We introduce three formal theories of increasing strength for linear algebra in order to study the complexity of the concepts needed to prove the basic theorems of the subject. We give what is apparently the first feasible proofs of the Cayley–Hamilton theorem and other properties of the determinant, and study the propositional proof complexity of matrix identities such as AB=I→BA=I.

We show that short bounded-depth Frege proofs of matrix identities, such as PQ=I⊃QP=I (over the field of two elements), imply short bounded-depth Frege proofs of the pigeonhole principle. Since the latter principle is known to require exponential-size bounded-depth Frege proofs, it follows that the propositional version of the matrix principle also requires bounded-depth Frege proofs of exponential size.

We investigate the theories of linear algebra, which were originally defined to study the question of whether commutativity of matrix inverses has polysize Frege proofs. We give sentences separating quantified versions of these theories, and define a fragment in which we can interpret a weak theory V 1 of bounded arithmetic and carry out polynomial time reasoning about matrices - for example, we can formalize the Gaussian elimination algorithm. We show that, even if we restrict our language, proves the commutativity (...) of inverses. (shrink)

We prove assorted properties of matrices over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Z}_{2}}$$\end{document}, and outline the complexity of the concepts required to prove these properties. The goal of this line of research is to establish the proof complexity of matrix algebra. It also presents a different approach to linear algebra: one that is formal, consisting in algebraic manipulations according to the axioms of a ring, rather than the traditional semantic approach via linear transformations.

The avocado (Persea americana) is a major crop commodity worldwide. Moreover, avocado, a paleopolyploid, is an evolutionary “outpost” among flowering plants, representing a basal lineage (the magnoliid clade) near the origin of the flowering plants themselves. Following centuries of selective breeding, avocado germplasm has been characterized at the level of microsatellite and RFLP markers. Nonetheless, little is known beyond these general diversity estimates, and much work remains to be done to develop avocado as a major subtropical‐zone crop. Among the goals (...) of avocado improvement are to develop varieties with fruit that will “store” better on the tree, show uniform ripening and have better post‐harvest storage. Avocado transcriptome sequencing, genome mapping and partial genomic sequencing will represent a major step toward the goal of sequencing the entire avocado genome, which is expected to aid in improving avocado varieties and production, as well as understanding the evolution of flowers from non‐flowering seed plants (gymnosperms). Additionally, continued evolutionary and other comparative studies of flower and fruit development in different avocado strains can be accomplished at the gene expression level, including in comparison with avocado relatives, and these should provide important insights into the genetic regulation of fruit development in basal angiosperms. BioEssays 30:386–396, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

By synthesizing evolutionary, attachment, and acoustic perspectives, Soltis has provided an innovative model of infant cry acoustics and parental responsiveness. We question some of his hypotheses, however, because of the limited extant data on infant crying among hunter-gatherers. We also question Soltis' distinction between manipulative and honest signaling based upon recent contributions from attachment theory.

This article defends the Fixed Point Thesis: that it is always a rational mistake to have false beliefs about the requirements of rationality. The Fixed Point Thesis is inspired by logical omniscience requirements in formal epistemology. It argues to the Fixed Point Thesis from the Akratic Principle: that rationality forbids having an attitude while believing that attitude is rationally forbidden. It then draws out surprising consequences of the Fixed Point Thesis, for instance that certain kinds of a priori justification are (...) indefeasible and that misleading all-things-considered evidence about rational requirements is impossible. Finally, the Fixed Point Thesis is applied to defend the Right Reasons position on peer disagreement, according to which an agent who has drawn the correct conclusion from her evidence should retain belief in that conclusion even in the face of disagreeing peers. (shrink)

This target article presents a theory of human cultural learning. Cultural learning is identified with those instances of social learning in which intersubjectivity or perspective-taking plays a vital role, both in the original learning process and in the resulting cognitive product. Cultural learning manifests itself in three forms during human ontogeny: imitative learning, instructed learning, and collaborative learning – in that order. Evidence is provided that this progression arises from the developmental ordering of the underlying social-cognitive concepts and processes involved. (...) Imitative learning relies on a concept of intentional agent and involves simple perspective-taking. Instructed learning relies on a concept of mental agent and involves alternating/coordinated perspective-taking (intersubjectivity). Collaborative learning relies on a concept of reflective agent and involves integrated perspective-taking (reflective intersubjectivity). A comparison of normal children, autistic children and wild and enculturated chimpanzees provides further evidence for these correlations between social cognition and cultural learning. Cultural learning is a uniquely human form of social learning that allows for a fidelity of transmission of behaviors and information among conspecifics not possible in other forms of social learning, thereby providing the psychological basis for cultural evolution. (shrink)

Healthcare priority-setting institutions have good reason to want to demonstrate that their decisions are morally justified—and those who contribute to and use the health service have good reason to hope for the same. However, finding a moral basis on which to evaluate healthcare priority-setting is difficult. Substantive approaches are vulnerable to reasonable disagreement about the appropriate grounds for allocating resources, while procedural approaches may be indeterminate and insufficient to ensure a just distribution. In this paper, we set out a complementary, (...) coherence-based approach to the evaluation of healthcare priority-setting. Drawing on Rawls, we argue that an institutional priority-setter’s claim to moral justification can be assessed, in part, based on the extent to which its many normative commitments are mutually supportive and free from dissonance; that is, on the ability to establish narrow reflective equilibrium across the normative content of a priority-setter’s policy and practice. While we do not suggest that the establishment of such equilibrium is sufficient for moral justification, we argue that failure to do so might—like the proverbial canary in the coalmine—act as a generalised warning that something is awry. We offer a theoretical argument in support of this view and briefly outline a practical method for systematically examining coherence across priority-setting policy and practice. (shrink)

Founder of GotQuestions.org, the most popular online biblical resource, S. Michael Houdmann answers 100 of the most-asked questions on the site in a compassionate, accessible, and straightforward manner. Cutting through the confusion on even the hardest of topics, he offers the biblical truth we all need to understand God's Word and apply it to our lives.

Michael J. Zimmerman explores whether and how our ignorance about ourselves and our circumstances affects what our moral obligations and moral rights are. He rejects objective and subjective views of the nature of moral obligation, and presents a new case for a 'prospective' view.

The COVID-19 pandemic crisis has necessitated widespread adaptation of revised treatment regimens for both urgent and routine medical problems in patients with and without COVID-19. Some of these alternative treatments maybe second-best. Treatments that are known to be superior might not be appropriate to deliver during a pandemic when consideration must be given to distributive justice and protection of patients and their medical teams as well the importance given to individual benefit and autonomy. What is required of the doctor discussing (...) these alternative, potentially inferior treatments and seeking consent to proceed? Should doctors share information about unavailable but standard treatment alternatives when seeking consent? There are arguments in defence of non-disclosure; information about unavailable treatments may not aid a patient to weigh up options that are available to them. There might be justified concern about distress for patients who are informed that they are receiving second-best therapies. However, we argue that doctors should tailor information according to the needs of the individual patient. For most patients that will include a nuanced discussion about treatments that would be considered in other times but currently unavailable. That will sometimes be a difficult conversation, and require clinicians to be frank about limited resources and necessary rationing. However, transparency and honesty will usually be the best policy. (shrink)

"Writing in a lively and refreshingly clear American English, Zimmerman provides an uncompromisingly honest and judicious account... of Heidegger’s views on technology and his involvement with National Socialism.... One of the most important books on Heidegger in recent years." —John D. Caputo "... superb... " —Thomas Sheehan, The New York Review of Books "... thorough and complex... " —Choice "... excellent guide to Heidegger as eco-philosopher." —Radical Philosophy "... engrossing, rich in substance... makes clear Heidegger's importance for the issue of (...) technology, ethics, and politics." —Religious Studies Review The relation between Martin Heidegger’s understanding of technology and his affiliation with and conception of National Socialism is the leading idea of this fascinating and revealing book. Zimmerman shows that the key to the relation between Heidegger’s philosophy and his politics was his concern with the nature of working and production. (shrink)

This work offers a new democratic case for federalism, understood as a form of governance in which multiple entities in a country possess final decision-making authority (viz., can make decisions free from others substituting their decisions, issuing fines, etc.) over at least one subject (e.g., immigration, defense). It argues that leading solutions to the democratic boundary problem provide overlapping arguments for federalism. The underlying logic and many details of the most commonly cited solutions focused on those relevantly affected by and (...) subject to decisions each support three distinct arguments (focused on voteshares, other forms of democratic influence, and persistent minorities) for multiple demoi possessing authority in a polity. Federalism is the best available method for recognizing the distinct demoi. This not only supports federal governance as opposed to unitary governance and subsidiarity. It also suggests that democracy and federalism are importantly related and have several implications for institutional design. (shrink)

This book presents the first critical examination of the overlapping ethical, sociocultural, and policy-related issues surrounding disasters, global bioethics, and public health ethics. These issues are elucidated under the conceptual rubric: Public health disasters. The book defines PHDs as public health issues with devastating social consequences, the attendant public health impacts of natural or man-made disasters, and latent or low prevalence public health issues with the potential to rapidly acquire pandemic capacities. This notion is illustrated using Ebola and pandemic influenza (...) outbreaks, atypical drug-resistant tuberculosis, and the health emergencies of earthquakes as focal points. Drawing on an approach that reckons with microbial, existential, and anthropological realities; the book develops a relational-based global ethical framework that can help address the local, anthropological, ecological, and transnational dynamics of the ethical issues engendered by public health disasters. The book also charts some of the critical roles that relevant local and transnational stakeholders may play in translating the proposed global ethical framework from the sphere of concept to the arena of action. This title is of immense benefit to bioethics scholars, public and global health policy experts, as well as graduate students working in the area of global health, public health ethics, and disaster bioethics. (shrink)

Metaethicists have recently devoted a great deal of attention to questions about when a fact counts as a reason for or against a particular conclusion, and how such reasons interact. Chapter 9 asks a broader question: When a set of facts counts in favor of some conclusion, is that always because at least one of those facts is a reason for that conclusion? Examples are offered in which a set supports a conclusion without any fact in that set’s being a (...) reason for. The chapter then assesses the significance of such examples for philosophical methodology, the ‘reasons-first’ program, and metanormative realism. (shrink)

Around 540 million years ago there was a sudden, dramatic adaptive radiation known as the Cambrian Explosion. This event marked the origin of almost all of the phyla (major lineages characterized by fundamental body plans) of animals that would ever live on earth, as well the appearance of many notable features such as rigid skeletons and other hard parts, complex jointed appendages, eyes, and brains. This radical evolutionary event has been a major puzzle for evolutionary biologists since Darwin, and while (...) our understanding of it has recently improved with new fossil finds, richer molecular phylogenies, and better grasp of ecological, evolutionary, and developmental processes generally, unanswered questions remain. In this paper I argue that a basic cognitive toolkit for embodied, object-oriented, spatial cognition (what I call Basic Cognitive Embodiment) is a practical necessity for control of a large, mobile, complexly articulated body in space. This hypothesis allows us to relate the complexification of animal bodies to the complexification of perception, cognition and behavior in a way that can help to fill in gaps in our emerging picture of the Cambrian Explosion, as well as shed light on the deep evolutionary origins of the mind. (shrink)

This article challenges conventional readings of Michel Foucault by examining his fascination with neoliberalism in the late 1970s. Foucault did not critique neoliberalism during this period; rather, he strategically endorsed it. The necessary cause for this approval lies in the broader rehabilitation of economic liberalism in France during the 1970s. The sufficient cause lies in Foucault's own intellectual development: drawing on his long-standing critique of the state as a model for conceptualizing power, Foucault concluded, during the 1970s, that economic liberalism, (...) rather than “discipline,” was modernity's paradigmatic power form. Moreover, this article seeks to clarify the relationship between Foucault's philosophical antihumanism and his assessment of liberalism. Rather than arguing that Foucault's antihumanism precluded a positive appraisal of liberalism, or that the apparent reorientation of his politics in a more liberal direction in the late 1970s entailed a partial retreat from antihumanism, this article contends that Foucault's brief, strategic, and contingent endorsement of liberalism was possible precisely because he saw no incompatibility between antihumanism and liberalism—but only liberalism of the economic variety. Economic liberalism alone, and not its political iteration, was compatible with the philosophical antihumanism that is the hallmark of Foucault's thought. (shrink)

This article critically examines the relations between epistemics in conversation analysis and linguistic and cognitivist conceptions of communicative interaction that emphasize information and information transfer. The epistemic program adheres to the focus on recorded instances of talk-in-interaction that is characteristic of CA, explicitly identifies its theoretical origins with ethnomethodology, and points to implications of its research for the social distribution of knowledge. However, despite such affiliations with CA and ethnomethodology, the EP is cognitivist in the way it emphasizes information exchange (...) as an underlying, extrasituational ‘driver’ in social interaction. To document how the EP draws upon cognitivist conceptions of information and knowledge, we review examples from the corpus of transcripts analyzed in key publications on epistemics. Our re-analysis casts doubt upon the way EP analysis invokes an underlying order that supposedly drives the evident sequential organization of those transcripts. (shrink)

Machine learning is an increasingly significant part of modern healthcare, transforming the way clinical decisions are made and health resources are managed. These developme...

In circulation, T cells are spherical with selectin enriched dynamic microvilli protruding from the surface. Following extravasation, these microvilli serve another role, continuously surveying their environment for antigen in the form of peptide‐MHC (pMHC) expressed on the surface of antigen presenting cells (APCs). Upon recognition of their cognate pMHC, the microvilli are initially stabilized and then flatten into F‐actin dependent microclusters as the T cell spreads over the APC. Within 1–5 min, clathrin is recruited by the ESCRT‐0 component Hrs to (...) mediate release of T cell receptor (TCR) loaded vesicles directly from the plasma membrane by clathrin and ESCRT‐mediated ectocytosis (CEME). After 5‐10 min, Hrs is displaced by the endocytic clathrin adaptor epsin‐1 to induce clathrin‐mediated trans‐endocytosis (CMTE) of TCR‐pMHC conjugates. Here we discuss some of the functional properties of the clathrin machinery which enables it to control these topologically opposite modes of membrane transfer at the immunological synapse, and how this might be regulated during T cell activation. (shrink)

Why are causal generalizations in the higher-level sciences “inexact”? That is, why do they have apparent exceptions? This paper offers one explanation: many causal generalizations cite as their antecedent—the \(F\) in \(Fs\,\, {\textit{are}}\,\, G\) —a property that is not causally relevant to the consequent, but which is rather “entangled” with a causally relevant property. Entanglement is a relation that may exist for many reasons, and that allows of exceptions. Causal generalizations that specify entangled but causally irrelevant antecedents therefore tolerate exceptions.

Humans are fundamentally social and tend to create emergent organizations when interacting with each other; from dyads to families, small groups, large groups, societies and civilizations. The study of the neuronal substrate of human social behavior is currently gaining momentum in the young field of social neuroscience. Hyperscanning is a neuroimaging technique by which we can study two or more brain simultaneously while participants interact with each other. The aim of this article is to discuss several factors that we deem (...) important in designing hyperscanning experiments. We first review hyperscanning studies performed by means of electroencephalography (EEG) that have been relying on a continuous interaction paradigm. Then, we provide arguments for favoring ecological paradigms, for studying the emotional component of social interactions and for performing longitudinal studies, the last two aspects being largely neglected so far in the hyperscanning literature despite their paramount importance in social sciences. Based on these premises we argue that music performance is a suitable experimental setting for hyperscanning and that for such studies EEG is an appropriate choice as neuroimaging modality. (shrink)

This paper proposes a five-part empirical typology of interconnections of race and class. We describe the mechanisms whereby (1) race is a form of class relation; (2) race relations and class relations reciprocally affect each other; (3) race acts as a sorting mechanism into class locations; (4) race acts as a mediating linkage to class locations; and (5) race interacts with class in determining other outcomes. Rather than insisting on one or another mechanism as the overarching framework for conceptualising the (...) interconnections between race and class, we propose a theoretical integration of all five within a functionalist model. The model reconciles the empirical effects of race variables with a class-functionalist explanation of race. Our typology of interconnections is useful for situating concrete empirical phenomena, and our theoretical integration of those interconnections offers a coherent explanatory system that captures the recursive causality of race and class. (shrink)

Many contemporary metaphysicians believe that the existence of a contingent object such as Socrates metaphysically explains the existence of the corresponding set {Socrates}. This paper argues that this belief is mistaken. The argument proposed takes the form of a dilemma. The expression “{Socrates}” is a shorthand either for the expression “the set that contains all and only those objects that are identical to Socrates” or for the expression “the set that contains Socrates and nothing else”. However, Socrates' existence does not (...) explain the existence of the set that contains all and only those objects that are identical to Socrates, because there is such a set no matter whether or not Socrates exists. And although Socrates' existence does explain that of the set that contains Socrates and nothing else, this explanation is a conceptual rather than a metaphysical one. Both these claims rely on a deflationary account of the use of set theoretic vocabulary that is explained, though not properly justified, in the paper. (shrink)

New brain-computer interface and neuroimaging techniques are making differentiation less ambiguous and more accurate between unresponsive wakefulness syndrome patients and patients with higher cognitive function and awareness. As research into these areas continues to progress, new ethical issues will face physicians of patients suffering from total locked-in syndrome, characterized by complete loss of voluntary muscle control, with retention of cognitive function and awareness detectable only with neuroimaging and brain-computer interfaces. Physicians, researchers, ethicists and hospital ethics committees should be aware of (...) and prepared to handle ethical issues unique to these totally locked-in patients. Several thought experiments are discussed, to highlight potential ethical dilemmas surrounding surrogate decision-making, autonomy, end-of-life care, and pediatric care, which will be unique to total LIS patients. These, along with other ethical problems especially relevant to total LIS patients, merit further discussion among physicians, researchers, ethicists and hospital ethics committees, to facilitate consensus regarding these issues, and improve patient care. (shrink)

It is shown (i) that causation exists, since we couldn't even ask whether causation existed unless it did; (ii) that any given case of causation is a case of persistence; and (iii) that spatiotemporal relations supervene on causal relations. (ii) is subject to the qualification that we tend not to become aware of instances of causation as such except when two different causal lines---i.e. two different cases of persistence---intersect, resulting in a breakdown of some other case of persistence, this being (...) why we tend to regard instances of causation as fundamentally disruptive, as opposed to preservative in nature. The meaning of (iii) is that spatiotemporal relations are causal relations considered in abstraction of the various specific differences holding between different kinds of causation. (shrink)

Introduction: Religious experience in modernity : faith itself as the "unknown God" -- Fides qua creditur : the Enlightenment mind and the theology of the heart -- Within the bounds of reason alone : the subjective justification of religious belief in the thought of Immanuel Kant -- Schleiermacher's "higher order Pietism" : subjectivity and Protestant liberal thought -- Søren Kierkegaard and the paradox of faith : subjectivity in Christian existentialism -- Subjectivity and religious belief in Anglo-American revivalism : Jonathan Edwards (...) and John Wesley -- Subjectivity and religious belief in Anglo-American revivalism : George Whitefield and Charles G. Finney. (shrink)

Strong property representationalism, as applied to visual experience, is the thesis that the phenomenal character of a visual experience is one and the same as the property complex or ‘sensible profile’ represented by that experience. Speaks discusses the following argument against this thesis:Let ‘RED’ stand for the phenomenal character of the experience of red.(1) Red = RED (strong property representationalism).(2) My pen has no representational properties, but is red.Hence,(3) My pen has a phenomenal character but no representational properties.Since (3) is (...) false, (1) is false too.(3) Follows from (1) and (2) only on the assumption that what it is for something to have a phenomenal character is for it to instantiate a certain property just as what it is for my pen to have the color red is for it to instantiate the property of being red. The property instantiation model of having a phenomenal character is not the only possible model, however, and I reject it.An alternative model is t. (shrink)