We continue the work of [14, 3, 1, 19, 16, 4, 12, 11, 20] investigating the strength of set existence axioms needed for separable Banach space theory. We show that the separation theorem for open convex sets is equivalent to WKL$_0$ over RCA$_0$. We show that the separation theorem for separably closed convex sets is equivalent to ACA$_0$ over RCA$_0$. Our strategy for proving these geometrical Hahn-Banach theorems is to reduce to the finite-dimensional case by means of a compactness argument.

A mass problem is a set of Turing oracles. If P and Q are mass problems, we say that P is weakly reducible to Q if for all Y ∈ Q there exists X ∈ P such that X is Turing reducible to Y. A weak degree is an equivalence class of mass problems under mutual weak reducibility. Let [Formula: see text] be the lattice of weak degrees of mass problems associated with nonempty [Formula: see text] subsets of the Cantor (...) space. The lattice [Formula: see text] has been studied in previous publications. The purpose of this paper is to show that [Formula: see text] partakes of hyperarithmeticity. We exhibit a family of specific, natural degrees in [Formula: see text] which are indexed by the ordinal numbers less than [Formula: see text] and which correspond to the hyperarithmetical hierarchy. Namely, for each [Formula: see text], let hα be the weak degree of 0, the αth Turing jump of 0. If p is the weak degree of any mass problem P, let p* be the weak degree of the mass problem P* = {Y | ∃X ⊆ BLR )} where BLR is the set of functions which are boundedly limit recursive in X. Let 1 be the top degree in [Formula: see text]. We prove that all of the weak degrees [Formula: see text], [Formula: see text], are distinct and belong to [Formula: see text]. In addition, we prove that certain index sets associated with [Formula: see text] are [Formula: see text] complete. (shrink)

Recall that [Formula: see text] is the lattice of Muchnik degrees of nonempty effectively compact sets in Euclidean space. We solve a long-standing open problem by proving that [Formula: see text] is dense, i.e. satisfies [Formula: see text]. Our proof combines an oracle construction with hyperarithmetical theory.

In order to introduce protists to philosophers, we outline the diversity, classification, and evolutionary importance of these eukaryotic microorganisms. We argue that an evolutionary understanding of protists is crucial for understanding eukaryotes in general. More specifically, evolutionary protistology shows how the emphasis on understanding evolutionary phenomena through a phylogeny-based comparative approach constrains and underpins any more abstract account of why certain organismal features evolved in the early history of eukaryotes. We focus on three crucial episodes of this history: the origins (...) of multicellularity, the origin of sex, and the origin of the eukaryote cell. Despite ongoing uncertainty about where the root of the eukaryote tree lies, and residual questions about the precise endosymbioses that have produced a diversity of photosynthesizing eukaryotes, evolutionary protistology has illuminated with considerable clarity many aspects of protist evolution. Our main message in light of evolutionary protistology is that these ‘other eukaryotes’ are in fact the organisms through which the rest of the eukaryotes should be understood. (shrink)

Research has shown that feelings of self-disgust may have a functional role in the genesis of depression by partially mediating the cross-sectional relationship between dysfunctional thoughts and depressive symptoms. However, there are many outstanding issues regarding these hypothesised associations. First, it is not yet clear whether self-disgust is a temporal antecedent, concomitant, or consequence of depressive experience. Second, it is not known whether the hypothesised mediation sequence is valid over time. Third, the relative contribution of disgust towards different aspects of (...) the self has not yet been examined. In the present longitudinal study, participants completed measures of dysfunctional cognitions, self-disgust and depressive symptoms at baseline, and at six and 12-month follow-ups. Analysis showed that self-disgust is best considered as antecedent to depressive symptoms; the hypothesised mediation model was partially supported, but is too simplistic; and disgust towards physical aspects of the self, rather than behaviour, was more important as a temporal predictor of depressive symptoms. The current results help elucidate the role of self-disgust as an antecedent of depressive experience. (shrink)

his volume investigates Proclus' own thought and his wide-ranging influence within late Neoplatonic, Alexandrine and Byzantinian philosophy and theology. It further explores how Procline metaphysics and doctrines of causality influence and transition into Arabic and Islamic thought, up until Richard Hooker in England, Spinoza in Holland and Pico in Italy. John Dillon provides a helpful overview of Proclus' thought, Harold Tarrant discusses Proclus' influence within Alexandrian philosophy and Tzvi Langermann presents ground breaking work on the Jewish reception of Proclus, focusing (...) on the work of Joseph Solomon Delmedigo (1591-1655), while Stephen Gersh presents a comprehensive synopsis of Proclus' reception throughout Christendom. The volume also presents works from notable scholars like Helen Lang, Sarah Wear and Crystal Addey and has a considerable strength in its presentation of Pseudo-Dionysius, Proclus' transmission and development in Arabic philosophy and the problem of the eternity of the world. It will be important for anyone interested in the development and transition of ideas from the late ancient world onwards. (shrink)

Platonic discourses concerning the soul are incredibly rich and multitiered. Plato's own diverse and disparate arguments and images offer competing accounts of how we are to understand the nature of the soul. Consequently, it should come as no surprise that the accounts of Platonists who engage Plato’s dialogues are often riddled with questions. This volume takes up the theories of well-known philosophers and theologians, including Plato, Plotinus, Proclus, the emperor Julian, and Origen, as well as lesser-known but equally important figures (...) in a collection of essays on topics such as transmigration of the soul, the nature of the Platonist enlightenment experience, soul and gender, pagan ritual practices, Christian and pagan differences about the soul, mental health and illness, and many other topics. Contributors include Crystal Addey, Sara Ahbel-Rappe, Dirk Baltzly, Robert Berchman, Jay Bregman, Luc Brisson, Kevin Corrigan, John Dillon, John F. Finamore, Lloyd P. Gerson, Dorian Gieseler Greenbaum, Elizabeth Hill, Sarah Klitenic Wear, Danielle A. Layne, Ilaria L. E. Ramelli, Gregory Shaw, Svetla Slaveva-Griffine, Suzanne Stern-Gillet, Harold Tarrant, Van Tu, and John D. Turner. (shrink)

Examines traditional sites of binary thinking in ancient Greek texts and culture to demonstrate surprising ambiguity, especially with regard to sexual difference.

The following hopes to bring Plato’s unwritten doctrines into proximity with Irigaray’s concept of the Two as found in works like To Be Two or I love to you. By focusing on the the indefinite Dyad, Plato's reported co-archai with the One, it will be evidenced that Platonism begins and ends with a One which is not One (a kind of Two). Further, in this Dyad's failure to be One, it ultimately comes to possess its own productive and destructive power (...) or, to use Irigaray's words, to love toward the Other in such a way as to produce or give birth to other others, real difference. Finally, Irigaray’s conception of the Two has dramatic social implications for her as a feminist, grounding a transformation of the political order of things. Due to this political import, the final section shifts to questioning whether Plato’s reported protological principles, the One and the indefinite Dyad, could perform a similar work. (shrink)

In the spirit of Pierre Hadot’s analysis of the value of the present moment in Hellenistic philosophies on happiness, the following argues that the Neoplatonic tradition heralded a similar view about the soul’s well-being. Primarily, the value of the present moment in Plotinus focuses on his arguments regarding the immortal soul’s desire for eternity that is lived in the ‘actuality of life’ right now. In contrast, the following analyzes the later Platonists and argues that Proclus offers a more practical and (...) thick understanding of human happiness in relation to the present. Overall, for Proclus the good is revealed in the connective nature of the present moment, a good discovered in the soul’s temporal activities. (shrink)

Many individuals with disabling conditions have difficulty with gait and balance control that may result in a fall. Exoskeletons are becoming an increasingly popular technology to aid in walking. Despite being a significant aid in increasing mobility, little attention has been paid to exoskeleton features to mitigate falls. To develop improved exoskeleton stability, quantitative information regarding how a user reacts to postural challenges while wearing the exoskeleton is needed. Assessing the unique responses of individuals to postural perturbations while wearing an (...) exoskeleton provides critical information necessary to effectively accommodate a variety of individual response patterns. This report provides kinematic and neuromuscular data obtained from seven healthy, college-aged individuals during posterior support surface translations with and without wearing a lower limb exoskeleton. A 2-min, static baseline standing trial was also obtained. Outcome measures included a variety of 0 dimensional measures such as center of pressure RMS, peak amplitude, velocities, pathlength, and electromyographic RMS, and peak amplitudes. These measures were obtained during epochs associated with the response to the perturbations: baseline, response, and recovery. T-tests were used to explore potential statistical differences between the exoskeleton and no exoskeleton conditions. Time series waveforms of the COP and EMG data were also analyzed. Statistical parametric mapping was used to evaluate the 1D COP and EMG waveforms obtained during the epochs with and without wearing the exoskeleton. The results indicated that during quiet stance, COP velocity was increased while wearing the exoskeleton, but the magnitude of sway was unchanged. The OD COP measures revealed that wearing the exoskeleton significantly reduced the sway magnitude and velocity in response to the perturbations. There were no systematic effects of wearing the exoskeleton on EMG. SPM analysis revealed that there was a range of individual responses; both behaviorally and among neuromuscular activation patterns. Using both the OD and 1D measures provided a more comprehensive representation of how wearing the exoskeleton impacts the responses to posterior perturbations. This study supports a growing body of evidence that exoskeletons must be personalized to meet the specific capabilities and needs of each individual end-user. (shrink)

We continue the work of [14, 3, 1, 19, 16, 4, 12, 11, 20] investigating the strength of set existence axioms needed for separable Banach space theory. We show that the separation theorem for open convex sets is equivalent to WKL 0 over RCA 0 . We show that the separation theorem for separably closed convex sets is equivalent to ACA 0 over RCA 0 . Our strategy for proving these geometrical Hahn-Banach theorems is to reduce to the finite-dimensional case (...) by means of a compactness argument. (shrink)

In hisCommentary on the AlcibiadesiProclus often discusses and links the peculiar epistemological category of “double ignorance” with evil and grievous error. To understand this more fully, the following analyzes Proclus’ concept of double ignorance, its characteristics and its causes. Markedly, due to his understanding of double ignorance, Proclus offers a response to the “Socratic” idea that no one willingly errs as this particular category of not-knowing enables him to explain how individuals, despite desiring and in some sense knowing the good, (...) fail or ‘miss the mark’ in articulating and doing the good. (shrink)

In The Neoplatonic Socrates, leading scholars in classics and philosophy address this gap by examining Neoplatonic attitudes toward the Socratic method, Socratic love, Socrates's divine mission and moral example, and the much-debated issue of moral rectitude. Collectively, they demonstrate the importance of Socrates for the majority of Neoplatonists, a point that has often been questioned owing to the comparative neglect of surviving commentaries on the Alcibiades, Gorgias, Phaedo, and Phaedrus, in favor of dialogues dealing explicitly with metaphysical issues. Supplemented with (...) a contextualizing introduction and a substantial appendix detailing where evidence for Socrates can be found in the extant literature, The Neoplatonic Socrates makes a clear case for the significant place Socrates held in the education and philosophy of late antiquity. (shrink)

In response to Timaeus’ invocation of the gods at Timaeus 27c1-d4, Proclus discusses, in his commentary on the text, the value of prayer. Heralding the fact that prayer marks the soul’s epistrophe or return to its causative principle, Proclus proceeds to exonerate those who invoke and pray to the gods, arguing that prayer enacts the emergence of human freedom in the determined world. He argues that since the gods are not only our superior causes but also the ones who have (...) wisely granted self-motion to human souls, we possess the freedom to acknowledge the role of providence or to remain, as Proclus describes, entrapped in the realm of Fate. In other words, human beings must decide (boulesis) to become what they are in the simple act of revering the gods, i.e. reverting to or knowing their divine cause. To pray is not to ask for things to be otherwise, but to pray is to fulfill providence freely, to become self-moved and self-knowing, therein becoming like and returning to our divine origins. Proclus concludes that this is the peculiar form of prayer for the philosopher as the philosophical life is dependent upon our will and the decisive commitment to articulating and communing with the highest metaphysical principles. Accordingly, for Proclus, Timaeus, in illustrating the order and providential nature of things in his “likely story,” frees himself from the trappings of fate, praying decisively and silently throughout his entire endeavor. (shrink)

During human evolutionary history, there were “trade-offs” between expending time and energy on child-rearing and mating, so both men and women evolved conditional mating strategies guided by cues signaling the circumstances. Many short-term matings might be successful for some men; others might try to find and keep a single mate, investing their effort in rearing her offspring. Recent evidence suggests that men with features signaling genetic benefits to offspring should be preferred by women as short-term mates, but there are trade-offs (...) between a mate's genetic fitness and his willingness to help in child-rearing. It is these circumstances and the cues that signal them that underlie the variation in short- and long-term mating strategies between and within the sexes. Key Words: conditional strategies; evolutionary psychology; fluctuating asymmetry; mating; reproductive strategies; sexual selection. (shrink)

Notorious for advancing a strict dichotomy between the masculine “demiurgic father” and the feminine “nurse/receptacle of becoming” as the “natural” origin of the cosmos, Plato's Timaeus has become a site for feminist interrogation. Most critics easily deem the text a masculine fantasy that projects feminine impotence and obligatory heterosexuality, reinforcing patriarchal power structures that are blindly reproduced in their historical reception. Consequently, this article analyzes the Neoplatonic replication of this framework, but with special attention given to Proclus's challenges to this (...) gendered and sexual context. In this late, sometimes forgotten figure, we find, rather surprisingly, a Platonist who neither sequesters the feminine to the domain of the passive receptacle nor charges her simply with being a bastard image of the masculine. Rather, for Proclus, the feminine becomes the site of lived, erotic power that produces and sustains the value of authentic otherness. Furthermore, Proclus offers a challenge to the naturalness of the sex binary, suggesting a radical queerness as the basis of all identity. Overall, we shall see how classical patriarchal thinkers may, despite themselves, offer subversive models that might present readers with possibilities for troubling the sexual prejudices of ancient metaphysical schemas. (shrink)

According to a widespread understanding among historians of philosophy, there is within the dialogues of Plato an underlying metaphysical dualism, one that devalues the body and the natural world, promoting, ultimately, an unattractive and repressive asceticism. An obvious support for this “standard” reading is provided by the Phaedo, wherein the soul is depicted as a prisoner in a cage ; but, as many readers would eagerly point out, most of Plato’s dialogues offer robust metaphors, images, or arguments that continuously suggest (...) that acolytes should denounce the body in favor of the soul.Indeed, it is against this background that Zoller’s book should be commended as an impressive endeavor to show just how... (shrink)

With regard to the theme “Reason in context,” the following stimulates a discussion on both Plato’s Socrates and the culpability of ignorance. By focusingon Plato’s Lysis, Alcibiades I, Philebus, and the Laws, I debunk the typical interpretation of Socratic moral intellectualism by evidencing that though there are various forms of ignorance in the Platonic dialogues, only one leads to shame-worthy error. Furthermore, in this endeavour to understand the “hierarchy” of ignorance in Plato, I take an unusual path and jump from (...) Antiquity to the Renaissance by connecting Plato’s Socrates to Erasmus’s Folly. By comparing these characters I show how both only condemn double ignorance, i.e., ignorance of ignorance joined with the pretence to knowledge. Ultimately, by analyzing this particularly heinous form of ignorance, I question whether in all periods and circumstances feigned wisdom more than “mere ignorance” leads to shame and disrepute. (shrink)

With regard to the theme “Reason in context,” the following stimulates a discussion on both Plato’s Socrates and the culpability of ignorance. By focusingon Plato’s Lysis, Alcibiades I, Philebus, and the Laws, I debunk the typical interpretation of Socratic moral intellectualism by evidencing that though there are various forms of ignorance in the Platonic dialogues, only one leads to shame-worthy error. Furthermore, in this endeavour to understand the “hierarchy” of ignorance in Plato, I take an unusual path and jump from (...) Antiquity to the Renaissance by connecting Plato’s Socrates to Erasmus’s Folly. By comparing these characters I show how both only condemn double ignorance, i.e., ignorance of ignorance joined with the pretence to knowledge. Ultimately, by analyzing this particularly heinous form of ignorance, I question whether in all periods and circumstances feigned wisdom more than “mere ignorance” leads to shame and disrepute. (shrink)

Regardless of the inconsistencies between Plato and his inheritors, the late neo-Platonist Proclus offers poignant answers to several contemporary debatesimbedded in Socratic scholarship. In the following, we will concentrate on Proclus’s interpretation of the Socratic elenchos and the provocative concept of double ignorance by clarifying their appearance in The Commentary on Plato’s Parmenides and The Commentary on the Alcibiades I. In this endeavor we shall unpack how Proclus characterizes the elenchos as an authentic dialectic purifying its recipients from an evil (...) caused by the conceit to knowledge, a condition which unfortunately almost all men suffer and require treatment. (shrink)

This chapter contains sections titled: Higher Yearning 101 Lesson 1: Socrates and Alcibiades on Stalking, Seduction, and Giving Birth Lesson 2: Peter Abelard and Heloise on Fondling and Losing “Tenure” Lesson 3: Heidegger and Arendt on Concealed Unconcealment “So I'll see you after class …”.

In this commentary, we attempt to broaden thinking and dialogue about how our ancestral past might have affected attachment and reproductive strategies. We highlight the theoretical benefits of formulating specific predictions of how different sources of stress might impact attachment and reproductive strategies differently, and we integrate some of these ideas with another recent evolutionary model of human mating.

31 chapters covering the Old Academy to Late Antiquity. See attached TOC.

Two studies examined the link between social dominance and male waist-to-hip ratio (WHR). Groups of four men interacted in a leaderless group discussion. In both studies, men with higher WHRs (associated with current and long-term health status) were rated by other group members as behaving more leader-like when an observer was present, and rated themselves as being more assertive. In Study 2, men with higher WHRs were rated by independent observers as behaving more dominantly, but only when the evaluator was (...) present. These results are discussed in terms of evolutionary models of health, attraction, and intrasexual competition. (shrink)

The last two decades have seen two significant trends emerging within the philosophy of science: the rapid development and focus on the philosophy of the specialised sciences, and a resurgence of Aristotelian metaphysics, much of which is concerned with the possibility of emergence, as well as the ontological status and indispensability of dispositions and powers in science. Despite these recent trends, few Aristotelian metaphysicians have engaged directly with the philosophy of the specialised sciences. Additionally, the relationship between fundamental Aristotelian concepts—such (...) as "hylomorphism", "substance", and "faculties"—and contemporary science has yet to receive a critical and systematic treatment. _Neo-Aristotelian Perspectives on Contemporary Science _aims to fill this gap in the literature by bringing together essays on the relationship between Aristotelianism and science that cut across interdisciplinary boundaries. The chapters in this volume are divided into two main sections covering the philosophy of physics and the philosophy of the life sciences. Featuring original contributions from distinguished and early-career scholars, this book will be of interest to specialists in analytical metaphysics and the philosophy of science. (shrink)

A distinguished critic explores the term "situatedness" - the self's position in time and place in the world and its treatment seen in legal theory, social ...

This response reinforces several major themes in our target article: (a) the importance of sex-specific, within-sex variation in mating tactics; (b) the relevance of optimality thinking to understanding that variation; (c) the significance of special design for reconstructing evolutionary history; (d) the replicated findings that women's mating preferences vary across their menstrual cycle in ways revealing special design; and (e) the importance of applying market phenomena to understand the complex dynamics of mating. We also elaborate on three points: (1) Men (...) who have indicators of genetic fitness may provide more direct benefits when female demand for extra-pair and short-term sex is very low; (2) both men and women track ecological cues to make mating decisions; and (3) more research on female orgasm is needed. (shrink)