We generalize the Bolzano-Weierstrass theorem on ideal convergence. We show examples of ideals with and without the Bolzano-Weierstrass property, and give characterizations of BW property in terms of submeasures and extendability to a maximal P-ideal. We show applications to Rudin-Keisler and Rudin-Blass orderings of ideals and quotient Boolean algebras. In particular we show that an ideal does not have BW property if and only if its quotient Boolean algebra has a countably splitting family.

Let μ be a universal lower enumerable semi-measure . Any computable upper bound for μ can be effectively separated from zero with a constant . Computable positive lower bounds for μ can be nontrivial and allow one to construct natural examples of hypersimple sets.

Call a set A n-correctable if every set Turing reducible to A via a Turing machine that on any input makes at most n queries is Turing reducible to A via a Turing machine that on any input makes at most n-queries and on any input halts no matter what answers are given to its queries. We show that if a c.e. set A is n-correctable for some n ≥ 2, then it is n-correctable for all n. We show that (...) this is the optimal such result by constructing a c.e. set that is 1-correctable but not 2-correctable. The former result is obtained by examining the logical closure properties of c.e. sets that are 2-correctable. (shrink)

The rational price of the Pasadena and Altadena games, introduced by Nover and Hájek (2004 ), has been the subject of considerable discussion. Easwaran (2008 ) has suggested that weak expectations — the value to which the average payoffs converge in probability — can give the rational price of such games. We argue against the normative force of weak expectations in the standard framework. Furthermore, we propose to replace this framework by a bounded utility perspective: this shift renders the problem (...) more realistic and accounts for the role of weak expectations. In particular, we demonstrate that in a bounded utility framework, all agents, even if they have different value functions and disagree on the price of an individual game, will finally agree on the rational price of a repeated, averaged game. Thus, we explain the intuitive appeal of weak expectations, while avoiding both trivialization of the original paradox and the drawbacks of previous approaches. (shrink)

Bayesians since Savage (1972) have appealed to asymptotic results to counter charges of excessive subjectivity. Their claim is that objectionable differences in prior probability judgments will vanish as agents learn from evidence, and individual agents will converge to the truth. Glymour (1980), Earman (1992) and others have voiced the complaint that the theorems used to support these claims tell us, not how probabilities updated on evidence will actually}behave in the limit, but merely how Bayesian agents believe they will behave, suggesting (...) that the theorems are too weak to underwrite notions of scientific objectivity and intersubjective agreement. I investigate, in a very general framework, the conditions under which updated probabilities actually converge to a settled opinion and the conditions under which the updated probabilities of two agents actually converge to the same settled opinion. I call this mode of convergence deterministic, and derive results that extend those found in Huttegger (2015b). The results here lead to a simple characterization of deterministic convergence for Bayesian learners and give rise to an interesting argument for what I call strong regularity, the view that probabilities of non-empty events should be bounded away from zero. (shrink)

We define two types of convergence for observables on a quantum logic which we call M-weak and uniform M-weak convergence. These convergence modes correspond to weak convergence of probability measures. They are motivated by the idea that two (in general unbounded) observables are “close” if bounded functions of them are “close.” We show that M-weak and uniform M-weak convergence generalize strong resolvent and norm resolvent convergence for self-adjoint operators on a Hilbert space. Also, these (...) types of convergence strengthen the weak operator convergence and operator norm convergence of bounded self-adjoint operators on a Hilbert space. Finally, we consider spectral perturbation by showing that the spectra of approximating observables approach the spectrum of the limit in a certain sense. (shrink)

We define the effective integrability of Fine-computable functions and effectivize some fundamental limit theorems in the theory of Lebesgue integrals such as the Bounded Convergence Theorem, the Dominated Convergence Theorem, and the Second Mean Value Theorem. It is also proved that the Walsh-Fourier coefficients of an effectively integrable Fine-computable function form a Euclidian computable sequence of reals which converges effectively to zero. This property of convergence is the effectivization of the Walsh-Riemann-Lebesgue Theorem. The article is closed with (...) the effective version of Dirichlet's test. (shrink)

A finite data set is consistent with infinitely many alternative theories. Scientific realists recommend that we prefer the simplest one. Anti-realists ask how a fixed simplicity bias could track the truth when the truth might be complex. It is no solution to impose a prior probability distribution biased toward simplicity, for such a distribution merely embodies the bias at issue without explaining its efficacy. In this note, I argue, on the basis of computational learning theory, that a fixed simplicity bias (...) is necessary if inquiry is to converge to the right answer efficiently, whatever the right answer might be. Efficiency is understood in the sense of minimizing the least fixed bound on retractions or errors prior to convergence. (shrink)

The dominated convergence theorem implies that if is a sequence of functions on a probability space taking values in the interval [0, 1], and converges pointwise a.e., then converges to the integral of the pointwise limit. Tao [26] has proved a quantitative version of this theorem: given a uniform bound on the rates of metastable convergence in the hypothesis, there is a bound on the rate of metastable convergence in the conclusion that is independent of the sequence (...) and the underlying space. We prove a slight strengthening of Tao’s theorem which, moreover, provides an explicit description of the second bound in terms of the first. Specifically, we show that when the first bound is given by a continuous functional, the bound in the conclusion can be computed by a recursion along the tree of unsecured sequences. We also establish a quantitative version of Egorov’s theorem, and introduce a new mode of convergence related to these notions. (shrink)

In chapter one I will try to reconstruct a plot, or a hidden agenda, in the discussion in ethics between the beginning of the twentieth century and 1958, the year of a decisive turning point in ethics, both Anglo-Saxon and Continental, and strangely enough also the year of the beginning of the end of the Cold War, of post-Tridentine Catholicism, and perhaps something else. My hypothesis will be that there are two similar starting points for the Anglo-Saxon and the Continental (...) twentieth-century discussion, the philosophies of Henry Sidgwick and Friedrich Nietzsche, both expressions of some kind of ethical scepticism, and that a third, somewhat analogous starting-point could be found in Émile Durkheim, the proponent of the dream of the morale laïque. I will discuss how far the diagnosis formulated by Karl-Otto Apel of a kind of ‘parallel convergence' between existentialism and analytic philosophy, based on the shared division of facts and values that eventually justified two kinds of 'decisionism' is useful in making sense of the agenda of the discussion. In the second chapter I will discuss the reasons for two parallel U-turns around 1958 which brought back traditional schools of normative ethics, 'deontologism' and utilitarianism, as well as the reasons for criticism to both schools from the heterogeneous alignment of virtue ethics. In the third chapter I will discuss the remarkable phenomenon of the emergence, starting with the Sixties or the early Seventies, of ‘applied’ ethics. I examine the reasons, both theoretical and political, for the revival, the point to which applied ethics may look as a grand return of a casuistic and natural law way of thinking, or in Alan Donagan’s words a case of “reverse subversion” of the modern secular world by traditional Scholastic ways of thinking, and the difficult coexistence between general normative ethics and procedures for settling issues in a ‘reasonable’ way while dissent on issues of principle is as alive as ever. Then I try to draw a provisional moral. My suggestions are that (i) casuistry is more alive than ever; (ii) natural law thinking is more alive than ever; (iii) moral dilemmas never arise; (iv) moral dissent is treatable, with the right strategy; (v) practical philosophy does not need the same degree of exactness as the theoretical sciences but this is no obstacle to its working in practice. (shrink)

Merker's insightful broad review fertilely recasts the mind/brain issue, but the phenomenological appeals require additional considerations of behavioral and neural flexibility. Motor equivalences and perceptual constancies may be cortical contributions to a “robotic” tectal orientation mechanism. Intermediate “third layers” of associative neural networks, each with a few diffusely summing convergence-divergence modules, may be the economical expedient by which evolution has extended the limited unity-in-diversity of sensorimotor coordination to perception, action, thinking, and memory. (Published Online May 1 2007).

We examine how insights made in socio-anthropological and evolutionary schools of thought necessitate us to reevaluate the classic philosophical distinction between epistemology and ontology. We adopt an applied evolutionary epistemological stance and demonstrate that both epistemology and ontology evolve. Epistemology is broadened to include all knowledge and information that all life forms evolve, and ontology encompasses all biologically informed realities that life builds. Through processes such as symbiosis and niche construction, organisms acquire and extend information and knowledge into their offspring, (...) onto unrelated organisms, and onto their niches. Life builds biorealities that change over time. Consequently, knowledge and reality are mutable and truth is spatiotemporally bounded. We conclude that the classic distinction between epistemology and ontology has become superfluous and instead, we argue that the evolving knowledge that comes in the form of organisms and their extended niches equals ontological realities. (shrink)

In this paper we develop a method for finding, under general conditions, explicit and highly uniform rates of convergence for the Picard iteration sequences for selfmaps on bounded metric spaces from ineffective proofs of convergence to a unique fixed point. We are able to extract full rates of convergence by extending the use of a logical metatheorem recently proved by Kohlenbach. In recent case studies we were able to find such explicit rates of convergence in two (...) concrete cases. Our novel method now provides an explanation in logical terms for these findings. This amounts, loosely speaking, to general conditions under which we in this specific setting can transform a ∀∃∀-sentence into a ∀∃-sentence via an argument involving product spaces. This reduction in logical complexity allows us to use the existing machinery to extract quantitative bounds of the sort we need. (shrink)

Let $\mathcal {I}$ be an ideal on $\omega $. For $f,\,g\in \omega ^{\omega }$ we write $f \leq _{\mathcal {I}} g$ if $f(n) \leq g(n)$ for all $n\in \omega \setminus A$ with some $A\in \mathcal {I}$. Moreover, we denote $\mathcal {D}_{\mathcal {I}}=\{f\in \omega ^{\omega }: f^{-1}[\{n\}]\in \mathcal {I} \text { for every } n\in \omega \}$ (in particular, $\mathcal {D}_{\mathrm {Fin}}$ denotes the family of all finite-to-one functions).We examine cardinal numbers $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {I}} \times \mathcal {D}_{\mathcal (...) {I}}))$ and $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathrm {Fin}}\times \mathcal {D}_{\mathrm {Fin}}))$ describing the smallest sizes of unbounded from below with respect to the order $\leq _{\mathcal {I}}$ sets in $\mathcal {D}_{\mathrm {Fin}}$ and $\mathcal {D}_{\mathcal {I}}$, respectively. For a maximal ideal $\mathcal {I}$, these cardinals were investigated by M. Canjar in connection with coinitial and cofinal subsets of the ultrapowers.We show that $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathrm {Fin}} \times \mathcal {D}_{\mathrm {Fin}})) =\mathfrak {b}$ for all ideals $\mathcal {I}$ with the Baire property and that $\aleph _1 \leq \mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {I}} \times \mathcal {D}_{\mathcal {I}})) \leq \mathfrak {b}$ for all coanalytic weak P-ideals (this class contains all $\bf {\Pi ^0_4}$ ideals). What is more, we give examples of Borel (even $\bf {\Sigma ^0_2}$ ) ideals $\mathcal {I}$ with $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {I}} \times \mathcal {D}_{\mathcal {I}}))=\mathfrak {b}$ as well as with $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {I}} \times \mathcal {D}_{\mathcal {I}})) =\aleph _1$.We also study cardinals $\mathfrak {b}(\geq _{\mathcal {I}}\cap (\mathcal {D}_{\mathcal {J}} \times \mathcal {D}_{\mathcal {K}}))$ describing the smallest sizes of sets in $\mathcal {D}_{\mathcal {K}}$ not bounded from below with respect to the preorder $\leq _{\mathcal {I}}$ by any member of $\mathcal {D}_{\mathcal {J}}\!$. Our research is partially motivated by the study of ideal-QN-spaces: those cardinals describe the smallest size of a space which is not ideal-QN. (shrink)

Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose two different methods for semiclassical quantization. The first method is based upon the harmonic inversion of semiclassical recurrence functions. A band-limited periodic orbit signal is obtained by analytical frequency windowing of the periodic orbit sum. The frequencies of the periodic orbit signal are the semiclassical eigenvalues, and are determined by either linear predictor, Padé approximant, or signal diagonalization. The second method is based upon the direct application (...) of the Padé approximant to the periodic orbit sum. The Padé approximant allows the resummation of the, typically exponentially, divergent periodic orbit terms. Both techniques do not depend on the existence of a symbolic dynamics, and can be applied to bound as well as to open systems. Numerical results are presented for two different systems with chaotic and regular classical dynamics, viz. the three-disk scattering system and the circle billiard. (shrink)

A nonlinear coupled wing model subject to unknown external disturbances is proposed in this paper. Since the model is modeled by partial differential equations, the traditional control design scheme based on the ordinary differential equation model is not applicable, and the control law design becomes very complex. In this paper, a new antidisturbance boundary control scheme based on a finite time convergent disturbance observer is proposed. The control laws are designed based on the new disturbance observers to make the external (...) disturbance errors converge to zero in a finite time and ensure the uniformly bounded stability of the controlled system. Finally, the effectiveness of the controllers and the finite-time convergence of disturbance errors are verified by the simulation and comparison. (shrink)

Constrained optimization plays an important role in many decision-making problems and various real-world applications. In the last two decades, various evolutionary algorithms were developed and still are developing under the umbrella of evolutionary computation. In general, EAs are mainly categorized into nature-inspired and swarm-intelligence- based paradigms. All these developed algorithms have some merits and also demerits. Particle swarm optimization, firefly algorithm, ant colony optimization, and bat algorithm have gained much popularity and they have successfully tackled various test suites of benchmark (...) functions and real-world problems. These SI-based algorithms follow the social and interactive principles to perform their search process while approximating solution for the given problems. In this paper, a multiswarm-intelligence-based algorithm is developed to cope with bound constrained functions. The suggested algorithm integrates the SI-based algorithms to evolve population and handle exploration versus exploitation issues. Thirty bound constrained benchmark functions are used to evaluate the performance of the proposed algorithm. The test suite of benchmark function is recently designed for the special session of EAs competition in IEEE Congress on Evolutionary Computation. The suggested algorithm has approximated promising solutions with good convergence and diversity maintenance for most of the used bound constrained single optimization problems. (shrink)

Taking inspiration from the film Wit (2001), adapted from Margaret Edson’s (1999) Pulitzer Prize-winning play, this article explores the particularities of witnessing a cinematic cancer narrative juxtaposed with the author’s own cancer narrative. The analysis reveals the tenuous line between death and dying, illness and wellness, life and living and the resulting identities shaped in the process of understanding both from a personal and professional lens. By framing these representations of illness experience within the narrative constructions of drama, time, metaphor (...) and morality, the personal stories of intellectual knowledge converging with intimate and embodied knowing are revealed. (shrink)

Inspired by a construction of the Tsirelson space , we prove a general theorem for omitting countably many positive formulas in normed spaces. This theorem can be used in functional analysis as a tool to guarantee the existence of complicated normed spaces without having to construct them. The proof of this result is based on the notion of approximate truth and on a study of the relationship between approximate truth and convergence in normed spaces. We illustrate the power of (...) this result with an application to functional analysis. (shrink)

The story of the body. Fay Bound Alberti takes the human body apart in order to put it back anew, telling the cultural history of our key organs and systems from the inside out, from blood to guts, brains to sex organs.

In this paper I draw from Martin Heidegger’s phenomenology of the 1920s to outline some basic features of his theory of intentionality that I believe have not been fully appreciated or utilized, and that allow for both novel and fruitful interventions in questions about meaning, the relationship between mind and the world, and epistemic justification, principally as they appear in John McDowell’s synoptic project in Mind and World. I argue that while elements of McDowell’s picture are ultimately unsatisfying and problematic, (...) much of his conceptual framework can and should be put into dialogue with Heidegger’s, and that in so doing we make available powerful resources for amending the McDowellian account. Moreover, these emendations have attractive implications for his distinctive desiderata. In particular, they provide original conceptions of normativity’s place in nature, of the boundaries of the space of reasons, and of the relationship between the answerability of thought both to the world and to human beings as a rational community. (shrink)

Many contemporary scholars argue that Schelling’s version of intellectual intuition retains certain central features of the Kantian and Fichtean conceptions. One of the common claims is that, as with Kant and Fichte, Schelling’s intellectual intuition is the power of the subject’s productive understanding. However, we show that for the Schelling of the Identitätsphilosophie period, intellectual intuition is the power not of an understanding that intuits, or a productive intellect, but of a receptive and penetrating sensibility that understands.

Loneliness is one of the most neglected aspects of emotion history, despite claims that the 21st century is the loneliest ever. This article argues against the widespread belief that modern-day loneliness is inevitable, negative, and universal. Looking at its language and etymology, it suggests that loneliness needs to be understood firstly as an “emotion cluster” composed of a variety of affective states, and secondly as a relatively recent invention, dating from around 1800. Loneliness can be positive, and as much a (...) part of the body as the mind. Using a longue durée approach, I argue that we cannot understand loneliness as a “modern epidemic” without considering its history, its meanings, its practice, and its links with the body. (shrink)

This essay explores small “ordinary” experiences of moral harm as problems of social injustice. Starting with two stories, we first argue against a dominant framework of personal responsibility that assigns responsibility to particular blameworthy agents. Instead we sketch an account of why structural responsibility for social harm must be considered, drawing on the work of Iris Marion Young and Pierre Bourdieu. Finally, drawing on Margaret Walker’s notion of moral repair and Christopher Marshall’s interpretation of the parable of the Good Samaritan, (...) we sketch an account of Christian moral responsibility grounded in restorative justice that seeks to address daily experiences of moral harm through the moral repair work of neighbor-love. (shrink)

Analyzing the rate at which languages change can clarify whether similarities across languages are solely the result of cognitive biases or might be partially due to descent from a common ancestor. To demonstrate this approach, we use a simple model of language evolution to mathematically determine how long it should take for the distribution over languages to lose the influence of a common ancestor and converge to a form that is determined by constraints on language learning. We show that modeling (...) language learning as Bayesian inference ofnbinary parameters or the ordering ofnconstraints results in convergence in a number of generations that is on the order ofn log n. We relax some of the simplifying assumptions of this model to explore how different assumptions about language evolution affect predictions about the time to convergence; in general, convergence time increases as the model becomes more realistic. This allows us to characterize the assumptions about language learning (given the models that we consider) that are sufficient for convergence to have taken place on a timescale that is consistent with the origin of human languages. These results clearly identify the consequences of a set of simple models of language evolution and show how analysis of convergence rates provides a tool that can be used to explore questions about the relationship between accounts of language learning and the origins of similarities across languages. (shrink)

"Divination and Human Nature" casts a new perspective on the rich tradition of ancient divination--the reading of divine signs in oracles, omens, and dreams. Popular attitudes during classical antiquity saw these readings as signs from the gods while modern scholars have treated such beliefs as primitive superstitions. In this book, Peter Struck reveals instead that such phenomena provoked an entirely different accounting from the ancient philosophers. These philosophers produced subtle studies into what was an odd but observable fact--that humans could (...) sometimes have uncanny insights--and their work signifies an early chapter in the cognitive history of intuition. Examining the writings of Plato, Aristotle, the Stoics, and the Neoplatonists, Struck demonstrates that they all observed how, setting aside the charlatans and swindlers, some people had premonitions defying the typical bounds of rationality. Given the wide differences among these ancient thinkers, Struck notes that they converged on seeing this surplus insight as an artifact of human nature, projections produced under specific conditions by our physiology. For the philosophers, such unexplained insights invited a speculative search for an alternative and more naturalistic system of cognition. Recovering a lost piece of an ancient tradition, "Divination and Human Nature" illustrates how philosophers of the classical era interpreted the phenomena of divination as a practice closer to intuition and instinct than magic. (shrink)

Convergent realists desire scientific methods that converge reliably to informative, true theories over a wide range of theoretical possibilities. Much attention has been paid to the problem of induction from quantifier-free data. In this paper, we employ the techniques of formal learning theory and model theory to explore the reliable inference of theories from data containing alternating quantifiers. We obtain a hierarchy of inductive problems depending on the quantifier prefix complexity of the formulas that constitute the data, and we provide (...) bounds relating the quantifier prefix complexity of the data to the quantifier prefix complexity of the theories that can be reliably inferred from such data without background knowledge. We also examine the question whether there are theories with mixed quantifiers that can be reliably inferred with closed, universal formulas in the data, but not without. (shrink)

I respond to six objections, raised by Selim Berker and Karl Schafer, against the theory offered in my Empiricism and Experience: (1) that the theory needs a problematic notion of subjective character of experience; (2) that the transition from the hypothetical to the categorical fails because of a logical difficulty; (3) that the constraints imposed on admissible views are too weak; (4) that the theory does not deserve the label 'empiricism'; (5) that the motivations provided for the Reliability constraint are (...) insufficient; and (6) that convergence is bound to fail since epistemic entitlements are permissions. (shrink)

Convergent scientific realism entails that science will sooner or later arrive at the final theory of the fundamental constituents of matter. At that stage, all fundamental truths about nature will be discovered so that the search for basic principle seems bound to come to a halt. I explore options for a non-convergent scientific realism that allows for sustained progress in basic research. I defend the views that the coherence of non-convergent realism requires an emergence claim and that this claim can (...) be supported. I develop the example of the relation between equivalence classes among biological functions and their physiological realizations. Given strongly emergent laws in the sense elaborated in the paper, progress in basic research may survive the discovery of the laws governing the tinymost parts of matter. (shrink)

Husserl’s lifelong interest in Kant eventually becomes a preoccupation in his later years when he finds his phenomenology in competition with Neokantianism for the title of transcendental philosophy. Some issues that Husserl is concerned with in Kant are bound up with the works of Lambert. Kant believed that the role played by principles of sensibility in metaphysics should be determined by a “general phenomenology” on which Lambert had written. Kant initially believed that man is capable only of symbolic cognition, not (...) intellectual intuition. Lambert saw an increasing need in mathematics for symbolic cognition as exemplified in his proofs of the irrationality of π and e. Kant takes from Leibniz and Lambert an unrestricted notion of construction, allowing him to view mathematics as constructing its concepts in intuition, while Lambert’s proofs convince him that all mathematical problems are eventually solvable. Husserl criticizes Kant’s intuitionism for its inadequate accommodation of meaning to intuition, which he redresses with his theory of categorial intuition. This may improve on Kant’s intuition of the axiom of parallels but not so clearly on his spatial intuition. Husserl opposes Kant’s view of space as the form of outer intuition with his own view of it as the form of things. Husserl’s exploration of the geometry of visual space, which involves his earliest uses of epoché and reduction, converges however with Hilbert’s logical analysis of Kantian spatial intuition in leading to Euclidean spatial judgments. Hilbert’s analysis leads him to affirm the solvability of all well posed mathematical problems, a thesis complicated by the outbreak of logical paradoxes. Untroubled by such paradoxes, Husserl develops a supramathematics of all possible deductive systems whose completeness implicitly would also provide solutions of all such problems. Husserl’s full transcendental turn coincides with his realization that in effecting his Copernican turn, Kant was really the first to detect the “secret longing” of modern philosophy for a phenomenological clarification of being. Husserl now finds that Kant’s transcendental deductions presuppose a pure ego not adequately analyzed by Kant that survives the phenomenological reduction. Husserl’s idealism leads him to develop his own intuitionism, which adds to Kant’s, a “method of clarification” of mathematical concepts intended to clarify difficult impossibility proofs, but neither Husserl nor Kant base arithmetic on time. Husserl’s critique of the room left in Kant’s idealism, for things in themselves, leads to his own monadological solution of the problem of intersubjectivity. Husserl’s final judgment on Kant is that his form of transcendental idealism did not enable him to achieve absolute subjectivity through a genuine transcendental reduction. (shrink)

This paper provides an empirical defense of credit theories of knowing against Mark Alfano’s challenges to them based on his theses of inferential cognitive situationism and of epistemic situationism. In order to support the claim that credit theories can treat many cases of cognitive success through heuristic cognitive strategies as credit-conferring, the paper develops the compatibility between virtue epistemologies qua credit theories, and dual-process theories in cognitive psychology. It also a response to Lauren Olin and John Doris’ “vicious minds” thesis, (...) and their “tradeoff problem” for virtue theories. A genuine convergence between virtue epistemology and dual-process theory is called for, while acknowledging that this effort may demand new and more empirically well-informed projects on both sides of the division between Conservative virtue epistemology (including the credit theory of knowing) and Autonomous virtue epistemology (including projects for providing guidance to epistemic agents). (shrink)

Given a convergence theorem in analysis, under very general conditions a model-theoretic compactness argument implies that there is a uniform bound on the rate of metastability. We illustrate with three examples from ergodic theory.

How can players reach a Nash equilibrium? I offer one possible explanation in terms of a low-rationality learning method called probe and adjust by proving that it converges to strict Nash equilibria in an important class of games. This demonstrates that decidedly limited learning methods can support Nash equilibrium play.

Some philosophers search for the mark of the cognitive: a set of individually necessary and jointly sufficient conditions identifying all instances of cognition. They claim that the mark of the cognitive is needed to steer the development of cognitive science on the right path. Here, I argue that, at least at present, it cannot be provided. First (§2), I identify some of the factors motivating the search for a mark of the cognitive, each yielding a desideratum the mark is supposed (...) to satisfy (§2.1). I then (§2.2) highlight a number of tensions in the literature on the mark of the cognitive, suggesting they’re best resolved by distinguishing two distinct programs. The first program (§3) is that of identifying a mark of the cognitive capturing our everyday notion of cognition. I argue that such a program is bound to fail for a number of reasons: it is not clear whether such an everyday notion exists; and even if it existed, it would not be able to spell out individually necessary and jointly sufficient conditions for cognition; and even if it were able to spell them out, these conditions won’t satisfy the desiderata a mark of the cognitive should satisfy. The second program is that of identifying a mark of the cognitive spelling out a genuine scientific kind. But the current state of fragmentation of cognitive science, and the fact that it is splintered in a myriad of different research traditions, prevent us from identifying such a kind. And we have no reason to think that these various research traditions will converge, allowing us to identify a single mark. Or so, at least, I will argue in (§4). I then conclude the paper (§5) deflecting an intuitive objection, and exploring some of the consequences of the thesis I have defended. (shrink)

We introduce a St. Petersburg-like game, which we call the ‘Pasadena game’, in which we toss a coin until it lands heads for the first time. Your pay-offs grow without bound, and alternate in sign (rewards alternate with penalties). The expectation of the game is a conditionally convergent series. As such, its terms can be rearranged to yield any sum whatsoever, including positive infinity and negative infinity. Thus, we can apparently make the game seem as desirable or undesirable as we (...) want, simply by reordering the pay-off table, yet the game remains unchanged throughout. Formally speaking, the expectation does not exist; but we contend that this presents a serious problem for decision theory, since it goes silent when we want it to speak. We argue that the Pasadena game is more paradoxical than the St. Petersburg game in several respects. We give a brief review of the relevant mathematics of infinite series. We then consider and rebut a number of replies to our paradox: that there is a privileged ordering to the expectation series; that decision theory should be restricted to finite state spaces; and that it should be restricted to bounded utility functions. We conclude that the paradox remains live. (shrink)

In this study, an accurate convergence time of the supertwisting algorithm is proposed to build up a framework for nonaffine nonlinear systems’ finite-time control. The convergence time of the STA is provided by calculating the solution of a differential equation instead of constructing Lyapunov function. Therefore, precise convergence time is presented instead of estimation of the upper bound of the algorithm’s reaching time. Regardless of affine or nonaffine nonlinear systems, supertwisting control provides a general solution based on (...) virtual control law skill ensuring the output of the systems converges to the origin point at exact time. Benchmark tests are simulated to demonstrate the effectiveness and efficiency of the algorithm. (shrink)

Differing views on reduction are briefly reviewed and a suggestion is made for a working definition of 'approximate reduction'. Ab initio studies in quantum chemistry are then considered, including the issues of convergence and error bounds. This includes an examination of the classic studies on CH2 and the recent work on the Si2C molecule. I conclude that chemistry has not even been approximately reduced.

Although nanotechnology is often defined as operations on the 10-9 meters, the lack of charisma in the scale-bound definitions has been fortified by remarkable dreams and alluring promises that spark excitement for nanotechnology. The story of the rhetorical development of nanotechnology reveals how speculative claims are powerful constructions that create legitimacy in this emerging technological domain. From its inception, nanotechnology has been more of a dream than reality, more fiction than fact. In recent years, however, the term nanotechnology has been (...) actively drawn toward the present to begin to deliver on the fantastic expectations. This debate over time and timing is loaded with paradox. This work examines how future claims work to define what counts as nanotechnology and reveals dilemmas that accompany temporal disjunctures. Science and politics converge in debates about the future of technology as expectations serve to create and enforce power and legitimacy in the emerging area. (shrink)