The Infinite Time Turing Machine model [8] of Hamkins and Kidder is, in an essential sense, a "Σ₂-machine" in that it uses a Σ₂ Liminf Rule to determine cell values at limit stages of time. We give a generalisation of these machines with an appropriate Σ n rule. Such machines either halt or enter an infinite loop by stage ζ(n) = df μζ(n)[∃Σ(n) > ζ(n) L ζ(n) ≺ Σn L Σ(n) ], again generalising precisely the ITTM case. The collection of (...) such machines taken together computes precisely those reals of the least model of analysis. (shrink)

Understanding the neuroanatomical correlates of individual differences in executive function (EF) is integral to a complete characterization of the neural systems supporting cognition. While studies have investigated EF-neuroanatomy relationships in adults, these studies often include samples with wide variation in age, which may mask relationships between neuroanatomy and EF specific to certain neurodevelopmental time points, and such studies often use unreliable single task measures of EF. Here we address both issues. First, we focused on a specific age at which the (...) majority of neurodevelopmental changes are complete but at which age-related atrophy is not likely ( N = 251; mean age of 28.71 years, SD = 0.57). Second, we assessed EF through multiple tasks, deriving three factors scores guided by the unity/diversity model of EF, which posits a common EF factor that influences all EF tasks, as well as an updating-specific and shifting-specific factor. We found that better common EF was associated with greater volume and surface area of regions in right middle frontal gyrus/frontal pole, right inferior temporal gyrus, as well as fractional anisotropy in portions of the right superior longitudinal fasciculus (rSLF) and the left anterior thalamic radiation. Better updating-specific ability was associated with greater cortical thickness of a cluster in left cuneus/precuneus, and reduced cortical thickness in regions of right superior frontal gyrus and right middle/superior temporal gyrus, but no aspects of white matter diffusion. In contrast, better shifting-specific ability was not associated with gray matter characteristics, but rather was associated with increased mean diffusivity and reduced radial diffusivity throughout much of the brain and reduced axial diffusivity in distinct clusters of the left superior longitudinal fasciculus, the corpus callosum, and the right optic radiation. These results demonstrate that associations between individual differences in EF ability and regional neuroanatomical properties occur not only within classic brain networks thought to support EF, but also in a variety of other regions and white matter tracts. These relationships appear to differ from observations made in emerging adults ( Smolker et al., 2015 ), which might indicate that the brain systems associated with EF continue to experience behaviorally relevant maturational process beyond the early 20s. (shrink)

Peter Abelard (1079–1142 ce) was the most wide‐ranging philosopher of the twelfth century. He quickly established himself as a leading teacher of logic in and near Paris shortly after 1100. After his affair with Heloise, and his subsequent castration, Abelard became a monk, but he returned to teaching in the Paris schools until 1140, when his work was condemned by a Church Council at Sens. His logical writings were based around discussion of the “Old Logic”: Porphyry's Isagoge, aristotle'S Categories and (...) On Interpretation and boethius'S textbook on topical inference. They comprise a freestanding Dialectica (“Logic”; probably c.1116), a set of commentaries (known as the Logica [Ingredientibus], c. 1119) and a later (c. 1125) commentary on the Isagoge (Logica Nostrorum Petititoni Sociorum or Glossulae). In a work Abelard called his Theologia, issued in three main versions (between 1120 and c.1134), he attempted a logical analysis of trinitarian relations and explored the philosophical problems surrounding God's claims to omnipotence and omniscience. The Collationes (“Debates,” also known as “Dialogue between a Christian, a Philosopher and a Jew”; probably c.1130) present a rational investigation into the nature of the highest good, in which the Christian and the Philosopher (who seems to be modeled on a philosopher of pagan antiquity) are remarkably in agreement. The unfinished Scito teipsum (“Know thyself,” also known as the “Ethics”; c.1138) analyses moral action. (shrink)

We say that R is strictly dominating if and only if for all x,yŒ[1,n], if R(x,y) then max(x) 3k ¥ [1,n], there exists A Õ [1,n] such that R = A. Furthermore, A Õ [1,n] is unique.

This paper investigates when it is possible for a partial ordering P to force Pκ(λ) \ V to be stationary in VP. It follows from a result of Gitik that whenever P adds a new real, then Pκ(λ) \ V is stationary in VP for each regular uncountable cardinal κ in VP and all cardinals λ > κ in VP [4]. However, a covering theorem of Magidor implies that when no new ω-sequences are added, large cardinals become necessary [7]. The (...) following is equiconsistent with a proper class of ω₁-Erdős cardinals: If P is N₁-Cohen forcing, then Pκ(λ) \ V is stationary in VP, for all regular κ ≥ N₂ and all λ > κ. The following is equiconsistent with an ω₁-Erdős cardinal: If P is N₁-Cohen forcing, then PN₂ (N₃) \ V is stationary in VP. The following is equiconsistent with κ measurable cardinals: If P is κ-Cohen forcing, then Pκ + (Nκ \ V is stationary in VP. (shrink)

Pada musim semi, entah kenapa, tidak banyak ikan. Karena tangkapannya sangat tidak stabil, Pekakak mulai berpikir. Lalu membuat beberapa rencana. Dengan otoritas komandonya, dia memanggil Bangau: – Ini adalah musim penangkapan ikan yang sangat sulit. Jika kita ingin kenyang, kita harus membuat usaha patungan. Bangau mengangguk, menambahkan: - Saya setuju; mari kita beternak ikan kakap putih dan ikan mas krusia. Jenis ini berumur panjang dan sangat produktif. Pekakak dan Bangau sepakat untuk berbagi tugas beternak, dan tidak ada diskriminasi yang diizinkan. (...) Namun imbalannya berbeda: Pekakak bertanggung jawab untuk ikan kakap putih dan, dengan demikian, dapat memiliki lebih banyak ikan kakap putih, sedangkan Bangau mendapat ikan mas krusia. Siapapun yang memelihara ikan mana yang lebih banyak akan menikmati 80% dari panen akhir ikan tersebut. Keduanya akan mengevaluasi dan membagi produk ternak pada akhir musim beternak. Ini berarti mengantongi sendiri ikan hasil usaha patungan untuk diri sendiri itu dilarang. (shrink)

Suatu pagi di musim panas, desa burung diselimuti keheningan. Semua orang sibuk mendengarkan pengembara baru. Burung pengembara ini berasal dari keluarga yang tidak jelas; bulunya berwarna-warni, gerak-geriknya lucu, dan ilmunya baru. Dia bercerita seolah-olah sedang memberi ceramah, tepat sekali, warga desa memanggilnya burung Guru – orang yang menjawab setiap pertanyaan aneh warga desa yang rajin belajar. Burung pelatuk telah belajar menangkap cacing di sore hari, sehingga mereka tidak perlu bangun pagi. Burung pipit sekarang tahu cara mencuri beras dari gudang saat (...) sawah mulai kering. Bulbul, sementara itu, telah mengambil kesempatan berkumpul untuk memamerkan kecantikan dan fashion mereka… . (shrink)

Pekakak selama ini tinggal di gua galiannya sendiri di tepi kolam, tapi sekarang dia memutuskan bahwa dia membutuhkan rumah baru. Dia melakukan tur keliling desa untuk melihat bagaimana burung-burung lain membangun rumah mereka. Dia mengunjungi Tuan Pipit, yang tinggal di pohon pinus yang bersiul. Bagian depan bangunannya tampak indah, dan lokasinya yang tinggi memberikan ventilasi yang baik. Tapi, semakin lama dia menginap, dia jadi semakin pusing. Hembusan angin apa pun yang menerpa membuat seluruh struktur bangunan bergetar seolah-olah akan hancur berantakan.

Exclusionary defeat is Joseph Raz’s proposal for understanding the more complex, layered structure of practical reasoning. Exclusionary reasons are widely appealed to in legal theory and consistently arise in many other areas of philosophy. They have also been subject to a variety of challenges. I propose a new account of exclusionary reasons based on their justificatory role, rejecting Raz’s motivational account and especially contrasting exclusion with undercutting defeat. I explain the appeal and coherence of exclusionary reasons by appeal to commonsense (...) value pluralism and the intermediate space of public policies, social roles, and organizations. We often want our choices to have a certain character or instantiate a certain value and in order to do so, that choice can only be based on a restricted set of reasons. Exclusion explains how pro tanto practical reasons can be disqualified from counting towards a choice of a particular kind without being outweighed or undercut. (shrink)

Standard accounts of civil disobedience include nonviolence as a necessary condition. Here I argue that such accounts are mistaken and that civil disobedience can include violence in many aspects, primarily excepting violence directed at other persons. I base this argument on a novel understanding of civil disobedience: the special character of the practice comes from its combination of condemnation of a political practice with an expressed commitment to the political. The commitment to the political is a commitment to engaging with (...) others as co-members in the on-going political project of living together. I show how such an understanding of civil disobedience is superior to the Rawlsian strain of thought, which focuses on fidelity to law. Rawls was concerned with civil disobedience solely in the context of overriding political obligation. The project of characterizing a contestatory political practice that can be distinguished and used in a wider variety of contexts than Rawls is concerned with, including under illegitimate regimes, beyond the nation-state, or on behalf of anarchism, requires a different understanding of civil disobedience. (shrink)

By appeal to the phenomenon of presupposition accommodation, Rae Langton and others have proposed that speakers can gain genuine authority over their audiences when they implicitly claim such autho...

Political legitimacy is best understood as one type of a broader notion, which I call institutional legitimacy. An institution is legitimate in my sense when it has the right to function. The right to function correlates to a duty of non-interference. Understanding legitimacy in this way favorably contrasts with legitimacy understood in the traditional way, as the right to rule correlating to a duty of obedience. It helps unify our discourses of legitimacy across a wider range of practices, especially including (...) the many evaluations we increasingly make of international institutions of various sorts, but also including domestic institutions. (shrink)

Courts and jurors sometimes refuse to assign liability to defendants on the basis of statistics alone, despite their apparent reliability. I argue that this refusal is best understood as a recognition of defendants’ right to security. Understood as a robust good in Philip Pettit’s sense, security requires that someone risking harm to others’ protected interests adopt a disposition of concern that controls against wrongfully harming them. Since trials risk harm, the state must adopt such a disposition. Statistics leave open the (...) possibility of innocence and so wrongful harm in a way that the state cannot ignore; if it does use such statistics, it makes defendants wrongfully insecure. This explanation of the problem of bare statistical evidence is especially apt because security grounds the right to a fair trial and judicial procedural rights more generally. (shrink)

In Morality and Socially Constructed Norms, Valentini searches for a unifying principle that underlies whatever genuine obligations we might have to obey the norms of any and all social practices, ranging from line queueing norms, through offsides rules in soccer, to obligations not to break the law. I argue that this search is driven, and distorted, by a commitment to what Bernard Williams labeled the ‘morality system’. Once we see this, we should question the value of the unifying project. Most (...) social norms can be considered on their own terms, as part of a rich and variegated ethical life, without subsuming them under the question of whether others’ moral rights are at stake. Similarly, political obligation needs to be understood in relation to the practical activity of politics, not as an abstract moral quandary. (shrink)

We propose a technical reformulation of the measurement problem of quantum mechanics, which is based on the postulate that the final state of a measurement is classical; this accords with experimental practice as well as with Bohr’s views. Unlike the usual formulation (in which the post-measurement state is a unit vector in Hilbert space), our version actually opens the possibility of admitting a purely technical solution within the confines of conventional quantum theory (as opposed to solutions that either modify this (...) theory, or introduce unusual and controversial interpretative rules and/or ontologies).To that effect, we recall a remarkable phenomenon in the theory of Schrödinger operators (discovered in 1981 by Jona-Lasinio, Martinelli, and Scoppola), according to which the ground state of a symmetric double-well Hamiltonian (which is paradigmatically of Schrödinger’s Cat type) becomes exponentially sensitive to tiny perturbations of the potential as ħ→0. We show that this instability emerges also from the textbook wkb approximation, extend it to time-dependent perturbations, and study the dynamical transition from the ground state of the double well to the perturbed ground state (in which the cat is typically either dead or alive, depending on the details of the perturbation).Numerical simulations show that adiabatically arising perturbations may (quite literally) cause the collapse of the wave-function in the classical limit. Thus, at least in the context of a simple mathematical model, we combine the technical and conceptual virtues of decoherence (which fails to solve the measurement problem but launches the key idea that perturbations may come from the environment) with those of dynamical collapse models à la grw (which do solve the measurement problem but are ad hoc), without sharing their drawbacks: single measurement outcomes are obtained (instead of merely diagonal reduced density matrices), and no modification of quantum mechanics is needed. (shrink)

The essays collected in this special issue explore what legitimacy means for actors and institutions that do not function like traditional states but nevertheless wield significant power in the global realm. They are connected by the idea that the specific purposes of non-state actors and the contexts in which they operate shape what it means for them to be legitimate and so shape the standards of justification that they have to meet. In this introduction, we develop this guiding methodology further (...) and show how the special issue’s individual contributions apply it to their cases. In the first section, we provide a sketch of our purpose-dependent theory of legitimacy beyond the state. We then highlight two features of the institutional context beyond the state that set it apart from the domestic case: problems of feasibility and the structure of international law. (shrink)

I argue for a new conception of practical authority based on an analysis of the relationship between authority and subject. Commands entail a demand for practical deference, which establishes a relationship of hierarchy and vulnerability that involves a variety of signals and commitments. In order for these signals and commitments to be justified, the subject must be under a preexisting duty, the authority’s commands must take precedence over the subject’s judgment regarding fulfillment of that duty, the authority must accept the (...) position and responsibilities of command, and the authority must be sufficiently trustworthy relative to how vulnerable the subject makes herself by deferring. This results in an instrumentalist conception of practical authority that can be favorably compared to Joseph Raz’s famous service conception. The relational conception’s main advantage is that it focuses on the authority as much as the subject, requiring that the authority accept responsibility for the relationship and be sufficiently trustworthy. (shrink)

I argue that legitimacy discourses serve a gatekeeping function. They give practitioners telic standards for riding herd on social practices, ensuring that minimally acceptable versions of the practice are implemented. Such a function is a necessary part of implementing formalized social practices, especially including law. This gatekeeping account shows that political philosophers have misunderstood legitimacy; it is not secondary to justice and only necessary because we cannot agree about justice. Instead, it is a necessary feature of actual human social practices, (...) which must be implemented via practitioners' discretion in changing contexts. (shrink)

Institutions undertake a huge variety of constitutive purposes. One of the roles of legitimacy is to protect and promote an institution’s pursuit of its purpose; state legitimacy is generally understood as the right to rule, for example. When considering legitimacy beyond the state, we have to take account of how differences in purposes change legitimacy. I focus in particular on how differences in purpose matter for the stringency of the standards that an institution must meet in order to be legitimate. (...) An important characteristic of an institution’s purpose is its deontic status, i.e. whether it is morally impermissible, merely permissible, or mandatory. Although this matters, it does so in some non-obvious ways; the mere fact of a morally impermissible purpose is not necessarily delegitimating, for example. I also consider the problem of conflicting, multiple, and contested institutional purposes, and the different theoretical roles for institutional purpose. Understanding how differences in purpose matter for an institution’s legitimacy is one part of the broader project of theorizing institutional legitimacy in the many contexts beyond the traditional context of the state. (shrink)

The problem of man is one of the most urgent of our day. Man is a product of history. His consciousness is shaped by the concrete historical experience of humanity. These principles of the Marxist-Leninist teaching on man have had the most substantive kind of confirmation in contemporary analysis of the problem of the relation between the social and the biological. In his biological features man is a part of nature. The social aspect has to do with his suprabiological sphere, (...) and is transmitted from generation to generation through different channels than the genetic information inscribed in molecules of DNA. (shrink)

Contrary to the widely accepted consensus, Christopher Heath Wellman argues that there are no pre-institutional judicial procedural rights. Thus commonly affirmed rights like the right to a fair trial cannot be assumed in the literature on punishment and legal philosophy as they usually are. Wellman canvasses and rejects a variety of grounds proposed for such rights. I answer his skepticism by proposing two novel grounds for procedural rights. First, a general right against unreasonable risk of punishment grounds rights to an (...) institutionalized system of punishment. Second, to complement and extend the first ground, I more controversially propose a right to provision of the robust good of security. People have a right to others' protecting for avoiding wrongfully harming them: when I take an action that is reasonably expected to threaten the protected interests of others, I must take appropriate care to avoid setting back those interests. Inflicting punishment on someone--intentionally harming them in response to a violation--is prima facie wrongful, so I can only count as taking appropriate care in punishing when I follow familiar procedures that reliably and redundantly test whether they are liable to such punishment, i.e. whether they have forfeited their right against punishment through a culpable act. (shrink)