Arendt's concept of common sense has generally been misunderstood. It is almost exclusively interpreted in light of Kant's common sense, either as an espousal of the latter or as a distortion of it. This narrow reading of Arendtian common sense has led to a problem, as her uses of the concept do not always fit its Kantian understanding. This has led to accusing her of being inconsistent, or as holding on to several, incompatible concepts of common sense.This article argues that (...) Arendt has one complex concept of common sense, used more or less consistently throughout her writings. Rather than understanding Arendt's common sense in light of Kant's, as most readers do, I demonstrate its links to Aristotle and to the eighteenth‐century Scottish school of common sense. By doing so I turn attention to a difficulty that has thus far not been adequately treated, namely the fact that Arendt presents two, allegedly contradictory pictures of the relation between common sense on the one hand and science and philosophy on the other: a picture in which science and philosophy depend upon common sense, versus one in which they find themselves in a conflict that eventually leads to the loss or demise of common sense. The last part of the article suggests a way to settle the tension between these two pictures, by understanding the political significance Arendt ascribes to them as two distinct yet complementary ways of approaching the modern phenomenon of totalitarianism. (shrink)

Post-critical pedagogy, which offers a significant alternative to the dominant trends in contemporary philosophy of education, objects to seeing education as instrumental to other ends: it attempts to conceive of education as autotelic, namely as having intrinsic value. While there are good reasons for accepting the post-critical reservations with the instrumentalization of education, I argue that its autonomy is equally problematic, as it risks turning the philosophy of education—perhaps education itself—into a privileged activity, out of touch with the most important (...) issues in the contemporary world. In this paper I offer post-critical pedagogy a way out of this dilemma, by drawing on Walter Benjamin’s essay “The Work of Art in the Age of Its Technological Reproducibility”. After presenting the thesis concerning the autonomy of art held by Benjamin’s Frankfurt School friends, and pointing to the similarity between their view and that of post-critical pedagogy, I articulate six Benjaminian theses on post-critical pedagogy. Following Benjamin’s claim that the technological reproducibility of art changes the way it is perceived as well as its political function, I argue that school is an educational technology that reproduces the world to the masses without an “aura”, in a way that allows for political critique that does not reduce education to politics. Next, I highlight the importance of the school to post-critical pedagogy, and contribute to developing the critical-political aspect that remains essential to post-critical pedagogy. Finally, the Benjaminian perspective also makes it possible to reflect on the relation of digital technologies of reproduction to post-critical pedagogy. (shrink)

The republican political tradition, which originated in Ancient Rome and picked up by several early-modern thinkers, has been revived in the last couple of decades following the seminal works of historian Quentin Skinner and political theorist Philip Pettit. Although educational questions do not normally occupy the center stage in republican theory, various theorists working within this framework have already highlighted the significance of education for any functioning republic. Looking at educational questions through the lens of freedom as non-domination has already (...) yielded important insights to discussions of political education. However, consideration of the existing republican educational discourse in light of the wide range of issues discussed in Pettit’s recent works reveals that it suffers from two major lacunae. First, it does not take into consideration the distinction (and deep connection) between democracy and social justice that has become central to Pettit’s republicanism. Thus, the current discussion focuses almost exclusively on education for democratic citizenship and hardly touches upon social justice. Second, the current literature thinks mainly in terms of educating future citizens, rather than conceiving of students also as political agents in the present, and of school itself as a site of non-domination. This paper aims at filling these voids, and it will therefore be oriented along two intersecting axes: the one between democracy and justice, and the other between future citizenship in the state and present citizenship at school. The resulting four categories will organize the discussion: future citizens and democracy; future citizens and social justice; present citizens and democracy; present citizens and social justice. This will not only enable us to draw a clearer line between the civic republican and liberal educational theories, but also make civic republican education a viable alternative to current educational approaches. (shrink)

This article offers a new interpretation of Adorno’s new categorical imperative : it suggests that the new imperative is an important element of Adorno’s moral philosophy and at the same time runs counter to some of its essential features. It is suggested that Adorno’s moral philosophy leads to two aporiae, which create an impasse that the new categorical imperative attempts to circumvent. The first aporia results from the tension between Adorno’s acknowledgement that praxis is an essential part of moral philosophy, (...) and his view according to which existing social conditions make it impossible for moral knowledge to be translated into right action. The second aporia results from the tension between the uncompromising sensitivity to suffering that underlies Adorno’s moral thought, and his analysis of the culture industry mechanisms which turn people into happy, satisfied customers—an incompatibility which threatens to pull the rug out from under Adorno’s moral philosophy. My interpretation of the new categorical imperative focuses on two characteristics it inherits from the old, Kantian one—self-evidence and unconditionality—in order to present the new imperative as a response to these two aporiae. (shrink)

This paper outlines a theory of radical democratic education by addressing a key concept in Laclau and Mouffe’s Hegemony and Socialist Strategy: articulation. Through their concept of articulation, Laclau and Mouffe attempt to liberate Gramsci’s theory of hegemony from Marxist economism, and adapt it to a political sphere inhabited by a plurality of struggles and agents none of which is predominant. However, while for Gramsci the political process of hegemony formation has an explicit educational dimension, Laclau and Mouffe ignore this (...) dimension altogether. My discussion starts with elaborating the concept of articulation and analysing it in terms of three dimensions: performance, connection and transformation. I then address the role of education in Gramsci’s politics, in which the figure of the intellectual is central, and argue that radical democratic education requires renouncing that figure. In the final section, I offer a theory of such education, in which both teacher and students articulate their political differences and identities. (shrink)

This paper approaches the question of the relations between laypeople and experts by examining the relations between common sense and philosophy. The analysis of the philosophical discussions of the concept of common sense reveals how it provides democratic politics with an egalitarian foundation, but also indicates how problematic this foundation can be. The egalitarian foundation is revealed by analyzing arguments for the validity of common sense in the writings of Thomas Reid. However, a look at three modern philosophers committed to (...) the link between philosophy and common sense – Descartes, Berkeley and, again, Reid – shows that each assigns very different contents to the concept. This raises the suspicion that modern common sense is not only an egalitarian element, but also a rhetorical tool with which intellectuals attempt to shape the views of the lay masses. The last part suggests that the way out of the predicament is rejecting the supposition that common sense is a unified, homogeneous whole. An alternative is sketched through Antonio Gramsci’s concept of common sense. (shrink)

According to a widespread view, one of the most important roles of education is the nurturing of common sense. In this article I turn to Gilles Deleuze’s concept of sense to develop a contrary view of education—one that views education as a radical challenge to common sense. The discussion will centre on the relation of sense and common sense to thinking. Although adherents of common sense refer to it as the basis of all thought and appeal to critical thinking as (...) instrumental in eliminating its occasional errors, I shall argue, following Deleuze, that common sense education in fact thwarts thinking, while only education which revolves around making sense may provoke thinking that goes beyond the self-evident. I demonstrate how making sense can become an educational encounter that breaks hierarchies and generates thinking independently of the thinker’s knowledge and place in the sociopolitical order. The present article attempts, therefore, to put some sense into Deleuzian education for thinking, and thereby shed new light on its radical-political, counter-commonsensical power. (shrink)

This paper addresses the question ‘what is school?’, and argues that the answer to this question has an essential political dimension. I focus on two very different attempts to characterize school – Ivan Illich’s Deschooling Society and Jan Masschelein and Maarten Simons’s In Defence of the School – and demonstrate that both texts miss the political potential which is inherent in school. The two texts are analyzed along two relational axes: relations between school and society, and relations between children and (...) political subjects. Illich rejects children’s de-politicization while accepting the assumption that school operates according to a similar logic as society in general. Masschelein and Simons, on the other hand, advocate a separation between school and society, but also accept the separation of children from politics. I aim to integrate Illich’s analytical categories into Masschelein and Simons’ discussion, in order to mark important directions for political struggles both over and within s... (shrink)

In this paper, I discuss the teacher’s role in Laclaudian democratic education in light of the notion of the organic intellectual as proposed by Antonio Gramsci. Unlike common readings of the figure of the organic intellectual, where it is understood as developing organically from within the ranks of the oppressed, I argue that the term “organic” also refers to organization, and that the role of the organic intellectual is to be a political organizer. In contrast to the figure of the (...) charismatic leader to which Laclau and Mouffe often appeal, a political organizer works dialogically, without altogether renouncing the position of active leadership. I argue, accordingly, that the democratic teacher should be an organizer who creates for the students the conditions for articulating their demands and identities and strives to stir the emerging political subjects in a democratic direction, namely against oppressive elites and mechanisms rather than other oppressed groups. (shrink)

In this paper I discuss two attempts to challenge mainstream liberal education, by Hannah Arendt and by contemporary Israeli philosopher Hanan Alexander. Arendt and Alexander both identify problems in liberal-secular modern politics and present alternatives based on reconnecting politics and education to tradition. I analyze their positions and bring them into a dialogue that suggests a complex conception of education that avoids many of the pitfalls of modern liberal thought. First, I outline Arendt and Alexander’s educational views and discuss their (...) similarities, arguing that both may be understood as opposed to the modern attempt to adopt a «view from nowhere» at the world. Next, I suggest that Alexander’s view may benefit from adopting Arendt’s conceptions of tradition and authority. In the consecutive section, I argue that Alexander sheds light on significant problems in Arendt’s approach to education, problems his understanding of critical dialogue can help solve. The succeeding section joins the two views together to form an approach I call «critical traditionalism», and examines it against prevailing approaches to political education. I conclude by pointing to an important point overlooked by both Arendt and Alexander, namely the need for internal political struggle within each tradition. (shrink)

The neo-republican political philosophy (sometimes referred to as civic republicanism) advances the idea of freedom as non-domination, in an attempt to provide democracy with a solid normative foundation upon which concrete principles and institutions can be erected so as to make freedom a reality. However, attempts to develop a republican educational theory are still hesitant, and fail to take the republican radical conception of freedom to its full conclusions. This article suggests that dialogue between neo-republicanism and critical pedagogy can be (...) mutually productive. In the first part of the article we present the neo-republican theory, and contrast it with traditional liberalism. In the second we focus on existing neo-republican theories of education, and claim that they do not take the republican presuppositions to their necessary conclusion, namely to an educational theory fully committed to the idea of freedom as dondomination. A republican educational theory, we argue, must take into consideration not only the freedom students will have in the future, but also their freedom in the present: it should think of school as a small-scale republic, which prepares its inhabitants to be future citizens of the state while at the same time treating them as free citizens in their own right. In the third part we use insights taken from critical pedagogy to chart the direction republican education must take by applying three key republican notions—democratic control, civic contestation, and trust. In the fourth and last part we outline four aspects in which neo-republicanism can shed new light on contemporary debates in critical pedagogy: the connection between democracy and justice, the multiplicity of forms of domination, critical education within schools, and work with students from relatively privileged backgrounds. (shrink)

While inequality between children and adults characterizes practically every aspect of contemporary society, school is considered a paradigmatic site of adult domination. Childist critiques tend to point to school as a place where adultism is not only conspicuous but also (re)produced. In this article, however, it is argued that the public school, obviously founded by adults for adult purposes, has an important childist dimension. Although it is based on a clear distinction between adult teachers and child students, school can problematize (...) key adultist norms and promote a more age-equal society. This does not imply that exiting schools are necessarily childist, but rather that a certain understanding of the school, which emphasizes its social-democratic significance, can uncover its childist aspects and build on them when reimagining public education. The conception of the school in which the article focuses is presented in Jan Masschelein and Maarten Simons’ 2013 book In Defence of the School: A Public Issue. Although the authors do not refer directly to childism (or child equality), and are clearly writing from an adultist perspective, I argue that the public school they describe does have a childist dimension: it challenges one of the root causes of adultism: considering children the property of their parents. Nevertheless, Masschelein and Simons’ conception of the school raises a problem of its own, which also has a childist aspect: the concern that uniform schooling supervised by the state will be detrimental to minority and indigenous groups, imposing a culture and identity determined by adults. The second part of this article addresses this concern, arguing that genuine school education can be key not only to preserving but also to revitalizing minority cultures and identities by allowing the students to bring their “newness” into the encounter with the cultures and identities of their families. (shrink)

This article focuses on the concept of common sense in order to shed new light on the radical and pluralist democracy developed by Ernesto Laclau and Chantal Mouffe in Hegemony and Socialist Strategy. It is argued that their move via Antonio Gramsci away from both Marxism and traditional liberal democracy cannot be fully understood without reference to the role common sense plays in it. Focusing on common sense reveals crucial aspects of the relations between intellectuals and ordinary people in Laclau (...) and Mouffe's political theory, and how they deal with problems of embedded hierarchy, characteristic of modern political thought. First I reconstruct Gramsci's concept of common sense, trace its origins and analyze its egalitarian aspect. Next I present the concept's novelty with regard to other modern political theories and their presuppositions, and discuss Gramsci's eventual commitment to the latter. I then turn to discussing both the reasons why Laclau and Mouffe cannot accept the traditional concept of common sense and why they assert that constructing some sort of common sense is necessary for the formation of democratic hegemony. Finally, I argue that Laclau and Mouffe can be seen as having dealt with the problems that result from the need for common sense and the inability to accept it only if we interpret their concept of common sense as a development of Gramsci's, namely as a heterogeneous matrix of various incompatible "common senses". (shrink)

Children have always been an essential part of politics. However, the political struggles in which children are involved are rarely, if at all, for the equality of children as such. Struggles for the benefit of children are nearly always led by adults, focusing on children’s rights in an adult-dominated world. In this paper, I develop the possibility of Children’s political struggle for equality, informed by the political philosophy of Jacque Rancière. I present the educational backdrop for Rancière’s claim that all (...) intelligences are equal, and argue that it implies that children are by nature equal to adults, hence also equally capable of political action. By demonstrating that children are a “part of those who have no part” in the existing sociopolitical order, I examine the possibility of a collective political subject of children, and articulate the implications child politics may have. (shrink)

ABSTRACT Our discussion addresses Benjamin’s antifascist education through the lens of aesthetic education and Herbert Marcuse’s aesthetic theory. While this theme is not explicitly discussed in Lewis’ book, we argue that it is essential for understanding the full political and educational potential of what he calls “the art of straying in the city”. Such straying is aesthetic in a twofold way: it allows for the city to be experienced as a massive work of art, and at the same time it (...) makes the one who strays an artist who creates herself as a work of art. This unique relation to the urban world is an antifascist and anticapitalist educational experience, as it becomes a politically creative catalyst for imagining another way of relating to self, others, and environment – a relation liberated from the imperatives of utility and profit. (shrink)

In his ‘Towards the Critique of Violence’, Walter Benjamin introduces the concept of ‘educative violence’ as a contemporary manifestation of ‘divine violence’. In this paper, we aim to interpret ‘educative violence’ by examining other instances where the young Benjamin addresses pedagogical issues. By connecting the concept of divine violence to Benjamin’s ideas of education in tradition and of the schooling of Geist, our goal is twofold: firstly, to comprehend the productive role that violence may play in the pedagogical context, and (...) secondly, to apply it to the conception of schooling presented by Jan Masschelein and Maarten Simons to highlight its relevance to school education. By linking scholastic violence to divine violence, we argue that schools must be defended not despite but because of the violence they inhere. In doing so, we contribute another layer to the defense of the school and offer fresh insights into Benjamin’s notion of divine violence. (shrink)

Background: The Voluntary Assisted Dying Act 2017 passed into law in Victoria, Australia, on the 29 November 2017. Internationally, nurses have been shown to be intimately involved in patient care throughout the voluntary assisted dying process. However, there is a paucity of research exploring Australian nurses’ perspectives on voluntary assisted dying and, in particular, how Victorian nurses anticipate the implementation of this ethically controversial legislation will impact their professional lives. Objectives: To explore Victorian nurses’ expectations of the ethical and practical (...) impacts the voluntary assisted dying legislation will have on their professional lives. Research design: This qualitative study analysed nurses’ free text responses collected as part of a larger mixed methods online survey investigating staff views on the Voluntary Assisted Dying Act. Data were collected during the period between the passing of the voluntary assisted dying legislation and the start date and were analysed using inductive content analysis. Participants and research context: Free text survey responses were analysed from 1873 nurses employed across seven Victorian health services located in both metropolitan and regional areas of the state. Ethical considerations: The study obtained research ethics approval and all participants were informed of the voluntary and anonymous nature of their participation. Findings: This study identified three broad areas of Victorian nurses’ professional lives that they expected to be impacted by the implementation of voluntary assisted dying: professional identity, career development and workplace relationships. Conclusion: Participants anticipate diverse and nursing-specific impacts of the implementation of voluntary assisted dying in Victoria. Their insights can inform health services in jurisdictions considering or already implementing voluntary assisted dying, to develop policies, procedures and staff training programmes that safeguard the well-being and legal rights of their nursing staff. (shrink)

This paper introduces cosmopsychism as a holistic alternative to atomistic panpsychism, and as a general perspective on the metaphysics of consciousness. I begin with some necessary background details concerning contemporary panpsychism and the problems it faces, and then proceed to the theory itself. The starting point of the theory is the assumption that an all pervading cosmic consciousness is the single ontological ultimate. From this assumption, a panpsychist ontology of mind with distinct holistic overtones is developed. In particular, I argue (...) that such universal consciousness serves as the ground for the emergence of individual conscious creatures. The result is a theory with significant conceptual resources which presents novel means for confronting some of the most recalcitrant problems facing contemporary panpsychism: in particular, the subject combination problem, and the problem of entailment associated with it. In so doing, cosmopsychism places itself as an viable alternative to atomi... (shrink)

In this paper I shall present a method for proving determinacy from large cardinals which, in many cases, seems to yield optimal results. One of the main applications extends theorems of Martin, Steel and Woodin about determinacy within the projective hierarchy. The method can also be used to give a new proof of Woodin's theorem about determinacy in L.The reason we look for optimal determinacy proofs is not only vanity. Such proofs serve to tighten the connection between large cardinals and (...) descriptive set theory, letting us bring our knowledge of one subject to bear on the other, and thus increasing our understanding of both. A classic example of this is the Harrington-Martin proof that -determinacy implies -determinacy. This is an example of a transfer theorem, which assumes a certain determinacy hypothesis and proves a stronger one. While the statement of the theorem makes no mention of large cardinals, its proof goes through 0#, first proving that-determinacy ⇒ 0# exists,and then that0# exists ⇒ -determinacyMore recent examples of the connection between large cardinals and descriptive set theory include Steel's proof thatADL ⇒ HODL ⊨ GCH,see [9], and several results of Woodin about models of AD+, a strengthening of the axiom of determinacy AD which Woodin has introduced. These proofs not only use large cardinals, but also reveal a deep, structural connection between descriptive set theoretic notions and notions related to large cardinals. (shrink)

We show that every sufficiently iterable countable mouse has a unique iteration strategy whose associated iteration maps are lexicographically minimal. This enables us to extend the results of [3] on the good behavior of the standard parameter from tame mice to arbitrary mice.

This paper explores cosmopsychism’s explanatory aspirations from a programmatic perspective. The bulk of the text consists of an argument in favor of the conclusion that cosmopsychism suffers from no insurmountable individuation problem. I argue that the widespread tendency to view IND as a mirror-image of micropsychism’s combination problem is mistaken. In particular, what renders CP insolvable, namely, the commitment to the coupling of phenomenal constitution with phenomenal inclusion, is, from the standpoint of cosmopsychism, an entirely nonmandatory assumption. I proceed to (...) show that severing this unhappy coupling is the key for defending cosmopsychism against the charge of theoretical incoherence. Moreover, I argue that successful defense against such accusation could be mounted regardless of whether or not we assume cosmic consciousness to be perspectival in nature. In addition, the paper touches upon another foundational issue: cautioning against the popular tendency to identify cosmopsychism’s monism with a mereological unity-in-diversity, and motivating an alternative conception which I call generative monism. Finally, as befitting this volume, I pause to reflect upon the question of which schools of Hindu philosophy might tally best, and connect most fruitfully, with cosmopsychism as I understand it. (shrink)

The aim of this paper is twofold. First, our purpose is to propose and motivate a novel and scientifically informed variant of cosmopsychism, namely, the view that the experiences of ordinary subjects are ultimately grounded in an all-pervading cosmic consciousness. Second, we will demonstrate that this approach generates promising avenues for addressing familiar problems of phenomenal constitution. We use stochastic electrodynamics (SED) as the physical bedrock of our approach, supplementing it with key insights about the nature of consciousness long emphasized (...) in eastern philosophy and other wisdom traditions. We proceed to show that our approach substantiates an intriguing way of thinking about the dynamical emergence of ordinary consciousness from cosmic consciousness, identifying the latter with the vacuum state of quantum field theory. Finally, we argue that the present approach is well suited to address problems of phenomenal constitution, in particular as they pertain to the qualities and structure of experience and to the generation of subjects. (shrink)

The notion of a complete type can be generalized in a natural manner to allow assigning a value in an arbitrary Boolean algebra $\mathcal {B}$ to each formula. We show some basic results regarding the effect of the properties of $\mathcal {B}$ on the behavior of such types, and show they are particularity well behaved in the case of NIP theories. In particular, we generalize the third author’s result about counting types, as well as the notion of a smooth type (...) and extending a type to a smooth one. We then show that Keisler measures are tied to certain Boolean types and show that some of the results can thus be transferred to measures—in particular, giving an alternative proof of the fact that every measure in a dependent theory can be extended to a smooth one. We also study the stable case. We consider this paper as an invitation for more research into the topic of Boolean types. (shrink)

We present a characterization of supercompactness measures for ω1 in L(R), and of countable products of such measures, using inner models. We give two applications of this characterization, the first obtaining the consistency of $\delta_3^1 = \omega_2$ with $ZFC+AD^{L(R)}$ , and the second proving the uniqueness of the supercompactness measure over ${\cal P}_{\omega_1} (\lambda)$ in L(R) for $\lambda > \delta_1^2$.

We present an approach to forcing with finite sequences of models that uses models of two types. This approach builds on earlier work of Friedman and Mitchell on forcing to add clubs in cardinals larger than $\aleph_{1}$, with finite conditions. We use the two-type approach to give a new proof of the consistency of the proper forcing axiom. The new proof uses a finite support forcing, as opposed to the countable support iteration in the standard proof. The distinction is important (...) since a proof using finite supports is more amenable to generalizations to cardinals greater than $\aleph_{1}$. (shrink)

Current attempts by historians of science to revise the narrative of the Scientific Revolution by using the concept of the Baroque have important implications for art history. Correspondences between baroque art and baroque science gain new complexity when the rational, epistemologically optimistic image of the New Science is put in doubt. Rather than a method of objective observation, early seventeenth‐century science and art share an acceptance of the constructed nature of reality, of human epistemological limitations and of the role of (...) passions in the observation of the world. While Caravaggio has revolutionised art precisely through his interest in questions of knowledge and sensorial perception and by his subversive transformation of Renaissance epistemological values and ideals, this article concentrates on the work of Jusepe de Ribera, who made the senses and their shortcomings a major theme of his pictorial research. Ribera's epistemology is examined in the context of contemporary Neapolitan philosophy and science. Through the confrontation of some of the Spagnoletto's paintings with the work of figures such as Giovanni Battista della Porta, Federico Cesi and particularly Colantonio Stigliola, it becomes clear that early modern Neapolitan faith in rational knowledge was more ambiguous than is sometimes assumed. (shrink)

We introduce the class of unshreddable theories, which contains the simple and NIP theories, and prove that such theories have exactly saturated models in singular cardinals, satisfying certain set-theoretic hypotheses. We also give criteria for a theory to have singular compactness.

Panpsychism is now a bona fide potential solution to the metaphysical quandary of consciousness. Much of the debate concerning the viability of panpsychism is centered on the combination problem. Intriguingly, the literature analyzing this problem displays two competing interpretations which differ in their modal force. According to the first, which we call the ‘no-necessitation view', CP consists in the absence of a priori necessitation of macro-level phenomenal facts from micro-level phenomenal facts. In contrast, the second interpretation, which we label the (...) ‘incoherence charge’, goes further by insisting that it can be positively demonstrated that micro-experiences cannot combine to yield integral macro-experiences. While conceivability arguments are vulnerable to debates over conflicting intuitions, as well as to the claim that a more complete picture will grant the desired necessitation, IC has the advantage that, if true, it removes these concerns and approaches a more final verdict. Nevertheless, while conceivability arguments are widely discussed IC has not been equally well understood or recognized. In this paper we conduct a systematic investigation and reevaluation of IC, as it applies to constitutive micropsychism. We argue that the problem is real and therefore that constitutive micropsychism is a blind alley. (shrink)

A theory [Formula: see text] is said to have exact saturation at a singular cardinal [Formula: see text] if it has a [Formula: see text]-saturated model which is not [Formula: see text]-saturated. We show, under some set-theoretic assumptions, that any simple theory has exact saturation. Also, an NIP theory has exact saturation if and only if it is not distal. This gives a new characterization of distality.

The tree property at κ+ states that there are no Aronszajn trees on κ+, or, equivalently, that every κ+ tree has a cofinal branch. For singular strong limit cardinals κ, there is tension between the tree property at κ+ and failure of the singular cardinal hypothesis at κ; the former is typically the result of the presence of strongly compact cardinals in the background, and the latter is impossible above strongly compacts. In this paper, we reconcile the two. We prove (...) from large cardinals that the tree property at κ+ is consistent with failure of the singular cardinal hypothesis at κ. (shrink)

We prove that in $\operatorname {NTP}_{\operatorname {2}}$ theories the dp-rank of a type can be witnessed by indiscernible sequences of tuples satisfying that type. If the type has dp-rank infinity, then this can be witnessed by singletons.

We show that Mitchell order on downward closed extenders below rank-to-rank type is wellfounded.

We extend the construction of Mitchell and Steel to produce iterable fine structure models which may contain Woodin limits of Woodin cardinals, and more. The precise level reached is that of a cardinal which is both a Woodin cardinal and a limit of cardinals strong past it.

Jullien's indecomposability theorem states that if a scattered countable linear order is indecomposable, then it is either indecomposable to the left, or indecomposable to the right. The theorem was shown by Montalbán to be a theorem of hyperarithmetic analysis. We identify the strength of the theorem relative to standard reverse mathematics markers. We show that it lies strictly between weak [Formula: see text] choice and [Formula: see text] comprehension.

We prove determinacy for open length ω1 games. Going further we introduce, and prove determinacy for, a stronger class of games of length ω1, with payoff conditions involving the entire run, the club filter on ω1, and a sequence of ω1 disjoint stationary subsets of ω1. The determinacy proofs use an iterable model with a class of indiscernible Woodin cardinals, and we show that the games precisely capture the theory of the minimal model for this assumption.

Answering a question of Sakai :29–45, 2013), we show that the existence of an ω1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega _1$$\end{document}-Erdős cardinal suffices to obtain the consistency of Chang’s Conjecture with □ω1,2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\square _{\omega _1, 2}$$\end{document}. By a result of Donder, volume 872 of lecture notes in mathematics. Springer, Berlin, pp 55–97, 1981) this is best possible. We also give an answer to another question of Sakai relating to (...) the incompatibility of □λ,2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\square _{\lambda, 2}$$\end{document} and ↠\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \twoheadrightarrow $$\end{document} for uncountable κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa $$\end{document}. (shrink)

We provide a new criterion for embedding.

We present equiconsistency results at the level of subcompact cardinals. Assuming SBHδ, a special case of the Strategic Branches Hypothesis, we prove that if δ is a Woodin cardinal and both □ and □δ fail, then δ is subcompact in a class inner model. If in addition □ fails, we prove that δ is Π12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi_1^2}$$\end{document} subcompact in a class inner model. These results are optimal, and lead to equiconsistencies. As a corollary (...) we also see that assuming the existence of a Woodin cardinal δ so that SBHδ holds, the Proper Forcing Axiom implies the existence of a class inner model with a Π12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi_1^2}$$\end{document} subcompact cardinal. Our methods generalize to higher levels of the large cardinal hierarchy, that involve long extenders, and large cardinal axioms up to δ is δ+ supercompact for all n < ω. We state some results at this level, and indicate how they are proved. (shrink)

In this essay I offer a theory of the outward directedness of intentional states, namely, an account of what makes intentional states directed at their respective intentional objects. The theory is meant to be complementary to the canonical interactivist account of mental content in that the latter emphasizes the predicative, intensional, and internal aspects of representation whereas here I shall focus on its denotative, extensional, and external aspects. Thus, the aim is to establish that the two projects are not only (...) consistent but mutually supportive. Further, it is hoped that supplementing the interactivist conception of representation with a theory of intentional directedness along such lines will increase its overall appeal to critical readers. Based on the core idea that the directedness of a representation is a function of the manner in which it is constructed within, and contributes to the ongoing unfolding of a dynamical interactive loop connecting information to focused action, the theory is subsequently extended to cover many problem domains familiarly associated with representation and reference. (shrink)

We present two applications of forcing with finite sequences of models as side conditions, adding objects of size \. The first involves adding a \ sequence and variants of such sequences. The second involves adding partial weak specializing functions for trees of height \.