A U-shaped curve in a cognitive-developmental trajectory refers to a three-step process: good performance followed by bad performance followed by good performance once again. U-shaped curves have been observed in a wide variety of cognitive-developmental and learning contexts. U-shaped learning seems to contradict the idea that learning is a monotonic, cumulative process and thus constitutes a challenge for competing theories of cognitive development and learning. U-shaped behavior in language learning (in particular in learning English past tense) has become a central (...) topic in the Cognitive Science debate about learning models. Antagonist models (e.g., connectionism versus nativism) are often judged on their ability of modeling or accounting for U-shaped behavior. The prior literature is mostly occupied with explaining how U-shaped behavior occurs. Instead, we are interested in the necessity of this kind of apparently inefficient strategy. We present and discuss a body of results in the abstract mathematical setting of (extensions of) Gold-style computational learning theory addressing a mathematically precise version of the following question: Are there learning tasks that require U-shaped behavior? All notions considered are learning in the limit from positive data. We present results about the necessity of U-shaped learning in classical models of learning as well as in models with bounds on the memory of the learner. The pattern emerges that, for parameterized, cognitively relevant learning criteria, beyond very few initial parameter values, U-shapes are necessary for full learning power! We discuss the possible relevance of the above results for the Cognitive Science debate about learning models as well as directions for future research. (shrink)

When the Canonical Ramsey’s Theorem by Erdős and Rado is applied to regressive functions, one obtains the Regressive Ramsey’s Theorem by Kanamori and McAloon. Taylor proved a “canonical” version of Hindman’s Theorem, analogous to the Canonical Ramsey’s Theorem. We introduce the restriction of Taylor’s Canonical Hindman’s Theorem to a subclass of the regressive functions, the $$\lambda $$ λ -regressive functions, relative to an adequate version of min-homogeneity and prove some results about the Reverse Mathematics of this Regressive Hindman’s Theorem and (...) of natural restrictions of it. In particular we prove that the first non-trivial restriction of the principle is equivalent to Arithmetical Comprehension. We furthermore prove that the well-ordering-preservation principle for base-$$\omega $$ ω exponentiation is reducible to this same principle by a uniform computable reduction. (shrink)

Hirst investigated a natural restriction of Hindman’s Finite Sums Theorem—called Hilbert’s Theorem—and proved it equivalent over \ to the Infinite Pigeonhole Principle for all colors. This gave the first example of a natural restriction of Hindman’s Theorem provably much weaker than Hindman’s Theorem itself. We here introduce another natural restriction of Hindman’s Theorem—which we name the Adjacent Hindman’s Theorem with apartness—and prove it to be provable from Ramsey’s Theorem for pairs and strictly stronger than Hirst’s Hilbert’s Theorem. The lower bound (...) is obtained by a direct combinatorial implication from the Adjacent Hindman’s Theorem with apartness to the Increasing Polarized Ramsey’s Theorem for pairs introduced by Dzhafarov and Hirst. In the Adjacent Hindman’s Theorem homogeneity is required only for finite sums of adjacent elements. (shrink)

We define a direct translation from finite rooted trees to finite natural functions which shows that the Worm Principle introduced by Lev Beklemishev is equivalent to a very slight variant of the well-known Kirby-Paris' Hydra Game. We further show that the elements in a reduction sequence of the Worm Principle determine a bad sequence in the well-quasi-ordering of finite sequences of natural numbers with respect to Friedman's gapembeddability. A characterization of gap-embeddability in terms of provability logic due to Lev Beklemishev (...) is also presented. (shrink)

We investigate a new paradigm in the context of learning in the limit, namely, learning correction grammars for classes of computably enumerable (c.e.) languages. Knowing a language may feature a representation of it in terms of two grammars. The second grammar is used to make corrections to the first grammar. Such a pair of grammars can be seen as a single description of (or grammar for) the language. We call such grammars correction grammars. Correction grammars capture the observable fact that (...) people do correct their linguistic utterances during their usual linguistic activities. We show that learning correction grammars for classes of c.e. languages in the TxtEx-model (i.e., converging to a single correct correction grammar in the limit) is sometimes more powerful than learning ordinary grammars even in the TxtBe-model (where the learner is allowed to converge to infinitely many syntactically distinct but correct conjectures in the limit). For each n ≥ 0, there is a similar learning advantage, again in learning correction grammars for classes of c.e. languages, but where we compare learning correction grammars that make n + 1 corrections to those that make n corrections. The concept of a correction grammar can be extended into the constructive transfinite, using the idea of counting-down from notations for transfinite constructive ordinals. This transfinite extension can also be conceptualized as being about learning Ershov-descriptions for c.e. languages. For u a notation in Kleene's general system $(O,\, < _o )$ of ordinal notations for constructive ordinals, we introduce the concept of an u-correction grammar, where u is used to bound the number of corrections that the grammar is allowed to make. We prove a general hierarchy result: if u and v are notations for constructive ordinals such that $u\, < _o \,v$ , then there are classes of c.e. languages that can be TxtEx-learned by conjecturing v-correction grammars but not by conjecturing u-correction grammars. Surprisingly, we show that— above "ω-many" corrections—it is not possible to strengthen the hierarchy: TxtEx-learning u-correction grammars of classes of c.e. languages, where u is a notation in O for any ordinal, can be simulated by TxtBe-learning ω-correction grammars, where ω is any notation for the smallest infinite ordinal ω. (shrink)

We formulate a restriction of Hindman’s Finite Sums Theorem in which monochromaticity is required only for sums corresponding to rooted finite paths in the full binary tree. We show that the resulting principle is equivalent to \-induction over \. The proof uses the equivalence of this Hindman-type theorem with the Pigeonhole Principle for trees \ with an extra condition on the solution tree.

We formulate a restriction of Hindman’s Finite Sums Theorem in which monochromaticity is required only for sums corresponding to rooted finite paths in the full binary tree. We show that the resulting principle is equivalent to Σ20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Sigma ^0_2$$\end{document}-induction over RCA0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {RCA}_0$$\end{document}. The proof uses the equivalence of this Hindman-type theorem with the Pigeonhole Principle for trees TT1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} (...) \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf {T}\,}{\mathsf {T}}^1$$\end{document} with an extra condition on the solution tree. (shrink)

In the present article, we investigated the relation between socio-demographic variables and personality factors with religious fundamentalism. Our data were collected from a sample of 125 Italian Catholic participants. Correlation analyses showed a significant association between RF and the openness domain of personality, including both facet scales. We also found a significant association between RF and conscientiousness. Regarding socio-demographic variables, we found significant correlations between RF and years of education, church attendance, belief, and age, while there was no significant correlation (...) between RF and gender. Path analysis showed that the effects on RF of socio-demographic factors are stronger than those of personality factors. (shrink)

Many recent events have contributed to the resurgence of the historically cyclical debate over euthanasia. Now, the focus rests on physician-assisted suicide. Many landmark events regarding physician-assisted suicide have occurred within the last year alone. For example, Derek Humphry's Final Exit recently became a best seller, giving people the detailed knowledge of how to “self-deliver” In The New England Journalbf Medicine, Dr. Timothy Quill shared his touching experience of assisting his patient “Diane” after she chose to decline treatment options for (...) leu- kemia. Dr. Jack Kevorkian made use of his highly publicized “death machine” to help Janet Adkins and subsequently, several other women, end their lives. (shrink)

In this paper, we embark on the complicated discussion about the nature of vice in Virtue Ethics through a twofold approach: first, by taking seriously the claim that virtues (and certain flavours of vices) are genuinely dispositional features possessed by agents, and secondly, by employing a pluralistic attitude borrowed from Battaly’s pluralism (2008). Through these lenses, we identify three varieties of viciousness: incontinence, indifference, and malevolence. The upshot is that the notion of vice is not as categorically homogeneous as that (...) of virtue: some states of viciousness consist in interference of present virtuous dispositions, or mimicking of absent vicious ones, whereas others can be considered genuine dispositions themselves. Furthermore, this set-up can provide an interesting, albeit highly idealized story as to how, through the interference in one’s environment, one gets acquainted with vice in various degrees. Finally, this approach can be illuminating vis-à-vis Virtue Ethics in general; e.g. we can employ it to discuss more productively Johnston’s (2003) objection to Hursthouse’s (1999) account of moral conduct. Finally, this approach can be illuminating vis-a-vis Virtue Ethics in general; e.g. we can employ it to discuss more productively Johnston’s (2003) objection to Hursthouse’s (1999) account of moral conduct. (shrink)

Theoretical and manipulative abduction conjectures and manipulations : the extra-theoretical dimension of scientific discovery. -- Non-explanatory and instrumental abduction : plausibility, implausibility, ignorance preservation. -- Semiotic brains and artificial minds : how brains make up material cognitive systems. -- Neuromultimodal abduction : pre-wired brains, embidiment, neurospaces. -- Animal abduction : from mindless organisms to srtifactual mediators. -- Abduction, affordances, and cognitive niches : sharing representations and creating chances through cognitive niche construction. -- Abduction in human and logical agents : hasty (...) generalizers, hybrid abducers, fallacies. -- Morphodynamical abduction : causation of hypotheses by attractors dynamics. (shrink)

Research is ongoing concerning the medical risks and benefits of routine neonatal male circumcision. Interpretation of the data, however, is controversial. Circumcision presents a number of challenges in obtaining informed consent because of a variety of interesting issues. It is a nonemergent, elective procedure that allows for evaluation and discussion over time. In this respect, observation of the informed consent process for circumcision is relevant to other medical decisions, such as advance directives, discussed between primary care providers and patients. Obtaining (...) informed consent for circumcision has its constraints. The process generally occurs over a brief hospital stay. There have been recent changes in the official position regarding the procedure by professional medical societies, and it raises considerable psychologic issues for the provider and may Impact the way in which Information is provided. (shrink)

ABSTRACT In 1991 the Dutch government released the results of the first national investigation into the nature and extent of decisions concerning end of life including euthanasia. A significant finding was that most cases of euthanasia were not reported. This prompted us to ask what effect, if any, not reporting caused. More specifically, we asked whether reporting has a positive or negative impact on the experiences of friends or relatives of patients who have received euthanasia. In cases of euthanasia, complications (...) of both process and experience can deter from a minimally complicated death. These difficulties arise when either the family or physician does not perceive the freedom to disclose euthanasia openly. On the basis of interviews with family members and patients, we illustrate that they generally benefit from reporting. Our premise is that reporting fosters open discussion of euthanasia. We further suggest physicians and society benefit from a milieu of openness initiated by reporting cases of euthanasia. (shrink)

This is the first dedicated commentary to Sextus Empiricus’ treatise _Against the Arithmeticians_, dealing with crucial issues in the history of the sceptical, Platonic and Pythagorean traditions and in the ancient philosophy of mathematics.

There are various forms of teleological thinking central to debates in the early modern and modern periods, debates in which David Hume (1711–1776) is a key figure. In the first section, we shall introduce three levels at which teleological considerations have been incorporated into philosophical accounts of man and nature, and sketch Hume’s criticisms of these approaches. In the second section, we turn to Hume’s non-teleological ‘science of man’. In the third section, we show how Hume has an account of (...) human flourishing that is not dependent on teleology. In the fourth section, we shall speculate as to the relation between Hume’s account of human nature and contemporary evolutionary accounts of morality and reasoning. (shrink)

This paper presents an interpretation of the 1945 forbidden film Scarlet Street in a way so as to touch the problem of gender in film noir. Firstly, I give an ac-count of film noir, agreeing with Robert Pippin’s argument concerning film genres. Then, I claim that time and repetition, irony and hierarchy, art and per-spective constitute the core subjects explored in Scarlet Street. Furthermore, I try to connect all the subjects into a single one. My point is to show how (...) art, perspective, time, repetition, irony and hierarchy are articulated in the main character’s gender identity. Finally, I suggest there is a deep connection be-tween the movie’s character constitution and Cavell’s understanding of gender and agency.Keywords: Film. Gender. Psychoanalysis. Cavell. Freud. (shrink)

Lorenzo Valla (1407–1457) ranks among the greatest scholars and thinkers of the Renaissance. He secured lasting fame for his brilliant critical skills, most famously in his exposure of the “Donation of Constantine,” the forged document upon which the papacy based claims to political power. Lesser known in the English-speaking world is Valla's work in the philosophy of language—the basis of his reputation as the greatest philosopher of the humanist movement. Dialectical Disputations, translated here for the first time into any (...) modern language, is his principal contribution to the philosophy of language and logic. With this savage attack on the scholastic tradition of Aristotelian logic, Valla aimed to supersede it with a new logic based on the actual historical usage of classical Latin and on a commonsense approach to semantics and argument. Valla provides a logic that could be used by lawyers, preachers, statesmen, and others who needed to succeed in public debate—one that was stylistically correct and rhetorically elegant, and thus could dispense with the technical language of the scholastics, a “tribe of Peripatetics, perverters of natural meanings.” Valla's reformed dialectic became a milestone in the development of humanist logic and contains startling anticipations of modern theories of semantics and language. Volume 1 contains Book I, in which Valla refutes Aristotle's logical works on the categories, transcendentals, and predicables, with excursions into natural and moral philosophy and theology. (shrink)

In recent years, a new dispute has risen to prominence: the dispute between realists and anti-realists about causal powers. Albeit sometimes overlooked, the meta-ontological features of this “question of realism for powers” are quite peculiar. For friends and foes of causal powers have characterized their contrasting views in a variety of different ways; as existence claims, as semantic or truth-making claims, as fundamentality claims, as claims about the nature of certain properties. Not only does this multiplicity of interpretations make it (...) unclear what the genuine bone of contention is, if there is one; some of them appear to be mutually exclusive. Some light can be shed on this apparent yet widespread confusion by distinguishing three degrees of ontological involvement in dispositional truths; viz., three ways, of increasing robustness, to read ontological commitments from dispositional truths. Relatedly, by exploring the literature, and focusing on some selected examples of power realism and anti-realism, we can observe that power realists vastly disagree over the intrinsic nature ad make-up of dispositional properties. Such examples furthermore invite the thought that the question of realism for powers is best understood not as the debate around the existence of properties with a distinctive identity, but rather as a debate about metaphysical hierarchy. Finally, some anti-realists positions are indistinguishable from realist ones, using merely intensional resources: power realism is best appreciated by going hyperintensional. (shrink)

This paper attempts a reconstruction of reason’s contribution to empirical truth in connection with Kant’s definition of truth as the agreement of cognition with its object. I argue that Kant’s treatment of truth in the Transcendental Analytic gets completed in the Appendix to the Transcendental Dialectic with an often neglected but compelling argument (what I shall call the Variety Argument). This argument postulates such a variety in the appearances as to undermine any attempt at formulating empirical truths. Crucially, I argue (...) that this variety does not depict an extreme-case scenario, but our own epistemic situation without reason. Reason completes Kant’s theory of truth by allowing the understanding (i.) to form empirical concepts and (ii.) approximate to empirical truth. (shrink)

Philosophers have debated at length the epistemological status of scientific thought experiments. I contend that the literature on this topic still lacks a common conceptual framework, a lacuna that produces radical disagreement among the participants in this debate. To remedy this problem, I suggest focusing on the distinction between the internal and the external validity of an experiment, which is also crucial for thought experiments. I then develop an account of both kinds of validity in the context of thought experiments. (...) I show that we can naturally conceptualise internal validity in terms of games of make-believe. Then, I argue that external validity is best defined as accurate representation of a target system. Finally, I turn back to the current debate on thought experiments and show that my diarchic account provides a general framework that can be shared by the competing philosophical views, as well as a fruitful guide for their reconciliation. (shrink)

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished]. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of [Tarski 1959]: a predicate of betwenness and a (...) four place predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane - which obeys the Euclidean axioms in [Tarski and Givant, 1999] - and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagora’s theorem. We conclude with a Representation Theorem relating models of our system that satisfy second order continuity to the mathematical structure called ‘Minkowski spacetime’ in physics textbooks. (shrink)

This article aims to justify the positive role in the empirical investigation of nature that Kant attributes to the idea of God in the Critique of Pure Reason. In particular, I propose to read the Transcendental Ideal section and the Appendix to the Transcendental Dialectic together to see whether they can reciprocally illuminate each other. I argue that it is only by looking at the transcendental deduction of the ideas of reason and the resulting analogical conception of God that a (...) fully legitimate positive use of the idea of God can be vindicated. (shrink)

Discussions about dispositional and categorical properties have become commonplace in metaphysics. Unfortunately, dispositionality and categoricity are disputed notions: usual characterizations are piecemeal and not widely applicable, thus threatening to make agreements and disagreements on the matter merely verbal—and also making it arduous to map a logical space of positions about dispositional and categorical properties in which all parties can comfortably fit. This paper offers a prescription for this important difficulty, or at least an inkling thereof. This will be achieved by (...) comparing pairs of positions and exploring their background metaphysics to discover where alleged agreements and disagreements concerning dispositionality and categoricity really lie; more specifically, the Pure Powers view and the Powerful Qualities view will be under scrutiny. Over this background, the prescription functions by isolating a successful identity-based characterization of categoricity, while abandoning the correspondent identity-based characterization of dispositionality. On the contrary, according to this prescription a property is dispositional if and only if it is solely in virtue of possessing that property that its bearer is assigned a certain dispositional profile. A crucial consequence of this prescription is that, while supporters of the Pure Powers view often characterize their position as an essentialist one, the dispositionality of properties needn’t always be a matter of essence. (shrink)

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in Maudlin and Malament. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of Tarski : a predicate of betwenness and a four place (...) predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane—which obeys the Euclidean axioms in Tarski and Givant, 175–214 1999)—and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagoras’ theorem. We conclude with a Representation Theorem relating models \ of our system \ that satisfy second order continuity to the mathematical structure \, called ‘Minkowski spacetime’ in physics textbooks. (shrink)

The Recursive Bayesian Net formalism was originally developed for modelling nested causal relationships. In this paper we argue that the formalism can also be applied to modelling the hierarchical structure of mechanisms. The resulting network contains quantitative information about probabilities, as well as qualitative information about mechanistic structure and causal relations. Since information about probabilities, mechanisms and causal relations is vital for prediction, explanation and control respectively, an RBN can be applied to all these tasks. We show in particular how (...) a simple two-level RBN can be used to model a mechanism in cancer science. The higher level of our model contains variables at the clinical level, while the lower level maps the structure of the cell's mechanism for apoptosis. (shrink)

This book aims to develop the tradition of philosophical hermeneutics, the theoretical account of interpretive (as opposed to explanatory) understanding--the account of meanings and contexts rather than causes and predictions--usually restricted to the domain of literary and textual analysis, in new directions by exploiting its potential as an instrument of critique. It refutes commonly held claims that hermeneutic analyses are necessarily relativistic, Eurocentric, or critically impotent and demonstrates how hermeneutic procedures can inform analyses of urgent current and cross-cultural issues such (...) as the biology of race, female genital excision, and the so-called "culture of poverty" thesis. Lorenzo Simpson demonstrates that a robust methodology of philosophical hermeneutics is well positioned to intervene in critical political and social issues in global ethics and justice in concert with critical theory's emancipatory aims. (shrink)

The standard representation of the Central Dogma (CD) of Molecular Biology conspicuously ignores metabolism. However, both the metabolites and the biochemical fluxes behind any biological phenomenon are encrypted in the DNA sequence. Metabolism constrains and even changes the information flow when the DNA‐encoded instructions conflict with the homeostasis of the biochemical network. Inspection of adaptive virulence programs and emergence of xenobiotic‐biodegradation pathways in environmental bacteria suggest that their main evolutionary drive is the expansion of their metabolic networks towards new chemical (...) landscapes rather than perpetuation and spreading of their DNA sequences. Faulty enzymatic reactions on suboptimal substrates often produce reactive oxygen species (ROS), a process that fosters DNA diversification and ultimately couples catabolism of the new chemicals to growth. All this calls for a revision of the CD in which metabolism (rather than DNA) has the leading role. (shrink)