Posner & Raichle illustrate how neuroimaging blends profitably with neuropsychology and electrophysiology to advance cognitive theory. Recognizing that there are limitations to each of these techniques, we nonetheless argue that their confluence has fundamentally changed the way cognitive psychologists think about problems of the mind.

Robert Ranisch’s and Stefan Lorenz Sorgner’s Post- and Transhumanism. An Introduction provides a broad background for anyone interested in the societal and philosophical repercussions of new technologies. As the title suggests, the volume specifically centers on the trans- and posthumanism debate, which, over the past two decades, has been focusing on the way our highly technological societies raise an entirely new set of questions that urge to be answered and discussed. Of particular importance to this debate is the necessity (...) for new understandings about what it means to be human in a world where the traditional distinctions between human and non-human, technology and biology, as well as nature and culture, are becoming increasingly ambiguous.The book’s self-announced aim is to address the concepts of trans- and posthumanism, exploring their ‘common foundations, topics, and resources of influence’ , as a means to help clarify a ‘widespread conceptual confusion’ . This is a .. (shrink)

continent. 1.2 (2011): 76-77. Please click to listen to the mp3 files of deep brain recordings of individual brain cells, the smallest unit of the brain, in a whole, intact living brain. Each brain region’s cells possess an electrical signature. During recordings electrical signals are transformed into sound to facilitate auditory identification of cells during a process called “mapping.” Subthalamic nucleus by continent Cortex by continent Mapping is an important step in successfully identifying and localizing the appropriate target site in (...) the brain for an experimental therapeutic procedure called deep brain stimulation which has been used for patients with movement disorders and, more recently, for patients with psychiatric disorders. Thalamus by continent I have pursued a career as a neuroscientist for the past decade because I wanted to learn about the mind. In my most recent research, I record electrical activity from individual cells in the brain, and look at individual brain cells with a high resolution, electron microscope. Globus Pallidus (internal segment) by continent Globus Pallidus (external segment) by continent The closer I examine the brain, the less I learn about the mind. Rather, what has been most informative about the mind is how people—neuroscientists and non-neuroscientists alike—interpret neuroscience data. Some cognitive neuroscientists have proposed the qualities we hold most precious as humans, like morality and free will, exist only in the context of human interaction. Likewise, I propose that the mind does not exist in a vacuum and one’s mind only necessitates distinction in a social context, and the mind’s existence may only be relevant due to its relative relationships. In sum, bodies have brains. People have minds. Striatum by continent I invite readers to reflect on and/or refute these statements after listening to these recordings of the brain in action. These regions are part of the cortico-basal ganglia-thalamo-cortical circuit, which is thought to possess parallel, functionally segregated loops including a motor-movement circuit and limbic-emotional circuit which work together to generate behavior (e.g. motivated movements) and have been researched for their role in Parkinson’s disease as well as Obsessive Compulsive Disorder. EDITOR'S SUGGESTED RESOURCES Michael Gazzaniga's lecture, “Free Yet Determined and Constrained” at Edinburgh University Gifford Lectures in 19 October, 2009 is an excellent discussion of the field. It can be viewed on Edinburgh University's Youtube channel . The Cognitive Neuroscience of the Mind . Eds. Patricia A. Reuter-Lorenz, Kathleen Baynes, George R. Mangun, and Elizabeth A. Phelps. Cambridge: MIT Press. 2010. Print. (shrink)

Introduction to the Institutional Logics Perspective -- Precursors to the Institutional Logics Perspective -- Defining the Inter-institutional System -- The Emergence, Stability and Change of the Inter-institutional System -- Micro-Foundations of Institutional Logics -- The Dynamics of Organizational Practices and Identities -- The Emergence and Evolution of Field-Level Logics -- Implications for Future Research.

English summary: In its core, this book represents a defense of the thesis that we are essentially biological creatures of the species Homo sapiens - and not essentially persons. This thesis has consequences for the problem of personal identity. An important aspect of its defense - and the book's second central line of argumentation - is, therefore, to substantiate that ours are the diachronic identity conditions of biological beings. Attempting to reach both argumentation goals, one has to overcome some obstacles, (...) from motivating an appropriate ontological framework via explaining the concept of the animate being to demonstrating that essentialism is still a viable option today. In this way, a picture gradually emerges which places us humans, as living beings among other living beings, in a biological world, without, however, playing down that we are, at least typically, also persons with a rich spiritual life. German description: Das Buch ist im Kern eine Verteidigung der These, dass wir wesentlich biologische Lebewesen der Spezies Homo sapiens sind - und nicht etwa wesentlich Personen. Diese These hat Konsequenzen fur das Problem der personalen Identitat. Ein wichtiger Aspekt ihrer Verteidigung - und der zweite zentrale Argumentationsstrang des Buchs - liegt demnach darin, zu begrunden, dass wir die diachronen Identitatsbedingungen biologischer Lebewesen haben. Der Versuch, beide Argumentstationsziele zu erreichen, muss einige Hurden nehmen: angefangen von einer Motivierung eines passenden ontologischen Rahmens uber eine Erlauterung des Begriffs des Lebewesens bis hin zu dem Nachweis, dass ein Essentialismus heutzutage noch eine gangbare Option ist. Auf diese Weise entsteht nach und nach ein Bild, das uns Menschen, als Lebewesen unter anderen Lebewesen, in eine biologische Welt einordnet, ohne dabei aber kleinzureden, dass wir, zumindest typischerweise, auch Personen mit einem reichhaltigen geistigen Leben sind. (shrink)

Overview -- Locke's internal sense and Kant's changing views -- Personal identity amd its problems -- Rationalist metaphysics of mind -- Consciousness, self-consciousness, and cognition -- Strands of Argument in the Duisburg Nachlass -- A transcendental deduction for a priori concepts -- Synthesis : why and how? -- Arguing for apperception -- The power of apperception -- "I-think" as the destroyer of rational psychology -- Is Kant's theory consistent? -- The normativity objection -- Is Kant's thinker (as such) a free (...) and responsible agent? -- Kant our contemporary. (shrink)

Duality in Logic and Language [draft--do not cite this article] Duality phenomena occur in nearly all mathematically formalized disciplines, such as algebra, geometry, logic and natural language semantics. However, many of these disciplines use the term ‘duality’ in vastly different senses, and while some of these senses are intimately connected to each other, others seem to be entirely … Continue reading Duality in Logic and Language →.

In recent years, a number of authors have started studying Aristotelian diagrams containing metalogical notions, such as tautology, contradiction, satisfiability, contingency, strong and weak interpretations of contrariety, etc. The present paper is a contribution to this line of research, and its main aims are both to extend and to deepen our understanding of metalogical diagrams. As for extensions, we not only study several metalogical decorations of larger and less widely known Aristotelian diagrams, but also consider metalogical decorations of another type (...) of logical diagrams, viz. duality diagrams. At a more fundamental level, we present a unifying perspective which sheds new light on the connections between new and existing metalogical diagrams, as well as between object- and metalogical diagrams. Overall, the paper studies two types of logical diagrams and four kinds of metalogical decorations. (shrink)

Abstract:During recent years, the principle and practice of employment-at-will have been under attack. While progress has been made in eroding the practice, the principle still governs the philosophical assumptions underlying employment practices in the United States, and, indeed, EAW has been promulgated as one of the ways to address economic ills in other countries. This paper will briefly review the major critiques of EAW. Given the failure of these arguments to erode the underpinnings of EAW, we shall suggest new avenues (...) for approaching employment issues to achieve the desirable goal of employee dignity and respect. (shrink)

The aim of this paper is to initiate a systematic exploration of the model theory of epistemic plausibility models (EPMs). There are two subtly different definitions in the literature: one by van Benthem and one by Baltag and Smets. Because van Benthem's notion is the most general, most of the paper is dedicated to this notion. We focus on the notion of bisimulation, and show that the most natural generalization of bisimulation to van Benthem-type EPMs fails. We then introduce parametrized (...) bisimulations, and prove various bisimulationimplies- equivalence theorems, a Hennessy-Milner theorem, and several (un)definability results. We discuss the problems arising from the fact that these bisimulations are syntax-dependent (and thus not fully structural), and we present and compare two different ways of coping with this issue: adding a modality to the language, and putting extra constraints on the models. We argue that the most successful solution involves restricting to uniform and locally connected (van Benthem-type) EPMs: for this subclass the intuitively most natural notion of bisimulation and the technically sound notion coincide. Such EPMs turn out to correspond exactly with Baltag/Smets-type EPMs, which can be interpreted as constituting a methodological argument, favoring Baltag and Smets's definition of EPM over that of van Benthem. (shrink)

In Frege's Conception of Logic Patricia A. Blanchette explores the relationship between Gottlob Frege's understanding of conceptual analysis and his understanding of logic.

This paper studies the Lockean thesis from the perspective of contemporary epistemic logic. The Lockean thesis states that belief can be defined as ‘sufficiently high degree of belief’. Its main problem is that it gives rise to a notion of belief which is not closed under conjunction. This problem is typical for classical epistemic logic: it is single-agent and static. I argue that from the perspective of contemporary epistemic logic, the Lockean thesis fares much better. I briefly mention that it (...) can successfully be extended from single-agent to multi-agent settings. More importantly, I show that accepting the Lockean thesis (and a more sophisticated version for conditional beliefs) leads to a significant and unexpected unification in the dynamic behavior of (conditional) belief and high (conditional) probability with respect to public announcements. This constitutes a methodological argument in favor of the Lockean thesis. Furthermore, if one accepts Baltag’s Erlangen program for epistemology, this technical observation has even stronger philosophical implications: because belief and high probability display the same dynamic behavior, it is plausible that they are indeed one and the same epistemic notion. (shrink)

The concepts expressed by social role terms such as artist and scientist are unique in that they seem to allow two independent criteria for categorization, one of which is inherently normative. This study presents and tests an account of the content and structure of the normative dimension of these “dual character concepts.” Experiment 1 suggests that the normative dimension of a social role concept represents the commitment to fulfill the idealized basic function associated with the role. Background information can affect (...) which basic function is associated with each social role. However, Experiment 2 indicates that the normative dimension always represents the relevant commitment as an end in itself. We argue that social role concepts represent the commitments to basic functions because that information is crucial to predict the future social roles and role-dependent behavior of others. (shrink)

This paper studies John Buridan's octagons of opposition for the de re modal propositions and the propositions of unusual construction. Both Buridan himself and the secondary literature have emphasized the strong similarities between these two octagons (as well as a third one, for propositions with oblique terms). In this paper, I argue that the interconnection between both octagons is more subtle than has previously been thought: if we move beyond the Aristotelian relations, and also take Boolean considerations into account, then (...) the strong analogy between Buridan's octagons starts to break down. These differences in Boolean structure can already be discerned within the octagons themselves; on a more abstract level, they lead to these two octagons having different degrees of Boolean complexity (i.e. Boolean closures of different sizes). These results are obtained by means of bitstring analysis, which is one of the key tools from contemporary logical geometry. Finally, I argue that this historical investigation is directly relevant for the theoretical framework of logical geometry, and discuss how it helps us to address certain open questions in this framework. (shrink)

Conceptual engineering is the practice of revising concepts to improve how people talk and think. Its ability to improve talk and thought ultimately hinges on the successful dissemination of desired conceptual changes. Unfortunately, the field has been slow to develop methods to directly test what barriers stand in the way of propagation and what methods will most effectively propagate desired conceptual change. In order to test such questions, this paper introduces the masked time-lagged method. The masked time-lagged method tests people's (...) conceptual understanding at two different points in time without their knowledge of being tested, allowing us to measure conceptual revision in action. Using a masked time-lagged design on a content internalist framework, we attempted to revise PLANET and DINOSAUR in online participants to match experts' concepts. We successfully revised PLANET but not DINOSAUR, demonstrating some of the difficulties conceptual engineers face. Nonetheless, this paper provides conceptual engineers, regardless of framework, with the tools to tackle questions related to implementation empirically and head-on. (shrink)

In the recent debate on future contingents and the nature of the future, authors such as G. A. Boyd, W. L. Craig, and E. Hess have made use of various logical notions, such as the Aristotelian relations of contradiction and contrariety, and the ‘open future square of opposition.’ My aim in this paper is not to enter into this philosophical debate itself, but rather to highlight, at a more abstract methodological level, the important role that Aristotelian diagrams can play in (...) organizing and clarifying the debate. After providing a brief survey of the specific ways in which Boyd and Hess make use of Aristotelian relations and diagrams in the debate on the nature of the future, I argue that the position of open theism is best represented by means of a hexagon of opposition. Next, I show that on the classical theist account, this hexagon of opposition ‘collapses’ into a single pair of contradictory statements. This collapse from a hexagon into a pair has several aspects, which can all be seen as different manifestations of a single underlying change. (shrink)

This paper studies Aumann’s agreeing to disagree theorem from the perspective of dynamic epistemic logic. This was first done by Dégremont and Roy (J Phil Log 41:735–764, 2012) in the qualitative framework of plausibility models. The current paper uses a probabilistic framework, and thus stays closer to Aumann’s original formulation. The paper first introduces enriched probabilistic Kripke frames and models, and various ways of updating them. This framework is then used to prove several agreement theorems, which are natural formalizations of (...) Aumann’s original result. Furthermore, a sound and complete axiomatization of a dynamic agreement logic is provided, in which one of these agreement theorems can be derived syntactically. These technical results are used to show the importance of explicitly representing the dynamics behind the agreement theorem, and lead to a clarification of some conceptual issues surrounding the agreement theorem, in particular concerning the role of common knowledge. The formalization of the agreement theorem thus constitutes a concrete example of the so-called dynamic turn in logic. (shrink)

It is generally assumed that emotion concepts are purely descriptive. However, recent investigations suggest that the concept of happiness includes information about the morality of the agent's life. In this study, we argue that normative influences on emotion concepts are not restricted to happiness and are not about moral norms. In a series of studies, we show that emotion attribution is influenced by whether the agent's psychological and bodily states fit the situation in which they are experienced. People consider that (...) emotions are not just about feeling in certain ways, but also about feeling the right way. (shrink)

This paper explores the interplay between logic-sensitivity and bitstring semantics in the square of opposition. Bitstring semantics is a combinatorial technique for representing the formulas that appear in a logical diagram, while logic-sensitivity entails that such a diagram may depend, not only on the formulas involved, but also on the logic with respect to which they are interpreted. These two topics have already been studied extensively in logical geometry, and are thus well-understood by themselves. However, the precise details of their (...) interplay turn out to be far more complicated. In particular, the paper describes an elegant and natural interaction between bitstrings and logic-sensitivity, which makes perfect sense when bitstrings are viewed as purely combinatorial entities. However, when we view bitstrings as semantically meaningful entities (which is actually the standard perspective, cf. the term ‘bitstring semantics’!), this interaction does not seem to have a full and equally natural counterpart. The paper describes some attempts to address this situation, but all of them are ultimately found wanting. For now, it thus remains an open problem to capture this interaction between bitstrings and logic-sensitivity from a semantic (rather than merely a combinatorial) perspective. (shrink)

This article describes a specific pedagogical context for an advanced logic course and presents a strategy that might facilitate students’ transition from the object-theoretical to the metatheoretical perspective on logic. The pedagogical context consists of philosophy students who in general have had little training in logic, except for a thorough introduction to syllogistics. The teaching strategy tries to exploit this knowledge of syllogistics, by emphasizing the analogies between ideas from metalogic and ideas from syllogistics, such as existential import, the distinction (...) between contradictories and contraries, and the square of opposition. This strategy helps to improve students’ understanding of metalogic, because it allows the students to integrate these new ideas with their previously acquired knowledge of syllogistics. (shrink)

The Sure-Thing Principle famously appears in Savage’s axiomatization of Subjective Expected Utility. Yet Savage introduces it only as an informal, overarching dominance condition motivating his separability postulate P2 and his state-independence postulate P3. Once these axioms are introduced, by and large, he does not discuss the principle any more. In this note, we pick up the analysis of the Sure-Thing Principle where Savage left it. In particular, we show that each of P2 and P3 is equivalent to a dominance condition; (...) that they strengthen in different directions a common, basic dominance axiom; and that they can be explicitly combined in a unified dominance condition that is a candidate formal statement for the Sure-Thing Principle. Based on elementary proofs, our results shed light on some of the most fundamental properties of rational choice under uncertainty. In particular they imply, as corollaries, potential simplifications for Savage’s and the Anscombe- Aumann axiomatizations of Subjective Expected Utility. Most surprisingly perhaps, they reveal that in Savage’s axiomatization, P3 can be weakened to a natural strengthening of so-called Obvious Dominance. (shrink)

In logic, Aristotelian diagrams are almost always assumed to be closed under negation, and are thus highly symmetric in nature. In linguistics, by contrast, these diagrams are used to study lexicalization, which is notoriously not closed under negation, thus yielding more asymmetric diagrams. This paper studies the interplay between logical symmetry and linguistic asymmetry in Aristotelian diagrams. I discuss two major symmetric Aristotelian diagrams, viz. the square and the hexagon of opposition, and show how linguistic considerations yield various asymmetric versions (...) of these diagrams. I then discuss a pentagon of opposition, which occupies an uneasy position between the square and the hexagon. Although this pentagon belongs neither to the symmetric realm of logic nor to the asymmetric realm of linguistics, it occurs several times in the literature. The oldest known occurrence can be found in the cosmological work of the 14th-century author Nicole Oresme. (shrink)

Burgess-Jackson has recently suggested that the debate between theism and atheism can be represented by means of a classical square of opposition. However, in light of the important role that the position of agnosticism plays in Burgess-Jackson’s analysis, it is quite surprising that this position is not represented in the proposed square of opposition. I therefore argue that the square of opposition should be extended to a slightly larger, more complex Aristotelian diagram, viz., a hexagon of opposition. Since this hexagon (...) does represent the position of agnosticism, it arguably yields a more helpful representation of the theism/atheism debate. It would be naïve to presume that Aristotelian diagrams can, by themselves, lead to a comprehensive solution of debates as intricate as that between theism and atheism. Nevertheless, this paper aims to show that these diagrams — especially if they are chosen carefully — have an important methodological role to play, by systematically organizing and clarifying the debate. (shrink)

The most common approach to understanding the semantics of the concept of pain is third-person thought experiments. By contrast, the most frequent and most relevant uses of the folk concept of pain are from a first-person perspective in conversational settings. In this paper, we use a set of linguistic tools to systematically explore the semantics of what people communicate when reporting pain from a first-person perspective. Our results suggest that only a pluralistic view can do justice to the way we (...) talk about pain from a first-person perspective: The semantic content of the folk concept of pain consists of information about both an unpleasant feeling and a disruptive bodily state. Pain linguistics thus provides new insights into ordinary pain language and poses an interesting challenge to the dominant unitary views of pain. (shrink)

Progress in the neurosciences is profoundly changing our conception of ourselves. Contrary to time-honored intuition, the mind turns out to be a complex of brain functions. And contrary to the wishful thinking of some philosophers, there is no stemming the revolutionary impact that brain research will have on our understanding of how the mind works. Brain-Wise is the sequel to Patricia Smith Churchland's Neurophilosophy, the book that launched a subfield. In a clear, conversational manner, this book examines old questions (...) about the nature of the mind within the new framework of the brain sciences. What, it asks, is the neurobiological basis of consciousness, the self, and free choice? How does the brain learn about the external world and about its own introspective world? What can neurophilosophy tell us about the basis and significance of religious and moral experiences? Drawing on results from research at the neuronal, neurochemical, system, and whole-brain levels, the book gives an up-to-date perspective on the state of neurophilosophy—what we know, what we do not know, and where things may go from here. (shrink)

In this paper, we consider certain cardinals in ZF (set theory without AC, the axiom of choice). In ZFC (set theory with AC), given any cardinals C and D, either C ≤ D or D ≤ C. However, in ZF this is no longer so. For a given infinite set A consider $\operatorname{seq}^{1 - 1}(A)$ , the set of all sequences of A without repetition. We compare $|\operatorname{seq}^{1 - 1}(A)|$ , the cardinality of this set, to |P(A)|, the cardinality of (...) the power set of A. What is provable about these two cardinals in ZF? The main result of this paper is that $ZF \vdash \forall A(|\operatorname{seq}^{1 - 1}(A)| \neq|\mathscr{P}(\mathscr{A})|)$ , and we show that this is the best possible result. Furthermore, it is provable in ZF that if B is an infinite set, then $|\operatorname{fin}(B)| <|\mathscr{P}(B)|$ even though the existence for some infinite set B* of a function f from $\operatorname{fin}(B^\ast)$ onto P(B*) is consistent with ZF. (shrink)

Several authors have recently studied Aristotelian diagrams for various metatheoretical notions from logic, such as tautology, satisfiability, and the Aristotelian relations themselves. However, all these metalogical Aristotelian diagrams focus on the semantic (model-theoretical) perspective on logical consequence, thus ignoring the complementary, and equally important, syntactic (proof-theoretical) perspective. In this paper, I propose an explanation for this discrepancy, by arguing that the metalogical square of opposition for semantic consequence exhibits a natural analogy to the well-known square of opposition for the categorical (...) statements from syllogistics, but that this analogy breaks down once we move from semantic to syntactic consequence. I then show that despite this difficulty, one can indeed construct metalogical Aristotelian diagrams from a syntactic perspective, which have their own, equally elegant characterization in terms of the categorical statements. Finally, I construct several metalogical Aristotelian diagrams that incorporate both semantic and syntactic consequence (and their interaction), and study how they are influenced by the underlying logical system’s soundness and/or completeness. All of this provides further support for the methodological/heuristic perspective on Aristotelian diagrams, which holds that the main use of these diagrams lies in facilitating analogies and comparisons between prima facie unrelated domains of investigation. (shrink)

For a set M, let \\) denote the set of all finite sequences which can be formed with elements of M, and let \ denote the set of all 2-element subsets of M. Furthermore, for a set A, let Open image in new window denote the cardinality of A. It will be shown that the following statement is consistent with Zermelo–Fraenkel Set Theory \: There exists a set M such that Open image in new window and no function Open image (...) in new window is finite-to-one. (shrink)

What is morality? Where does it come from? And why do most of us heed its call most of the time? In Braintrust, neurophilosophy pioneer Patricia Churchland argues that morality originates in the biology of the brain. She describes the "neurobiological platform of bonding" that, modified by evolutionary pressures and cultural values, has led to human styles of moral behavior. The result is a provocative genealogy of morals that asks us to reevaluate the priority given to religion, absolute rules, (...) and pure reason in accounting for the basis of morality. Moral values, Churchland argues, are rooted in a behavior common to all mammals--the caring for offspring. The evolved structure, processes, and chemistry of the brain incline humans to strive not only for self-preservation but for the well-being of allied selves--first offspring, then mates, kin, and so on, in wider and wider "caring" circles. Separation and exclusion cause pain, and the company of loved ones causes pleasure; responding to feelings of social pain and pleasure, brains adjust their circuitry to local customs. In this way, caring is apportioned, conscience molded, and moral intuitions instilled. A key part of the story is oxytocin, an ancient body-and-brain molecule that, by decreasing the stress response, allows humans to develop the trust in one another necessary for the development of close-knit ties, social institutions, and morality. A major new account of what really makes us moral, Braintrust challenges us to reconsider the origins of some of our most cherished values. (shrink)

In order to elucidate his logical analysis of modal quantified propositions (e.g. ‘all men are necessarily mortal’), the 14th century philosopher John Buridan constructed a modal octagon of oppositions. In the present paper we study this modal octagon from the perspective of contemporary logical geometry. We argue that the modal octagon contains precisely six squares of opposition as subdiagrams, and classify these squares based on their logical properties. On a more abstract level, we show that Buridan’s modal octagon precisely captures (...) the interaction between two classical squares of opposition, viz. one for the quantifiers and one for the modalities. Finally, we argue that several aspects of our contemporary formal analyses were already hinted at by Buridan himself. (shrink)

In recent years, a number of prominent scientists have argued that free will is an illusion, appealing to evidence demonstrating that information about brain activity can be used to predict behavior before people are aware of having made a decision. These scientists claim that the possibility of perfect prediction based on neural information challenges the ordinary understanding of free will. In this paper we provide evidence suggesting that most people do not view the possibility of neuro-prediction as a threat to (...) free will unless it also raises concerns about manipulation of the agent’s behavior. In Experiment 1 two scenarios described future brain imaging technology that allows perfect prediction of decisions and actions based on earlier neural activity, and this possibility did not undermine most people’s attributions of free will or responsibility, except in the scenario that also allowed manipulation. In Experiment 2 the scenarios increased the salience of the physicalist implications of neuro-prediction, while in Experiment 3 the scenarios suggested dualism, with perfect prediction by mindreaders. The patterns of results for these two experiments were similar to the results in Experiment 1, suggesting that participants do not understand free will to require specific metaphysical conditions regarding the mind–body relation. Most people seem to understand free will in a way that is not threatened by perfect prediction based on neural information, suggesting that they believe that just because “my brain made me do it,” that does not mean that I didn’t do it of my own free will. (shrink)

If we assume the axiom of choice, then every two cardinal numbers are comparable, In the absence of the axiom of choice, this is no longer so. For a few cardinalities related to an arbitrary infinite set, we will give all the possible relationships between them, where possible means that the relationship is consistent with the axioms of set theory. Further we investigate the relationships between some other cardinal numbers in specific permutation models and give some results provable without using (...) the axiom of choice. (shrink)

For \(n\in \omega \), the weak choice principle \(\textrm{RC}_n\) is defined as follows: _For every infinite set_ _X_ _there is an infinite subset_ \(Y\subseteq X\) _with a choice function on_ \([Y]^n:=\{z\subseteq Y:|z|=n\}\). The choice principle \(\textrm{C}_n^-\) states the following: _For every infinite family of_ _n_-_element sets, there is an infinite subfamily_ \({\mathcal {G}}\subseteq {\mathcal {F}}\) _with a choice function._ The choice principles \(\textrm{LOC}_n^-\) and \(\textrm{WOC}_n^-\) are the same as \(\textrm{C}_n^-\), but we assume that the family \({\mathcal {F}}\) is linearly orderable (...) (for \(\textrm{LOC}_n^-\) ) or well-orderable (for \(\textrm{WOC}_n^-\) ). In the first part of this paper, for \(m,n\in \omega \) we will give a full characterization of when the implication \(\textrm{RC}_m\Rightarrow \textrm{WOC}_n^-\) holds in \({\textsf {ZF}}\). We will prove the independence results by using suitable Fraenkel-Mostowski permutation models. In the second part, we will show some generalizations. In particular, we will show that \(\textrm{RC}_5\Rightarrow \textrm{LOC}_5^-\) and that \(\textrm{RC}_6\Rightarrow \textrm{C}_3^-\), answering two open questions from Halbeisen and Tachtsis (Arch Math Logik 59(5):583–606, 2020). Furthermore, we will show that \(\textrm{RC}_6\Rightarrow \textrm{C}_9^-\) and that \(\textrm{RC}_7\Rightarrow \textrm{LOC}_7^-\). (shrink)

For an integer \, Ramsey Choice\ is the weak choice principle “every infinite setxhas an infinite subset y such that\ has a choice function”, and \ is the weak choice principle “every infinite family of n-element sets has an infinite subfamily with a choice function”. In 1995, Montenegro showed that for \, \. However, the question of whether or not \ for \ is still open. In general, for distinct \, not even the status of “\” or “\” is known. (...) In this paper, we provide partial answers to the above open problems and among other results, we establish the following:1.For every integer \, if \ is true for all integers i with \, then \ is true for all integers i with \.2.If \ are any integers such that for some prime p we have \ and \, then in \: \ and \.3.For \, \\\ implies \, and \ implies neither \ nor \ in \.4.For every integer \, \ implies “every infinite linearly orderable family of k-element sets has a partial Kinna–Wagner selection function” and the latter implication is not reversible in \ ). In particular, \ strictly implies “every infinite linearly orderable family of 3-element sets has a partial choice function”.5.The Chain-AntiChain Principle implies neither \ nor \ in \, for every integer \. (shrink)

Parmenides of Elea was the most important and influential philosopher before Plato. He rejected as impossible the scientific inquiry practiced by the earlier Presocratic philosophers and held that generation, destruction, and change are unreal and that only one thing exists. In this book, Patricia Curd argues that Parmenides sought to reform rather than to reject scientific inquiry, and she offers a more coherent account of his influence on later philosophers._ _The Legacy of Parmenides_ examines Parmenides' arguments, considering his connection (...) to earlier Greek thought and how his account of what-is could have served as a model for later philosophers. Curd also explores the theories of his successors, including the Pluralists, the Atomists, the later Eleatics, and the later Presocratics. She concludes with a discussion of the importance of Parmenides' work to Plato's _Theory of Forms._ _The Legacy of Parmenides_ challenges traditional views of early Greek philosophy and provides new insights into the work of Parmenides. "_The Legacy of Parmenides_ represents a milestone... of Parmenides' interpretation. It is full of ideas and tells a coherent story about Parmenides and early Greek thought." --_ Alexander Nehamas, Princeton University___ "Professor Curd offers a genuinely original and possibly correct interpretation of the core thesis of the poem of Parmenides in a field so well worked over that saying something both new and true is profoundly difficult, this is a notable achievement." --_ Thomas M. Robinson, University of Toronto___ "This will be a substantial book in the story of early Greek philosophy, and future writers on the tradition from Thales through Plato will not be able to ignore it without missing an important interpretive alternative. It will be of value to students of Presocratic philosophy or the Greek tradition, as well as to students of the scientific revolution, cosmology, the origins of logic, or comparative mysticism." --_ Scott W. Austin, Texas A&M University___ PATRICIA CURD_ is professor at Purdue University where she works primarily in Ancient Philosophy. She is a co-editor of _Readings in Ancient Greek Philosophy_, and is the editor of _A Presocratics Reader._. (shrink)