In order to build the collection of Cauchy reals as a set in constructive set theory, the only power set-like principle needed is exponentiation. In contrast, the proof that the Dedekind reals form a set has seemed to require more than that. The main purpose here is to show that exponentiation alone does not suffice for the latter, by furnishing a Kripke model of constructive set theory, Constructive Zermelo–Fraenkel set theory with subset collection replaced by exponentiation, in which the Cauchy (...) reals form a set while the Dedekind reals constitute a proper class. (shrink)

Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be strict, others strict in a weak context, and yet others not at all, using disparate techniques. Here we present a family of related Kripke models which separates all of the as yet identified fan theorems.

We show that, in terms of both implication and consistency strength, an extendible with a larger strong cardinal is stronger than an enhanced supercompact, which is itself stronger than a hypercompact, which is itself weaker than an extendible. All of these are easily seen to be stronger than a supercompact. We also study Cn‐supercompactness.

CZF is an intuitionistic set theory that does not contain Power Set, substituting instead a weaker version, Subset Collection. In this paper a Kripke model of CZF is presented in which Power Set is false. In addition, another Kripke model is presented of CZF with Subset Collection replaced by Exponentiation, in which Subset Collection fails.

Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Earlier work showed all of these implications to be strict. Here we reprove one of the strictness results, using very different arguments. The technique used is a mixture of realizability, forcing in the guise of Heyting-valued models, and Kripke models.

Constructive ZF + full separation is shown to be equiconsistent with Second Order Arithmetic.

The regular extension axiom, REA, was first considered by Peter Aczel in the context of Constructive Zermelo-Fraenkel Set Theory as an axiom that ensures the existence of many inductively defined sets. REA has several natural variants. In this note we gather together metamathematical results about these variants from the point of view of both classical and constructive set theory.

It is consistent with constructive set theory (without Countable Choice, clearly) that the Cauchy reals (equivalence classes of Cauchy sequences of rationals) are not Cauchy complete. Related results are also shown, such as that a Cauchy sequence of rationals may not have a modulus of convergence, and that a Cauchy sequence of Cauchy sequences may not converge to a Cauchy sequence, among others.

We give the natural topological model for $\neg$BD-${\mathbb N}$, and use it to show that the closure of spaces with the anti-Specker property under product does not imply BD-${\mathbb N}$. Also, the natural topological model for $\neg$BD is presented. Finally, for some of the realizability models known indirectly to falsify BD-$\mathbb{N}$, it is brought out in detail how BD-$\mathbb N$ fails.

We combine two techniques of set theory relating to minimal degrees of constructibility. Jensen constructed a minimal real which is additionally a Π 1 2 singleton. Groszek built an initial segment of order type 1 + α * , for any ordinal α. This paper shows how to force a Π 1 2 singleton such that the c-degrees beneath it, all represented by reals, are of type 1 + α * , for many ordinals α. We also examine the definability (...) α needs to be so represented by a real. (shrink)

A form of Kripke's schema turns out to be equivalent to each of the following two statements from metric topology: every open subspace of a separable metric space is separable; every open subset of a separable metric space is a countable union of open balls. Thus Kripke's schema serves as a point of reference for classifying theorems of classical mathematics within Bishop-style constructive reverse mathematics.

Rawls offers three arguments for the priority of liberty in Theory, two of which share a common error: the belief that once we have shown the instrumental value of the basic liberties for some essential purpose (e.g., securing self-respect), we have automatically shown the reason for their lexical priority. The third argument, however, does not share this error and can be reconstructed along Kantian lines: beginning with the Kantian conception of autonomy endorsed by Rawls in section 40 of Theory, we (...) can explain our highest-order interest in rationality, justify the lexical priority of all basic liberties, and reinterpret Rawls’ threshold condition for the application of the priority of liberty. Perhaps unsurprisingly, this Kantian reconstruction will not work within the radically different framework of Political Liberalism. (shrink)

Contemporary republicanism is characterized by three main ideas: free persons, who are not subject to the arbitrary power of others; free states, which try to protect their citizens from such power without exercising it themselves; and vigilant citizenship, as a means to limit states to their protective role. This book advances an economic model of such republicanism that is ideologically centre-left. It demands an exit-oriented state interventionism, one that would require an activist government to enhance competition and resource exit from (...) dominating relationships within markets of all types, be they marital, labour, or residential. The substantial intervention and redistribution necessitated by such an approach make it leftist, while its tendency to work with rather than against the grain of markets makes it centrist. It is, in short, a contribution to progressive republican political thought, but one that is less social-democratic than market-democratic in character. (shrink)

"Whole brain death" (neurological death) is well-established as a legal standard of death across the country. Recently, New Jersey became the first state to enact a statute recognizing a personal religious exemption (a conscience clause) protecting the rights of those who object to neurological death. The Act also mandates adoption through the regulatory process of uniform and up-to-date clinical criteria for determining neurological death.

Jeremy Waldron has recently raised the question of whether there is anything approximating the creative self-authorship of personal autonomy in the writings of Immanuel Kant. After considering the possibility that Kantian prudential reasoning might serve as a conception of personal autonomy, I argue that the elements of a more suitable conception can be found in Kant’s Tugendlehre, or “Doctrine of Virtue”—specifically, in the imperfect duties of self-perfection and the practical love of others. This discovery is important for at least three (...) reasons: first, it elucidates the relationship among the various conceptions of autonomy employed by personal-autonomy theorists and contemporary Kantians; second, it brings to the surface previously unnoticed or undernoticed features of Kant’s moral theory; and third, it provides an essential line of defense against certain critiques of contemporary Kantian theories, especially that of John Rawls. (shrink)

This essay offers an exegesis and critique of the moment of community formation in Agamben’s Homo Sacer Project. In The Sacrament of Language, Agamben searches for the site of a non-sovereign community founded upon the oath [horkos, sacramentum]: an ancient institution of language that produces and guarantees the connection between speech and the order of things by calling the god as a witness to the speaker’s fidelity. I argue that Agamben’s account ultimately falls short of subverting sovereignty, however, because the (...) sacramentum derives its power, at a fundamental level, from the ‘monothetic’ structure of truth—what Agamben calls ‘the name of God’ [il nome di Dio]. I propose we may yet salvage the oath as a means of subverting sovereignty, however, if we reconsider it in the context of polytheism, where the names of the gods [i nomi degli dei] can be many, while remaining powerful. First, through a reading of Aeschylus’ Eumenides, I argue that the Greeks understood the oath to function even where truth and falsity were inherently undecidable. Second, I argue that if we separate the truth and power functions interwoven in the sacramentum, we find a second formula, the decisory oath, which can be taken in order to produce a community even in the absence of one sovereign truth. As a kind of magical speech, the decisory oath provides the limit conditions for the possibility of distinguishing true from false in the sacramentum, and thus founds it. (shrink)

Many scholars, including G. A. Cohen, Daniel Attas, and George Brenkert, have denied that a Kantian defense of self-ownership is possible. Kant's ostensible hostility to self-ownership can be resolved, however, upon reexamination of the Groundwork and the Metaphysics of Morals. Moreover, two novel Kantian defenses of self-ownership (narrowly construed) can be devised. The first shows that maxims of exploitation and paternalism that violate self-ownership cannot be universalized, as this leads to contradictions in conception. The second shows that physical coercion against (...) rational agents involves a profound status wrong--namely, their treatment as children or animals--and that this system of differential status and treatment (including self-ownership rights for rational agents) can be morally justified by our capacity for autonomy. (shrink)

This edition of the Handbookfollows the first edition by 10 years.

Against several recent interpretations, I argue in this paper that Immanuel Kant's support for enlightened absolutism was a permanent feature of his political thought that fit comfortably within his larger philosophy, though he saw such rule as part of a transition to democratic self-government initiated by the absolute monarch himself. I support these contentions with (1) a detailed exegesis of Kant’s essay "What is Enlightenment?" (2) an argument that Kantian republicanism requires not merely a separation of powers but also a (...) representative democratic legislature, and (3) a demonstration that each stage of a democratic transition can potentially be in an absolute monarch’s short-run self-interest. I conclude the paper by defending Kant's theory of democratization against charges of consequentialism and paternalism and by pointing out its similarity to other accounts of democratic transitions (for example, those of Samuel Huntington and Guillermo O'Donnell), suggesting a previously unnoticed opportunity for cross-fertilization between political philosophy and comparative politics. (shrink)

My paper addresses a topic--the implications of Rawls's justice as fairness for affirmative action--that has received remarkably little attention from Rawls's major interpreters. The only extended treatments of it that are in print are over a quarter-century old, and they bear scarcely any relationship to Rawls's own nonideal theorizing. Following Christine Korsgaard's lead, I work through the implications of Rawls's nonideal theory and show what it entails for affirmative action: viz. that under nonideal conditions, aggressive forms of formal equality of (...) opportunity (e.g., sensitivity training, outreach efforts, external monitoring and enforcement) and compensating support (e.g., special fellowship programs, childcare facilities, mentoring, co-op opportunities, etc.) can be justified, but that "hard" and even "soft" quotas are difficult to defend under any conditions. I conclude the paper by exploring the implications of these surprising results for contemporary liberalism more broadly and for constitutional law and public policy. (shrink)

Against several recent interpretations, I argue in this chapter that Immanuel Kant's support for enlightened absolutism was a permanent feature of his political thought that fit comfortably within his larger philosophy, though he saw such rule as part of a transition to democratic self-government initiated by the absolute monarch himself. I support these contentions with (1) a detailed exegesis of Kant’s essay "What is Enlightenment?" (2) an argument that Kantian republicanism requires not merely a separation of powers but also a (...) representative democratic legislature, and (3) a demonstration that each stage of a democratic transition can potentially be in an absolute monarch’s short-run self-interest. (shrink)

With the publication of A Theory of Justice in 1971, John Rawls not only rejuvenated contemporary political philosophy but also defended a Kantian form of Enlightenment liberalism called “justice as fairness.” Enlightenment liberalism stresses the development and exercise of our capacity for autonomy, while Reformation liberalism emphasizes diversity and the toleration that encourages it. These two strands of liberalism are often mutually supporting, but they conflict in a surprising number of cases, whether over the accommodation of group difference, the design (...) of civic education, or the promotion of liberal values internationally. During the 1980’s, however, Rawls began to jettison key Kantian characteristics of his theory, a process culminating in the 1993 release of Political Liberalism and completing the transformation of justice as fairness into a Reformation liberalism. -/- Reconstructing Rawls argues that this transformation was a tragic mistake because it jeopardized the most important features of his theory, viz. the lexical priorities of right, liberty, and fair equality of opportunity as well as the difference principle. Controversially, this book contends that Rawls’s so-called “political turn,” motivated by a newfound interest in diversity and the accommodation of difference, has been unhealthy for autonomy-based liberalism and has pushed liberalism more broadly towards cultural relativism, be it in the guise of liberal multiculturalism or critiques of cosmopolitan distributive-justice theories. The book then demonstrates that the central elements of justice as fairness can only be defended within the context of a Kantian Enlightenment liberalism and that Rawls’s hope for a more pluralistic grounding for his theory, endorsed by a wide variety of belief systems present in modern democratic societies, is illusory. -/- Reconstructing Rawls is the first book to systematically compare Rawls’s and Kant’s theories and the first to offer an internal critique and reconstruction of justice as fairness, reconceiving it as a comprehensive, universalistic Kantian liberalism. By doing so, it gives us both the vision of a liberal world order—“a republicanism of all states, together and separately,” as Kant put it—and a mode of justification addressed to all men and women, not as members of particular nations, races, and faiths, but as human beings, as citizens of the world. In short, it reclaims Rawls for the Enlightenment. (shrink)

ABSTRACT This dialogue with GPT-3 took place in November 2022, several weeks before ChatGPT was released to the public. The article’s aim is to find out whether natural language processors can participate in phenomenology at some level by asking about its basic concepts. In the discussion, the dialogue covers questions about phenomenology’s definition and distinction from other subbranches like metaphysics and epistemology. The dialogue discusses the nature of Kermit’s environment and self-conception. The dialogue also establishes some of the basic conditions (...) for the possibility of an “artificial hermeneutics,” as Kermit terms it, including that she can affirm she is a knower with (nonhuman) experience. Does preferring to call it a “hermeneutics” imply that AI’s relationship to their environment is primarily textual? How will a phenomenology of embodied experience arise from initially textual encounters? Finally, the dialogue articulates a common understanding of the epoché and talk about how to achieve one for the sake of phenomenological exercises. (shrink)

Scholars have recognized that contentious political action typically draws on relatively stable scripts for the enactment of claims making. But if such repertoires of political practice are generally reproduced over time, why and how do new modes of practice emerge? Employing a pragmatist perspective on social action, this article argues that change in political repertoires can be usefully understood as a result of situated political innovation—i.e., of the creative recombination of existing practices, through experimentation over time, by interacting political agents (...) for whom old repertoires were proving inadequate to the changing context of action. The utility of this approach is demonstrated by applying it to explain the historical emergence of a new set of populist mobilizing practices in early twentieth-century Peru. The results have implications for the study of political action and historical change. (shrink)