in those who disagreed with him in contemporary theological disputes. Moreover, it is likely that the work was never intended for the general public (who could easily mistake the pseudonym as genuine) but, rather, was written for those “already initiated in a particular Neoplatonic school of Christian theology,” who would recognize the author as being “one of their own” but without knowing his precise identity. Finally, in taking the particular name of “Dionysius,” the author of the Divine Names was indicating his intention for the work: Just as the biblical Dionysius was a Greek philosopher who converted to Christianity, so the works of Pseudo-Dionysius [End Page 345] are an attempt to reconcile Greek philosophy with the Christian faith.It therefore seems likely, as Augros observes, that Aquinas would still have accorded a great deal of respect to the Divine Names even if he had learned the truth of the author’s identity. The work would not have had the same deuterocanonical authority for him that comes with being written by a direct disciple of St. Paul himself, but “the inherent cogency, coherence, and beauty” of Pseudo-Dionysius’s theology would have been the same. Hence, Pseudo-Dionysius would surely have earned from Aquinas the “docile attitude” appropriate “for a philosopher and theologian of the first order, such as Boethius.”That Aquinas was right to see the author of the Divine Names as a master philosopher and theologian becomes evident when one dives into the text itself, in which Aquinas sees a truly dazzling order, both externally and internally. According to Aquinas, the Divine Names discusses those truths about God of which there are intelligible likenesses in creatures, such as goodness or wisdom, whereas the truths about God of which there are sensible likenesses (for example, “when God is called a lion, or a rock”) are treated by Pseudo-Dionysius in The Symbolic Theology; meanwhile, in the lost or fictional work The Divine Characteristics, Dionysius claims to have treated those truths about God (such as the Trinity) that cannot be known through any likenesses in creatures.Aquinas finds a still more intricate order within the Divine Names itself. Since this work is dedicated to “the divine names by which the processions of God to creatures are manifested,” the plan of the work... (shrink)

We present some techniques in c.c.c. forcing, and apply them to prove consistency results concerning the isomorphism and embeddability relations on the family of ℵ 1 -dense sets of real numbers. In this direction we continue the work of Baumgartner [2] who proved the axiom BA stating that every two ℵ 1 -dense subsets of R are isomorphic, is consistent. We e.g. prove Con). Let K H, be the set of order types of ℵ 1 -dense homogeneous subsets of R (...) with the relation of embeddability. We prove that for every finite model L, : Con iff L is a distributive lattice. We prove that it is consistent that the Magidor-Malitz language is not countably compact. We deal with the consistency of certain topological partition theorems. E.g. We prove that MA is consistent with the axiom OCA which says: “If X is a second countable space of power ℵ 1, and { U 0,\h.;, U n−1 } is a cover of D ▪ X x X -} x,x> ¦ x ϵ X } consisting of symmetric open sets, then X can be partitioned into { X i \brvbar; i ϵ ω } such that for every i ϵ ω there is l such that D ⊇ U l ”. We also prove that MA+OCA [xrArr] 2 ℵ 0 = ℵ 2. (shrink)

In this article, we defend that incorporating a rejection operator into a paraconsistent language involves fully specifying its inferential characteristics within the logic. To do this, we examine a recent proposal by Berto for a paraconsistent rejection, which — according to him — avoids paradox, even when introduced into a language that contains self-reference and a transparent truth predicate. We will show that this proposal is inadequate because it is too incomplete. We argue that the reason it avoids trouble is (...) that the inferential characteristics of the new operator are left unspecified, exporting the task of specifying them to metaphysicians. Additionally, we show that when completing this proposal with some plausible rules for the rejection operator, paradoxes do arise. Finally, we draw some more general implications from the study of this example. (shrink)

A key objection to naturalistic versions of moral realism is that the (meta)semantics to which they are committed yields incorrect semantic verdicts about so-called Moral Twin Earth cases. Recently, it has been proposed that the Moral Twin Earth challenge can be answered by adopting a neo-Aristotelian semantics for moral expressions. In this paper, I argue that this proposal fails. First, however attractive the central claims of neo-Aristotelianism are, they do not for us have the status of analytic constraints on the (...) use of ethical expressions, as they must if they are to block Moral Twin Earth counterexamples. Second, even when the neo-Aristotelian’s claims are taken as non-negotiable analytic constraints, the semantics faces a dilemma: if characteristic human functioning is understood in an ethically neutral way, the semantics yields an incorrect intension for ‘good human.’ If human functioning is understood in an ethically partisan way, the semantics fails to avoid problematic Moral Twin Earth counterexamples. (shrink)

The existence of probability in the sense of the frequency interpretation, i.e., probability as “long term relative frequency,” is shown to follow from the dynamics and the interpretational rules of Everett quantum mechanics in the Heisenberg picture. This proof is free of the difficulties encountered in applying to the Everett interpretation previous results regarding relative frequency and probability in quantum mechanics. The ontology of the Everett interpretation in the Heisenberg picture is also discussed.

It has seemed, to many, that there is an important connection between the ways in which some theoretical posits explain our observations, and our reasons for being ontologically committed to those posits. One way to spell out this connection is in terms of what has become known as the explanatory criterion of ontological commitment. This is, roughly, the view that we ought to posit only those entities that are indispensable to our best explanations. Our primary aim is to argue that (...) the moral nonnaturalist places herself in an invidious position if she simply accepts that the nonnatural moral facts that she posits are not explanatory. Instead, we offer the nonnaturalist an alternative strategy for dealing with moral explanations. The strategy is to retain the explanatory criterion of ontological commitment and maintain that moral properties are, in fact, explanatory. The explanations they provide are not causal explanations; instead, moral properties make a non-causal difference to the physical facts. (shrink)

In order to defend the Cornell variety of naturalistic moral realism from Horgan and Timmons’ Moral Twin Earth objection, several philosophers have proposed what I call Normatively Enriched Moral Meta-Semantics. According to NEMMS, the natural properties that serve as the contents of moral predicates are fixed by non- moral normative facts. In this paper, I elucidate two versions of NEMMS: one proposed by David Brink, and the other proposed by Mark van Roojen. I show what these meta-semantics have in common, (...) and how each one promises the Cornell realist a response to the Moral Twin Earth objection. I then argue that Cornell realists ought to be wary of adopting NEMMS. A naturalist realist who adopts this meta-semantics confronts a trilemma. The proponent of NEMMS owes a meta-ethical account of the relevant content-fixing normative facts. Such facts are either reducible to recognizably natural facts or they are not. If they are not reducible, then NEMMS entails the denial of ethical naturalism. If such facts are taken to be reducible to facts about agents’ actual or hypothetical attitudes, then the account renders moral facts stance-dependent. Consequently, moral realism is false. Alternatively, one might propose that the content-fixing normative facts are reducible to attitude-independent natural facts. However, such a proposal is refuted by its own Twin Earth objection. (shrink)

Stapp claims that, when spatial degrees of freedom are taken into account, Everett quantum mechanics is ambiguous due to a “core basis problem.” To examine an aspect of this claim I generalize the ideal measurement model to include translational degrees of freedom for both the measured system and the measuring apparatus. Analysis of this generalized model using the Everett interpretation in the Heisenberg picture shows that it makes unambiguous predictions for the possible results of measurements and their respective probabilities. The (...) presence of translational degrees of freedom for the measuring apparatus affects the probabilities of measurement outcomes in the same way that a mixed state for the measured system would. Examination of a measurement scenario involving several observers illustrates the consistency of the model with perceived spatial localization of the measuring apparatus. (shrink)

In this article, we explore the semantic characterization of the (right) pure refined variable inclusion companion of all logics, which is a further refinement of the nowadays well-studied pure right variable inclusion logics. In particular, we will focus on giving a characterization of these fragments via a single logical matrix, when possible, and via a class of finite matrices, otherwise. In order to achieve this, we will rely on extending the semantics of the logics whose companions we will be discussing (...) with infectious values in direct and in more subtle ways. This further establishes the connection between infectious logics and variable inclusion logics. (shrink)

A Boolean algebra B that has a well-founded sublattice L which generates B is called a well-generated Boolean algebra. If in addition, L is generated by a complete set of representatives for B , then B is said to be canonically well-generated .Every WG Boolean algebra is superatomic. We construct two basic examples of superatomic non well-generated Boolean algebras. Their cardinal sequences are 1,0,1,1 and 0,0,20,1.Assuming MA , we show that every algebra with one of the cardinal sequences , α<1, (...) λ<20, or 0,20,1,1 is CWG.Assuming CH, or alternatively assuming MA , we determine which cardinal sequences admit only WG Boolean algebras.We find a necessary and sufficient condition for the canonical well-generatedness of algebras whose cardinal sequence has the form , α<1. We conclude that if such an algebra is CWG, then all of its quotients are CWG. We show that the above is not true for general Boolean algebras. We also conclude that if the cardinality of such an algebra is less than the cardinal defined below, then it is CWG. The cardinal is the least cardinality of an unbounded subset of {f f : ω → ω}.We investigate questions concerning embeddability, quotients and subalgebras of WG and CWG Boolean algebras, and construct various counter-examples. (shrink)

Terence Horgan and Mark Timmons? Moral Twin Earth thought experiment shows that realist ethical naturalism entails a kind of conceptual relativism about moral predicates. This conceptual relativism implies, further, that Earthlings and Twin Earthlings do not express substantive disagreement with one another. Because this latter implication clashes with considered linguistic intuitions, Horgan and Timmons conclude that we should reject realist ethical naturalism. Against this, several critics recommend that realists ?bite the bullet? with respect to Moral Twin Earth: despite our intuitions, (...) we should accept that the speakers do not disagree. These critics argue that the intuitions elicited by the thought experiment are either the result of a failure on the part of readers to appreciate hidden details of the Moral Twin Earth case, or else they are mere artifacts of readers? epistemic limitations. In this paper, I show that the Moral Twin Earth argument prevails against this line of attack. (shrink)

Terence Horgan and Mark Timmons's Moral Twin Earth thought experiment poses a serious challenge for an influential kind of moral realism. It presents us with a case in which it is intuitive that two speakers are expressing a substantive disagreement with one another. However, the meta-semantics associated with this relevant form of moral realism entails that the speakers' moral predicates express different semantic contents, and thus, the moral sentences they utter do not express conflicting propositions. Consequently, this variety of moral (...) realism implies, wrongly, that the speakers do not express substantive disagreement after all. Some philosophers have objected to the Moral Twin Earth argument on the grounds that is possible for two speakers to express disagreement with one another, even if the moral sentences they utter do not express conflicting propositions. Heimer Geirsson supports this claim by appeal to the distinction between semantic reference and speaker reference. David Merli supports the same claim by noting that speakers whose moral sentences do not express conflicting propositions may nevertheless express a non-moral, practical disagreement over what to do. In this article, I argue that neither Geirsson nor Merli provides moral realists with a satisfying response to the Moral Twin Earth argument. (shrink)

Thomas Aquinas consistently maintains that there are two kinds of beauty: bodily or sensible beauty and spiritual or intelligible beauty. Due to the lively debate over whether intelligible beauty is a transcendental for Thomas, discussions of his aesthetics have tended either to ignore his views on sensible beauty or to mention them only in passing. The present paper will therefore give a brief overview of Thomas’s thought on bodily beauty. The first section will discuss the objective aspects of sensible beauty (...) for Thomas, i.e., its definition and three conditions, while the second will present his views on its subjective aspects, i.e., how we experience it, why it pleases us, and its importance for human flourishing. The third and final section will examine how Thomas’s account of sensible beauty affects his views on the beauty of the glorified human body and of the universe as a whole after the Last Judgment. (shrink)

For a complete theory of Boolean algebras T, let MT denote the class of countable models of T. For B1, B2 ∈ MT, let B1 ≤ B2 mean that B1 is elementarily embeddable in B2. Theorem 1. For every complete theory of Boolean algebras T, if T ≠ Tω, then $\langle M_T, \leq\rangle$ is well-quasi-ordered. ■ We define Tω. For a Boolean algebra B, let I(B) be the ideal of all elements of the form a + s such that $B\upharpoonright (...) a$ is an atomic Boolean algebra and $B\upharpoonright s$ is an atomless Boolean algebra. The Tarski derivative of B is defined as follows: B(0) = B and B(n + 1) = B(n)/I(B(n)). Define Tω to be the theory of all Boolean algebras such that for every n ∈ ω, B(n) ≠ {0}. By Tarski [1949], Tω is complete. Recall that $\langle A, \leq\rangle$ is a partial well-quasi-ordering, if it is a partial quasi-ordering and for every $\{a_i\mid i \in \omega\} \subseteq A$ , there are $i < j < \omega$ such that ai ≤ aj. Theorem 2. $\langle M_{T_\omega}, \leq\rangle$ contains a subset M such that the partial orderings $\langle M, \leq \upharpoonright M \rangle$ and $\langle\mathscr{P}(\omega), \subseteq\rangle$ are isomorphic. ■ Let M'0 denote the class of all countable Boolean algebras. For B1, B2 ∈ M'0, let B1 ≤' B2 mean that B1 is embeddable in B2. Remark. $\langle M'_0, \leq'\rangle$ is well-quasi-ordered. ■ This follows from Laver's theorem [1971] that the class of countable linear orderings with the embeddability relation is well-quasi-ordered and the fact that every countable Boolean algebra is isomorphic to a Boolean algebra of a linear ordering. (shrink)

Let B be a superatomic Boolean algebra (BA). The rank of B (rk(B)), is defined to be the Cantor Bendixon rank of the Stone space of B. If a ∈ B - {0}, then the rank of a in B (rk(a)), is defined to be the rank of the Boolean algebra $B b \upharpoonright a \overset{\mathrm{def}}{=} \{b \in B: b \leq a\}$ . The rank of 0 B is defined to be -1. An element a ∈ B - {0} is (...) a generalized atom $(a \in \widehat{At}(B))$ , if the last nonzero cardinal in the cardinal sequence of B $\upharpoonright$ a is 1. Let a,b $\in\widehat{At}$ (B). We denote a ∼ b, if rk(a) = rk(b) = rk(a · b). A subset H $\subseteq \widehat{At}$ (B) is a complete set of representatives (CSR) for B, if for every a $\in \widehat{At}$ (B) there is a unique h ∈ H such that h ∼ a. Any CSR for B generates B. We say that B is canonically well-generated (CWG), if it has a CSR H such that the sublattice of B generated by H is well-founded. We say that B is well-generated, if it has a well-founded sublattice L such that L generates B. THEOREM 1. Let B be a Boolean algebra with cardinal sequence $\langle\aleph_0: i . If B is CWG, then every subalgebra of B is CWG. A superatomic Boolean algebra B is essentially low (ESL), if it has a countable ideal I such that rk(B/I) ≤ 1. Theorem 1 follows from Theorem 2.9, which is the main result of this work. For an ESL BA B we define a set F B of partial functions from a certain countably infinite set to ω (Definition 2.8). Theorem 2.9 says that if B is an ESL Boolean algebra, then the following are equivalent. (1) Every subalgebra of B is CWG; and (2) F B is bounded. THEOREM 2. If an ESL Boolean algebra is not CWG, then it has a subalgebra which is not well-generated. (shrink)

We prove that the poset algebra of every scattered poset with finite width is embeddable in the poset algebra of a well ordered poset.

Since its founding in 1943, Medievalia et Humanistica has won worldwide recognition as the first scholarly publication in America to devote itself entirely to medieval and Renaissance studies. Since 1970, a new series, sponsored by the Modern Language Association of America and edited by an international board of distinguished scholars and critics, has published interdisciplinary articles. In yearly hardbound volumes, the new series publishes significant scholarship, criticism, and reviews treating all facets of medieval and Renaissance culture: history, art, literature, music, (...) science, law, economics, and philosophy. (shrink)

As out-of-hospital emergencies become more commonplace, so does the call for a “doctor in the house”. New York City paediatrician Mitchell Rubin has responded to numerous such crises over the past 25 years. He explores reactions on all sides of this peculiar physician–victim relationship, his growing concerns and fears, and possible reasons why many doctors hesitate to act. His thoughts and experiences instigate the discussion about the need for a universal system of Good Samaritan physician respondersWhile flying to Italy last (...) spring, the pilot’s voice came over the loudspeaker: “Is there a doctor on board”? How many times have I heard this request in the last 25 years? A passenger had fainted. As I began caring for her, the pilot asked me, “Should we take the plane down?”. Surprised to be given this responsibility, I took my best guess and answered “no”. After a stressful landing, while I gave oxygen to the prostrate woman, we were met by an ambulance on the tarmac. The woman was appreciative and gracious, the pilot scarcely offered thanks, and I began my vacation exhausted.Having been trained as a paediatrician, I have responded to nearly two dozen “Good Samaritan” scenarios, where a person was injured or became critically sick in a public setting. Perhaps I have had more than my fair share, but I wonder if this is an important and mounting phenomenon. With America growing older and more and more people with serious, chronic illnesses remaining active in the community, we should not be surprised to see increasing numbers of out-of-hospital emergencies. And, as this becomes more commonplace, I become less and less certain of the role I—and other physicians like me—should have.When I was young, cocky and fearless, the call to meet an emergency was exciting. Shortly after training, an …. (shrink)

Why do voters seek to change the political landscape or to retain it? System justification theory proposes that a separate system motive to preserve the existing order drives support for the status-quo, and that this motivation operates independently from personal and collective interests. But how does this explanation apply to recent populist shifts in the political order such as Brexit and the emergence of Donald Trump? While the system motive may seem useful in understanding why the usual progressives may want (...) to stick with an established order, it seems insufficient to explain why the more conservative voters would want to upend the establishment. Thus, we compared SJT’s system motive explanation for the system attitudes of voters on both sides of the political divide to an alternative explanation drawn from the newer social identity model of system attitudes. According to SIMSA, the difficulty in explaining the system attitudes of Brexit/Trump and Remain/Clinton voters from SJT’s system motive standpoint can be resolved by focusing instead on the collective interests that both camps seek to satisfy with their votes. We examined these explanations in two studies conducted soon after Brexit and Trump’s election in 2016, with results providing more support for SIMSA than for SJT. (shrink)

This research draws from three distinct lines of research on the link between emotions and intergroup bias as springboard to integrative, new hypotheses. Past research suggests that emotions extrinsic to the outgroup (or “incidental”), and intrinsic to the outgroup (or “integral”), produce valence-congruent effects on intergroup bias when relevant or “applicable” to the outgroup (e.g., incidental/integral anger and ethnic outgroups). These emotions produce valenceincongruent effects when irrelevant or “non-applicable” to the outgroup (e.g., incidental/integral sadness and happiness, and ethnic outgroups). Internally (...) valid and ecologically sound tests of these contrasting effects are missing; hence we examined them experimentally in meaningful settings of interethnic contact. To this end, we hybridized established research paradigms in mood and intergroup contact research; this approach enabled us to use same materials and induction methods to instigate incidental and integral emotions in a single research design. In Experiment 1, White Australian students (N= 93) inin vivoreal face-to-face contact with an ethnic tutor in their classroom displayed less interethnic bias when incidentally sad (vs. happy) or integrally happy (vs. sad). In Experiment 2, White American males' (N= 492) anti-Arab bias displayed divergent effects under incidental vs. integral (non-applicable) sadness/happiness and similar effects under incidental vs. integral (applicable) anger. The role of perceptions of agency in the emotion-inducing situation is also explored, tested, and explained drawing from mainstream emotion theory. As expected, integral and incidentalapplicableemotions caused valence congruent effects, at the opposite sides of the subjective agency spectrum, by encouraging the generalization of dislike from the outgroup contact partner to the outgroup as a whole. On the other hand, incidental-non-applicable emotions caused valence-incongruent effects on bias, under high agency conditions, by encouraging (non-partner-centered) heuristic processing. Because of the improved methodology, these effects can be regarded as genuine and not the byproduct of methodological artifacts. This theory-driven and empirically sound analysis of the interplay between emotion source, emotion applicability and subjective agency in intergroup contact can increase the precision of emotion-based bias reduction strategies by deepening understanding of the emotion conditions that lead to intergroup bias attenuation vs. exacerbation. (shrink)

Assuming GCH, we prove that for every successor cardinal μ > ω1, there is a superatomic Boolean algebra B such that |B| = 2μ and |Aut B| = μ. Under ◊ω1, the same holds for μ = ω1. This answers Monk's Question 80 in [Mo].

The aim of this paper is to provide a philosophical interpretation of bilateralism in terms of probabilism. In particular, to interpret the main concepts of bilateralism –acceptance, rejection and incoherence– in terms of the probabilistic notions of degree of belief and coherence. According to bilateralism, the meaning of logical connectives is determined by the acceptance and rejection conditions of the sentences in which they are involved, where acceptance and rejection cannot be reduced to one another. I will focus on a (...) variant of bilateralism that understands logical consequence as the statement that it is incoherent to accept all the premises of a valid argument while rejecting all its conclusions. On the other hand, probabilism states that it is possible to interpret our degrees of belief in terms of probabilities. The aim of this work is then to interpret the concept of incoherence in terms of probability functions and determine when it is coherent to accept or to reject a proposition according to some threshold defined in terms of degrees of belief. To achieve this goal, we need both an interpretation of the concept of incoherence coined by the bilateralists as well as an interpretation of acceptance and rejection. I will show that a good interpretation of coherence in probabilistic terms can already be found in the literature. Then, I will give an interpretation of acceptance and rejection in terms of degrees of belief. In particular, I will show that it is possible to interpret these concepts in accordance with Locke’s thesis, the thesis that states that there is some threshold r such that if you believe some sentence in degree equal or higher than r you should accept it, without falling into epistemic paradoxes. (shrink)