Intellectualism is the widespread view that practical reason is a species of theoretical reason, distinguished from others by its objects: reasons to act. I argue that if practical reason is a species of theoretical reason, practical judgments by nature have nothing to do with action. If they have nothing to do with action, I cannot act from my representation of reasons for me to act. If I cannot act from those representations, those reasons cannot exist. If they cannot exist, neither (...) can a species of theoretical reason about them. Intellectualism is thus self-undermining. (shrink)

Cuneo and Shafer-Landau have argued that there are moral conceptual truths that are substantive and non-vacuous in content, what they called ‘moral fixed points’. If the moral proposition ‘torturing kids for fun is pro tanto wrong’ is such a conceptual truth, it is because the essence of ‘wrong’ necessarily satisfies and applies to the substantive content of ‘torturing kids for fun’. In critique, Killoren :165–173, 2016) has revisited the old skeptical ‘why be moral?’ question and argued that the moral (...) fixed points give us no reason to care about morality and, therefore, they are normatively irrelevant. He concluded that this is a counterintuitive implication that undermines the proposal. In this paper, I develop a rejoinder to Killoren’s argument that explains why, at least from the perspective of the moral fixed points framework, if the moral fixed points exist, they are necessarily normatively relevant for rational agents. I supplement this explanation with an explanation of why it might prima facie appear that moral fixed points are not normatively relevant, although ultima facie they are relevant. The supplementary explanation explains prima facie normative irrelevance as the upshot of failures of rational agency. I conclude that the moral fixed points, can, in principle, offer an interesting response to the skeptical ‘why be moral?’ question’. (shrink)

One of the problems in economics that economists have devoted a considerable amount of attention in prevalent years has been to ensure consistency in the models they employ. Assuming markets to be generally in some state of equilibrium, it is asked under what circumstances such equilibrium is possible. The fundamental mathematical tools used to address this concern are fixed point theorems: the conditions under which sets of assumptions have a solution. This book gives the reader access to the mathematical (...) techniques involved and goes on to apply fixed point theorems to proving the existence of equilibria for economics and for co-operative and noncooperative games. Special emphasis is given to economics and games in cases where the preferences of agents may not be transitive. The author presents topical proofs of old results in order to further clarify the results. He also proposes fresh results, notably in the last chapter, that refer to the core of a game without transitivity. This book will be useful as a text or reference work for mathematical economists and graduate and advanced undergraduate students. (shrink)

The aim of this research work is to find out some results in fixed point theory for a pair of families of multivalued mappings fulfilling a new type of U -contractions in modular-like metric spaces. Some new results in graph theory for multigraph-dominated contractions in modular-like metric spaces are developed. An application has been presented to ensure the uniqueness and existence of a solution of families of nonlinear integral equations.

In recent years, social workers have raised a new concern about the appearance of a new category among the working poor. Even employed, there are people so overburdened by the cost of living and so under compensated that they cannot afford a place to sleep. Contrary to popular opinion, according to the website for the Coalition for the Homeless, forty-four percent of the homeless in first world countries actually have jobs. In _No Fixed Abode_, Marc Augé’s pathbreaking ethnofiction—a fictional (...) ethnography—a man named Henri narrates his strange existence in the margins of Paris. By day he walks the streets, lingers in conversation with the local shopkeepers, and sits writing in cafés, but at night he takes shelter in an abandoned house. From here, we see a progressive erosion of Henri’s identity, a loss of bearings, and a slow degeneration of his ability to relate to others. But then he meets the artist Dominique, whose willingness to share her life with him raises questions about who he has become and about what a person needs in order to be a part of society. This is a book about how we live in geographical space and how work and patterns of domicile affect our status and our inner being. Despite the apparent simplicity of the fictional premise, Augé’s book asks serious questions about the nature of our culture. (shrink)

It is fair enough to refer, as Father Clarke does, to the God of the Christians and the Jews as ‘the one infinite Creator of all other things’. It is reasonable to take ‘God’ as a term that has certain conditions associated with it. These conditions fix its meaning. The central conditions associated with ‘God’ are: being infinite or unlimited, eternal, self-existent, the creator of everything that exists other than himself, the being upon whom all other beings are dependent but (...) who depends on nothing himself, being personal, good, loving and holy. These conditions determine our concept of God, determine what could count as a referent for the term ‘God’. In short, God, as John Hick remarks, is conceived in Western Religions ‘as the infinite, eternal, uncreated, personal reality, who has created all that exists other than himself, and who has revealed himself to his human creatures as holy and loving’. (shrink)

In Aczel [1], the existence of largest fixed points of set continuous operators is proved assuming the schema version of dependent choices in Zermelo-Fraenkel set theory without the axiom of Foundation. In the present paper, we study whether the existence of largest fixed points of set continuous operators is provable without the schema version of dependent choices, using Boffa's weak antifoundation axioms.

Efforts to address algorithmic harms have gathered particular steam over the last few years. One area of proposed opportunity is the notion of an “algorithmic audit,” specifically an “internal audit,” a process in which a system’s developers evaluate its construction and likely consequences. These processes are broadly endorsed in theory—but how do they work in practice? In this paper, we conduct not only an audit but an autoethnography of our experiences doing so. Exploring the history and legacy of a facial (...) recognition dataset, we find paradigmatic examples of algorithmic injustices. But we also find that the process of discovery is interwoven with questions of affect and infrastructural brittleness that internal audit processes fail to articulate. For auditing to not only address existing harms but avoid producing new ones in turn, we argue that these processes must attend to the “mess” of engaging with algorithmic systems in practice. Doing so not only reduces the risks of audit processes but—through a more nuanced consideration of the emotive parts of that mess—may enhance the benefits of a form of governance premised entirely on altering future practices. (shrink)

This paper proposes a novel robust fixed-time control for the robot manipulator system with uncertainties. Based on the uniform robust exact differentiator algorithm, a robust control term is constructed. Then, a robust fixed-time inverse dynamics control is proposed. For the proposed control method, the fixed-time stability of a closed-loop system with uncertainties is strictly proved. The newly proposed method exhibits the following two attractive features. First, the proposed control scheme extends the existing fixed-time IDC for the (...) robot manipulator system to the robust control scheme. Second, the proposed method is strictly nonsingular rather than the commonly used approximate approach. Simulation result demonstrates the effectiveness of the proposed control scheme. (shrink)

Assuming that $0^\#$ exists, we prove that there is a structure that can effectively interpret its own jump. In particular, we get a structure $\mathcal A$ such that \[ \textit{Sp}({\mathcal A}) = \{{\bf x}'\colon {\bf x}\in \textit{Sp}({\mathcal A})\}, \] where $\textit{Sp}({\mathcal A})$ is the set of Turing degrees which compute a copy of $\mathcal A$. More interesting than the result itself is its unexpected complexity. We prove that higher-order arithmetic, which is the union of full $n$th-order arithmetic for all $n$, (...) cannot prove the existence of such a structure. (shrink)

In recent years, social workers have raised a new concern about the appearance of a new category among the working poor. Even employed, there are people so overburdened by the cost of living and so under compensated that they cannot afford a place to sleep. Contrary to popular opinion, according to the website for the Coalition for the Homeless, forty-four percent of the homeless in first world countries actually have jobs. In No Fixed Abode, Marc Augé's pathbreaking ethnofiction--a fictional (...) ethnography--a man named Henri narrates his strange existence in the margins of Paris. By day he walks the streets, lingers in conversation with the local shopkeepers, and sits writing in cafés, but at night he takes shelter in an abandoned house. From here, we see a progressive erosion of Henri's identity, a loss of bearings, and a slow degeneration of his ability to relate to others. But then he meets the artist Dominique, whose willingness to share her life with him raises questions about who he has become and about what a person needs in order to be a part of society. This is a book about how we live in geographical space and how work and patterns of domicile affect our status and our inner being. Despite the apparent simplicity of the fictional premise, Augé's book asks serious questions about the nature of our culture. (shrink)

The need for urgent, structural transformations to dominant food systems is increasingly recognized in research and policy. The direction these transformations take is in great part influenced by how the problem is framed and what future pathways become seen as plausible and desirable. Scientific knowledge and the organizations producing it hold considerable authority in suggesting what alternatives are or are not worth pursuing, ultimately shaping frames and in turn being shaped by them. This paper examines Brazil’s federal Agricultural Research Corporation (...) (Embrapa), a major contributor to technological advances that made Brazil into an agricultural powerhouse. We examine the ways in which Embrapa’s leadership has framed sustainable agriculture in its public communication and the wider implications for food systems transformation. Drawing from Embrapa news articles in the period 2015–2020, we identify four interrelated frames forming Embrapa’s prevalent position on sustainability. Our results show that while Embrapa promotes practices based on alternative approaches such as agroecology, its deeper framing often reflects the core assumptions driving dominant industrial food systems. This framing reinforces underlying logics of control, efficiency, and competition aligned with the productivist paradigm and excludes divergent perspectives that exist within the organization. (shrink)

Minimal predicates P satisfying a given first-order description φ(P) occur widely in mathematical logic and computer science. We give an explicit first-order syntax for special first-order ‘PIA conditions’ φ(P) which guarantees unique existence of such minimal predicates. Our main technical result is a preservation theorem showing PIA-conditions to be expressively complete for all those first-order formulas that are preserved under a natural model-theoretic operation of ‘predicate intersection’. Next, we show how iterated predicate minimization on PIA-conditions yields a language MIN(FO) equal (...) in expressive power to LFP(FO), first-order logic closed under smallest fixed-points for monotone operations. As a concrete illustration of these notions, we show how our sort of predicate minimization extends the usual frame correspondence theory of modal logic, leading to a proper hierarchy of modal axioms: first-order-definable, first-order fixed-point definable, and beyond. (shrink)

It is well known that, in Peano arithmetic, there exists a formula Theor (x) which numerates the set of theorems. By Gödel's and Löb's results, we have that Theor (˹p˺) ≡ p implies p is a theorem ∼Theor (˹p˺) ≡ p implies p is provably equivalent to Theor (˹0 = 1˺). Therefore, the considered "equations" admit, up to provable equivalence, only one solution. In this paper we prove (Corollary 1) that, in general, if P (x) is an arbitrary formula built (...) from Theor (x), then the fixed-point of P (x) (which exists by the diagonalization lemma) is unique up to provable equivalence. This result is settled referring to the concept of diagonalizable algebra (see Introduction). (shrink)

Considering whether existence, i.e., being, is a thing might seem like the height of aimless metaphysical chin stroking. However, the issue—specifically, whether existence is a quality—is significant, bearing on how reality, this all-encompassing totality, is. On one view, reality at large is ontologically fixed, the sum total of things does not (and cannot) vary; on another view, reality is ontologically transient, the sum total of things varies. I first show that if existence is a thing, that reality is ontologically (...) fixed follows. So I consider whether existence is indeed a thing. I demonstrate that “it” could not be: existence is no existent. I then discuss what it is to exist, given existence is nothing at all. I maintain there are no grounds for the view that reality is ontologically fixed. I argue, from the irrefragable basis of temporal differentiation—the world going from thus…to as so—that reality is ontologically transient. I consider some objections to ontological transience and conclude by considering the key to understanding the overall structure in reality and what it reveals about how very inconstant all this is. (shrink)

In this article we show how to use the result in Jäger and Probst [7] to adapt the technique of pseudo-hierarchies and its use in Avigad [1] to subsystems of set theory without foundation. We prove that the theory KPi0 of admissible sets without foundation, extended by the principle (Σ-FP), asserting the existence of fixed points of monotone Σ operators, has the same proof-theoretic ordinal as KPi0 extended by the principle (Σ-TR), that allows to iterate Σ operations along ordinals. (...) By Jäger and Probst [6] we conclude that the metapredicative Mahlo ordinal φ ω00 is also the ordinal of KPi0+(Σ-FP). Hence the relationship between fixed points and iteration persists in the framework of set theory without foundation. (shrink)

Minimal predicates P satisfying a given first-order description ϕ(P) occur widely in mathematical logic and computer science. We give an explicit first-order syntax for special first-order 'PIA conditions' ϕ(P) which quarantees unique existence of such minimal predicates. Our main technical result is a preservation theorem showing PIA-conditions to be expressively complete for all those first-order formulas that are preserved under a natural model-theoretic operation of 'predicate intersection'. Next, we show how iterated predicate minimization on PIA-conditions yields a language MIN(FO) equal (...) in expressive power to LFP(FO), first-order logic closed under smallest fixed-points for monotone operations. As a concrete illustration of these notions, we show how our sort of predicate minimization extends the usual frame correspondence theory of modal logic, leading to a proper hierarchy of modal axioms: first-order-definable, first-order fixed-point definable, and beyond. (shrink)

We study the expressive power in the finite of the logic Fixed-Point+Counting, the extension of first-order logic which is obtained through adding both the fixed-point constructor and the ability to count. To this end an isomorphism preserving (`generic') model of computation is introduced whose PTime restriction exactly corresponds to this level of expressive power, while its PSpace restriction corresponds to While+Counting. From this model we obtain a normal form which shows a rather clear separation of the relational vs. (...) the arithmetical side of the algorithms involved. In parallel, we study the relations of Fixed-Point+Counting with the infinitary logics L r ∞ω (∃ ≥ m ) m∈ω and the corresponding pebble games. The main result, however, involves the concept of an arithmetical invariant. By this we mean a functor taking every finite relational structure to an expansion of (an initial segment of) the standard arithmetical structure. In particular its values are linearly ordered structures. We establish the existence of a family of arithmetical invariants (J r ) r≥ 1 with the following properties: $\bullet$ The invariants themselves can be evaluated in polynomial time. $\bullet$ A class of finite relational structures is definable in Fixed-Point+Counting if and only if membership can be decided in polynomial time on the basis of the values of one of the invariants. $\bullet$ The invariant J r classifies all finite relational structures exactly up to equivalence with respect to the logic L r ∞ω (∃ ≥ m ) m∈ω . We also give a characterization of Fixed-Point+Counting in terms of sequences of formulae in the L r ωω (∃ ≥ m ) m∈ω : It corresponds exactly to the polynomial time computable families (φ n ) n∈ω in these logics. Towards a positive assessment of the expressive power of Fixed-Point+Counting, it is shown that the natural extension of fixed-point logic by Lindström quantifiers, which capture all the PTime computable properties of cardinalities of definable predicates, is strictly weaker than what we get here. This implies in particular that every extension of fixed-point logic by means of monadic Lindstrom quantifiers, which stays within PTime, must be strictly contained in Fixed-Point+Counting. (shrink)

In this article, we compare two fixed-point constructions of common knowledge in sequential coordination problems. The first one corresponds to the standard maximal fixed-point construction of common knowledge in a possible worlds framework; the second construction provides an even larger fixed-point and involves iterated epistemic updates. We call the first fixed-point the maximal fixed-point, and the second the update fixed-point. Both fixed-points define a set of sequential actions that solve the coordination problem such (...) that success is mutually guaranteed. The main application intended is the study of signalling games as introduced by [15]. We introduce a non-probabilistic version of these games as multi-agent signalling games. We use them for modelling prototypical accommodation phenomena following [16]. We show especially that accommodation, which involves presupposition violation, is only licensed due to the existence of the super large update fixed-point, whereas the literal language use without presupposition violations can be characterized by the maximal fixed-point. (shrink)

In computational mathematics, it is a matter of deep concern to recognize which of the given iteration schemes converges quickly with lesser error to the desired solution. Fixed point iterative schemes are constructed to be used for solving equations emerging in many fields of science and engineering. These schemes reformulate a nonlinear equation f s = 0 into a fixed point equation of the form s = g s ; such application determines the solution of the original equation (...) via the support of fixed point iterative method and is subject to existence and uniqueness. In this manuscript, we introduce a new modified family of fixed point iterative schemes for solving nonlinear equations which generalize further recursive methods as particular cases. We also prove the convergence of our suggested schemes. We also consider some of the mathematical models which are categorically nonlinear in essence to authenticate the performance and effectiveness of these schemes which can be seen as an expansion and rationalization of some existing techniques. (shrink)

C endorses the doctrine of Composition as Identity, which holds that a composite object is identical to its many parts, and entails that one object can be identical to several others. In this dialogue, N argues that many‐one identity, and thus composition as identity, is conceptually confused. In particular, N claims it violates two conceptual truths: that existence facts fix identity facts, and that identity is no addition to being. In response to pressure from C, N considers several candidate interpretations (...) of the first slogan. Each interpretation imagines God issuing a divine existential decree that counts as ‘fixing the existence facts’, and then considers what questions about identity are left open by it. N eventually hits on an appealing interpretation of the slogan that C can neither undermine nor accommodate, and uses it to interpret the second slogan as well. (shrink)

Fix 2 < n < ω. Let CA n denote the class of cylindric algebras of dimension n, and let RCA n denote the variety of representable CA n ’s. Let L n denote first-order logic restricted to the first n variables. Roughly, CA n, an instance of Boolean algebras with operators, is the algebraic counterpart of the syntax of L n, namely, its proof theory, while RCA n algebraically and geometrically represents the Tarskian semantics of L n. Unlike Boolean (...) algebras having a Stone representation theorem, RCA n ⊊ CA n. Using combinatorial game theory, we show that the existence of certain finite relation algebras RA, which are algebras whose domain consists of binary relations, implies that the celebrated Henkin omitting types theorem fails in a very strong sense for L n. Using special cases of such finite RA ’s, we recover the classical nonfinite axiomatizability results of Monk, Maddux, and Biro on RCA n and we re-prove Hirsch and Hodkinson’s result that the class of completely representable CA n ’s is not first-order definable. We show that if T is an L n countable theory that admits elimination of quantifiers, λ is a cardinal < 2 ℵ 0, and F = 〈 Γ i : i < λ 〉 is a family of complete nonprincipal types, then F can be omitted in an ordinary countable model of T. (shrink)

C endorses the doctrine of Composition as Identity, which holds that a composite object is identical to its many parts, and entails that one object can be identical to several others. In this dialogue, N argues that many‐one identity, and thus composition as identity, is conceptually confused. In particular, N claims it violates two conceptual truths: that existence facts fix identity facts, and that identity is no addition to being. In response to pressure from C, N considers several candidate interpretations (...) of the first slogan. Each interpretation imagines God issuing a divine existential decree that counts as ‘fixing the existence facts’, and then considers what questions about identity are left open by it. N eventually hits on an appealing interpretation of the slogan that C can neither undermine nor accommodate, and uses it to interpret the second slogan as well. (shrink)

A logic is a pair (P,Q) where P is a set of formulas of a fixed propositional language and Q is a set of rules. A formula is deducible from X in the logic (P, Q) if it is deducible from XP via Q. A matrix is strongly adequate to (P, Q) if for any , X, is deducible from X iff for every valuation in , is designated whenever all the formulas in X are. It is proved in (...) the present paper that if Q = {modus ponens, adjunction } and P {E, R, E +, R +, E I, R I } then there exists a matrix strongly adequate to (P, Q). (shrink)

Our results concern the existence of a countable extension U of the countable atomless Boolean algebra B such that U is a "nonconstructive" extension of B. It is known that for any fixed admissible indexing φ of B there is a countable nonconstructive extension U of B (relative to φ). The main theorem here shows that there exists an extension U of B such that for any admissible indexing φ of B, U is nonconstructive (relative to φ). Thus, in (...) this sense U is a countable totally nonconstructive extension of B. (shrink)

Medical research saves lives--yet all too often, it is thwarted by a review system supposed to safeguard patients that instead creates needless delays and expense. Institutional Review Boards, which exist at every hospital and medical school that conducts medical research, have ended up imposing such complex, draconian conditions that research is frequently damaged, delayed, and distorted. This is why medical miracles like the COVID-19 vaccines, which were developed at warp speed, are far too rare. Instead, medical research in countless areas (...) is kept at a horse-and-buggy pace. The result: unnecessary suffering and avoidable deaths. From Oversight to Overkill vividly recounts the story behind this crisis, one that remains unknown to the general public. Family physician and ethicist Simon Whitney shows how the IRB system was launched in response to scandals like the notorious Tuskegee syphilis study--and how, in recent decades, this well-intentioned program has become increasingly bureaucratic, convoluted, and stifling. Readers will learn how vital breakthroughs in treating conditions from kidney stones to heart attacks and premature birth have been delayed by IRB red tape, forcing doctors and patients to settle for less-effective treatments. They'll see how ill-informed demands from Congressional leaders that regulators "get tough" on scientists have caused respected research institutions to be shut down-with no benefit to the public. And they'll learn about a balanced, common-sense approach to reforming the system that can free scientists from pointless wheel-spinning while still protecting the public from the risks of unethical or careless experimentation. Until now, the debate about the IRB system's failures has been confined to specialty journals in medicine, law, and ethics. From Oversight to Overkill will finally alert citizens about this little-known crisis with America's medical research system-and what can be done about it. (shrink)

Wittgenstein speaks of the fog that surrounds the workings of language. Our ways of thinking about reference contribute generously to the fog. While a full discussion would constitute a book-length project, my aims here are quite limited. I want to have a look at the idea that reference is a relation between a piece of language and a piece of reality. The idea might seem unexceptional and unexceptionable; names, for example, name things, and “relation” seems just right. But there is (...) casual relation-talk, and then more serious talk of a genuine relation, one that requires the existence, in every case, of a referent. Referential expressions, I’ll argue, sometimes lack such a relatum, and other timeswhen in some straightforward way there is such a thingit’s quite difficult to know what we are talking about. (shrink)

This work identifies the influence of chaos theory on fractional calculus by providing a theorem for the existence and stability of solution in fractional-order gyrostat model with the help of a fixed-point theorem. We modified an integer order gyrostat model consisting of three rotors into fractional order by attaching rotatory fuel-filled tank and provided an iterative scheme for our proposed model as a working rule of obtained analytical results. Moreover, this iterative scheme is injected into algorithms for a system (...) of integer order dynamical systems to observe Lyapunov exponents and a bifurcation diagram for our proposed fractional-order dynamical model. Furthermore, we obtained five equilibrium points, including four unstable spirals and one saddle node, using local dynamical analysis which acted as self-exciting attractors and a separatrix in a global domain. (shrink)

In this study, under some inequality conditions, necessary and sufficient conditions, using fixed-point theorem in cones, are established for the existence of C 1 -positive solutions for a class of second-order impulsive differential equations. Two examples are given in the last section to illustrate the abstract results.

In this article, we make analysis of the implicit fractional differential equations involving integral boundary conditions associated with Stieltjes integral and its corresponding coupled system. We use some sufficient conditions to achieve the existence and uniqueness results for the given problems by applying the Banach contraction principle, Schaefer’s fixed point theorem, and Leray–Schauder result of the cone type. Moreover, we present different kinds of stability such as Hyers–Ulam stability, generalized Hyers–Ulam stability, Hyers–Ulam–Rassias stability, and generalized Hyers–Ulam–Rassias stability by using (...) the classical technique of functional analysis. At the end, the results are verified with the help of examples. (shrink)

In this essay, I use encounters with the white-tailed deer of Fire Island to explore the “call of the wild”—the attraction to value that exists in a natural world outside of human control. Value exists in nature to the extent that it avoids modification by human technology. Technology “fixes” the natural world by improving it for human use or by restoring degraded ecosystems. Technology creates a “new world,” an artifactual reality that is far removed from the “wildness” of nature. The (...) technological “fix” of nature thus raises a moral issue: how is an artifact morally different from a natural and wild entity? Artifacts are human instruments; their value lies in their ability to meet human needs. Natural entities have no intrinsic functions; they were not created for any instrumental purpose. To attempt to manage natural entities is to deny their inherent autonomy: a form of domination. The moral claim of the wilderness is thus a claim against human technological domination. We have an obligation to struggle against this domination by preserving as much of the natural world as possible. (shrink)

This paper continues investigations of the monotone fixed point principle in the context of Feferman's explicit mathematics begun in [14]. Explicit mathematics is a versatile formal framework for representing Bishop-style constructive mathematics and generalized recursion theory. The object of investigation here is the theory of explicit mathematics augmented by the monotone fixed point principle, which asserts that any monotone operation on classifications (Feferman's notion of set) possesses a least fixed point. To be more precise, the new axiom (...) not merely postulates the existence of a least solution, but, by adjoining a new constant to the language, it is ensured that a fixed point is uniformly presentable as a function of the monotone operation. Let T 0 + UMID denote this extension of explicit mathematics. [14] gave lower bounds for the strength of two subtheories of T 0 + UMID in relating them to fragments of second order arithmetic based on Π 1 2 comprehension. [14] showed that T $_0 \upharpoonright$ + UMID and T $_0 \upharpoonright$ + IND N + UMID have at least the strength of (Π 1 2 - CA) $\upharpoonright$ and (Π 1 2 - CA), respectively. Here we are concerned with the exact reversals. Let UMID N be the monotone fixed-point principle for subclassifications of the natural numbers. Among other results, it is shown that T $_0 \upharpoonright$ + UMID N and T $_0 \upharpoonright$ + IND N + UMID N have the same strength as (Π 1 2 - CA) $\upharpoonright$ and (Π 1 2 - CA), respectively. The results are achieved by constructing set-theoretic models for the aforementioned systems of explicit mathematics in certain extensions of Kripke-Platek set theory and subsequently relating these set theories to subsystems of second arithmetic. (shrink)

I examine the debate between substantivalists and relationalists about the ontological character of spacetime and conclude it is not well posed. I argue that the hole argument does not bear on the debate, because it provides no clear criterion to distinguish the positions. I propose two such precise criteria and construct separate arguments based on each to yield contrary conclusions, one supportive of something like relationalism and the other of something like substantivalism. The lesson is that one must fix an (...) investigative context in order to make such criteria precise, but different investigative contexts yield inconsistent results. I examine questions of existence about spacetime structures other than the spacetime manifold itself to argue that it is more fruitful to focus on pragmatic issues of physicality, a notion that lends itself to several different explications, all of philosophical interest, none privileged a priori over any of the others. I conclude by suggesting an extension of the lessons of my arguments to the broader debate between realists and instrumentalists. 1 Introduction2 The Hole Argument3 Limits of Spacetimes4 Pointless Constructions5 The Debate between Substantivalists and Relationalists6 Existence and Physicality: An Embarassment of Spacetime Structures7 Valedictory Remarks on Realism and Instrumentalism, and the Structure of Our Knowledge of Physics. (shrink)

The context for this paper is Feferman's theory of explicit mathematics, a formal framework serving many purposes. It is suitable for representing Bishop-style constructive mathematics as well as generalized recursion, including direct expression of structural concepts which admit self-application. The object of investigation here is the theory of explicit mathematics augmented by the monotone fixed point principle, which asserts that any monotone operation on classifications possesses a least fixed point. To be more precise, the new axiom not merely (...) postulates the existence of a least solution, but, by adjoining a new functional constant to the language, it is ensured that a fixed point is uniformly presentable as a function of the monotone operation. The upshot of the paper is that the latter extension of explicit mathematics embodies considerable proof-theoretic strength. It is shown that it has at least the strength of the subsystem of second order arithmetic based on $\Pi^1_2$ comprehension. (shrink)

This paper argues that true singular existentials are rationally indubitable. After the claim is clarified and motivated (Section 1), it is defended against objections inspired by Cartesian skepticism and semantic externalism (Section 2), a Fregean fine‐grained conception of propositional content (Section 3), Kripke's causal theory of reference (Section 4), a Stalnakerian coarse‐grained conception of propositional content (Section 5), as well as Evans's account of descriptive reference fixing (Section 6). The discussion is brought to a close by concluding that either true (...) singular existentials are a priori or apriority is not necessary for rational indubitability (Section 7). (shrink)

The context for this paper is Feferman's theory of explicit mathematics, a formal framework serving many purposes. It is suitable for representing Bishop-style constructive mathematics as well as generalized recursion, including direct expression of structural concepts which admit self-application. The object of investigation here is the theory of explicit mathematics augmented by the monotone fixed point principle, which asserts that any monotone operation on classifications (Feferman's notion of set) possesses a least fixed point. To be more precise, the (...) new axiom not merely postulates the existence of a least solution, but, by adjoining a new functional constant to the language, it is ensured that a fixed point is uniformly presentable as a function of the monotone operation. The upshot of the paper is that the latter extension of explicit mathematics (when based on classical logic) embodies considerable proof-theoretic strength. It is shown that it has at least the strength of the subsystem of second order arithmetic based on Π 1 2 comprehension. (shrink)

I examine the debate between substantivalists and relationalists about the ontological character of spacetime and conclude it is not well posed. I argue that the hole argument does not bear on the debate, because it provides no clear criterion to distinguish the positions. I propose two such precise criteria and construct separate arguments based on each to yield contrary conclusions, one supportive of something like relationalism and the other of something like substantivalism. The lesson is that one must fix an (...) investigative context in order to make such criteria precise, but different investigative contexts yield inconsistent results. I examine questions of existence about spacetime structures other than the spacetime manifold itself to argue that it is more fruitful to focus on pragmatic issues of physicality, a notion that lends itself to several different explications, all of philosophical interest, none privileged a priori over any of the others. I conclude by suggesting an extension of the lessons of my arguments to the broader debate between realists and instrumentalists. 1 Introduction2 The Hole Argument3 Limits of Spacetimes4 Pointless Constructions5 The Debate between Substantivalists and Relationalists6 Existence and Physicality: An Embarassment of Spacetime Structures7 Valedictory Remarks on Realism and Instrumentalism, and the Structure of Our Knowledge of Physics. (shrink)

La discussion bioéthique au sein d ’ institutions consiste-t-elle à peser rationnellement entre eux tous les arguments disponibles? Les institutions qui conduisent le débat bioéthique – comme le Parlement, le Comité consultatif national d ’ éthique (CCNE) ou le Conseil d ’ orientation de l ’ Agence de la biomédecine – ne semblent pas vouloir utiliser les arguments rationnels qui iraient à l ’ encontre de la volonté politique préalable qui leur a fixé le cadre de leur mission.

This paper continues investigations of the monotone fixed point principle in the context of Feferman's explicit mathematics begun in [14]. Explicit mathematics is a versatile formal framework for representing Bishop-style constructive mathematics and generalized recursion theory. The object of investigation here is the theory of explicit mathematics augmented by the monotone fixed point principle, which asserts that any monotone operation on classifications possesses a least fixed point. To be more precise, the new axiom not merely postulates the (...) existence of a least solution, but, by adjoining a new constant to the language, it is ensured that a fixed point is uniformly presentable as a function of the monotone operation. Let T$_0$ + UMID denote this extension of explicit mathematics. [14] gave lower bounds for the strength of two subtheories of T$_0$ + UMID in relating them to fragments of second order arithmetic based on $\Pi^1_2$ comprehension. [14] showed that T$_0 \upharpoonright$ + UMID and T$_0 \upharpoonright$ + IND$_\mathbb{N}$ + UMID have at least the strength of $\upharpoonright$ and, respectively. Here we are concerned with the exact reversals. Let UMID$_\mathbb{N}$ be the monotone fixed-point principle for subclassifications of the natural numbers. Among other results, it is shown that T$_0 \upharpoonright$ + UMID$_\mathbb{N}$ and T$_0 \upharpoonright$ + $IND_\mathbb{N}$ + UMID$_\mathbb{N}$ have the same strength as $ $\upharpoonright$ and, respectively. The results are achieved by constructing set-theoretic models for the aforementioned systems of explicit mathematics in certain extensions of Kripke-Platek set theory and subsequently relating these set theories to subsystems of second arithmetic. (shrink)

I comment on two problems in Glover's account. First, semantic representations are not always available to awareness. Second, some functional properties, the affordances of objects, should be encoded in the dorsal system. Then I argue that the existence of Glover's two types of representations is supported by studies on “object-centered” attention. Furthermore, it foreshadows a nondescriptive causal reference fixing process.

Is the exemplar of modern ethical theory estranged from their intimates because the motive of duty dominates their motivational psychology? While this challenge against modern ethical theory is familiar, I argue that with respect to a certain strand of Kantian ethical theory, it does not so much as make sense. I explain the content and functional role of the motive of duty in the psychology of the moral exemplar, stressing in particular how that motive shapes and informs the content of (...) others, including those characteristic of intimacy. I argue that to the extent that a subject does not integrate their motive of duty with their other motives, their moral and intimate relationships are compromised, and on the same grounds, because intimate relationships are interpersonal relationships and the motive of duty just is the motive to respect another person as a separate person. (shrink)

In this paper we investigate a particular two-stage supply chain network design problem with fixed costs. In order to solve this complex optimization problem, we propose an efficient hybrid algorithm, which was obtained by incorporating a linear programming optimization problem within the framework of a genetic algorithm. In addition, we integrated within our proposed algorithm a powerful local search procedure able to perform a fine tuning of the global search. We evaluate our proposed solution approach on a set of (...) large size instances. The achieved computational results prove the efficiency of our hybrid genetic algorithm in providing high-quality solutions within reasonable running-times and its superiority against other existing methods from the literature. (shrink)

Suppose that λ=λ <λ ≥ℵ0, and we are considering a theory T. We give a criterion on T which is sufficient for the consistent existence of λ++ universal models of T of size λ+ for models of T of size ≤λ+, and is meaningful when 2λ +>λ++. In fact, we work more generally with abstract elementary classes. The criterion for the consistent existence of universals applies to various well known theories, such as triangle-free graphs and simple theories. Having in mind (...) possible applications in analysis, we further observe that for such λ, for any fixed μ>λ+ regular with μ=μλ+, it is consistent that 2λ=μ and there is no normed vector space over ℚ of size <μ which is universal for normed vector spaces over ℚ of dimension λ+ under the notion of embedding h which specifies (a,b) such that ||h(x)/||x∈(a,b) for all x. (shrink)

This paper is concerned with a problem of an equitable allocation. We consider the concept of ψ‐equity, which is a general concept of equity. We provide a series of examples of equity concepts that are captured by ψ‐equity. We show the existence of an efficient and ψ‐equitable allocation by employing Kakutani's fixed‐point theorem.

Dozens of articles have addressed the challenge that gambles having undefined expectation pose for decision theory. This paper makes two contributions. The first is incremental: we evolve Colyvan's ``Relative Expected Utility Theory'' into a more viable ``conservative extension of expected utility theory" by formulating and defending emendations to a version of this theory proposed by Colyvan and H\'ajek. The second is comparatively more surprising. We show that, so long as one assigns positive probability to the theory that there is a (...) uniform bound on the utility of possible gambles (and assuming a uniform bound on the amount of utility that can accrue in a fixed amount of time), standard principles of anthropic reasoning (as formulated by Brandon Carter) place lower and upper bounds on the expected values of gambles advertised as having no expectation--even assuming that with positive probability, all gambles advertised as having infinite expected utility are administered faithfully. Should one accept the uniform bound premises, this reasoning thus dissolves (or nearly dissolves, in some cases) several puzzles in infinite decision theory. (shrink)

We consider the problem of the existence of uniform interpolants in the modal logic K4. We first prove that all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square}$$\end{document}-free formulas have uniform interpolants in this logic. In the general case, we shall prove that given a modal formula \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\phi}$$\end{document} and a sublanguage L of the language of the formula, we can decide whether \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} (...) \setlength{\oddsidemargin}{-69pt} \begin{document}$${\phi}$$\end{document} has a uniform interpolant with respect to L in K4. The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square}$$\end{document}-free case is proved using a reduction to the Gödel Löb Logic GL, while in the general case we prove that the question of whether a modal formula has uniform interpolants over transitive frames can be reduced to a decidable expressivity problem on the μ-calculus. (shrink)

According to Jerry Fodor, meaningful expressions denoting no actual entity, like „unicom", do not constitute an exception to his project of semantic naturalization based on the notion of asymmetrical dependence between causal relations. But Fodor does not give any principled reason in order to show that, say, a non-unicom caused "unicom"-token means UNICORN, as he on the contrary does regarding a non-X caused "X"-token for any existing X. Nevertheless, his claim that one such expression has a mere denotational meaning can (...) be accounted for, though in a non-naturalistic way. Suffice it that one appeals to the weak Meinongianism contained in the thesis that one can directly refer to possible entities by means of suitable fixing reference description. (shrink)

Some things, but only some things, are by nature subject to standards. Why? I explain and develop what I call nature-first constitutivism, which says that what something is determines what it should be. Nature is the basis of normativity. I explain this view in terms of a unique type of property which particulars of a genus can lack even though those properties partially determines the nature of the genus. Such properties partially describe the nature of a genus and are thereby (...) normative for the particulars of that genus. Particulars of genera with such essential properties are by nature subject to standards with respect to those properties. Particulars of genera without such properties are not by nature subject to standards. (shrink)

What explains why we are subjects for whom objects can have value, and what explains which objects have value for us? Axiologicians say that the value of humanity is the answer. I argue that our value, no matter what it is like, cannot perform this task. We are animals among others. An explanation of the value of objects for us must fit into an explanation of the value of objects for animals generally. Different objects have value for different animals. Those (...) differences depend on differences in animal natures and, in particular, on the diverse characteristic capacities of different animals. Once we invoke animal natures, there is nothing for the value of animality, including the value of humanity, to explain. (shrink)

The possibility of error conditions the possibility of normative principles. I argue that extant interpretations of this condition undermine the possibility of normative principles for our action because they implicitly treat error as a perfection of an action. I then explain how a constitutivist metaphysics of capacities explains why error is an imperfection of an action. Finally, I describe and defend the interpretation of the error condition which follows.