Let f be a computable function from finite sequences of 0ʼs and 1ʼs to real numbers. We prove that strong f-randomness implies strong f-randomness relative to a PA-degree. We also prove: if X is strongly f-random and Turing reducible to Y where Y is Martin-Löf random relative to Z, then X is strongly f-random relative to Z. In addition, we prove analogous propagation results for other notions of partial randomness, including non-K-triviality and autocomplexity. We prove that f-randomness relative to a (...) PA-degree implies strong f-randomness, hence f-randomness does not imply f-randomness relative to a PA-degree. (shrink)

In this paper, we show within ${\mathsf{RCA}_0}$ that both the Jordan curve theorem and the Schönflies theorem are equivalent to weak König’s lemma. Within ${\mathsf {WKL}_0}$ , we prove the Jordan curve theorem using an argument of non-standard analysis based on the fact that every countable non-standard model of ${\mathsf {WKL}_0}$ has a proper initial part that is isomorphic to itself (Tanaka in Math Logic Q 43:396–400, 1997).

In this paper, we show that equation image is a equation image-conservative extension of BΣ1 + exp, thus it does not imply IΣ1.

We investigate the reverse-mathematical status of several theorems to the effect that the natural number system is second-order categorical. One of our results is as follows. Define a system to be a triple A,i,f such that A is a set and i∈A and f:A→A. A subset X⊆A is said to be inductive if i∈X and ∀a ∈X). The system A,i,f is said to be inductive if the only inductive subset of A is A itself. Define a Peano system to be (...) an inductive system such that f is one-to-one and i∉the range of f. The standard example of a Peano system is N,0,S where N={0,1,2,…,n,…}=the set of natural numbers and S:N→N is given by S=n+1 for all n∈N. Consider the statement that all Peano systems are isomorphic to N,0,S. We prove that this statement is logically equivalent to WKL0 over RCA0⁎ source. From this and similar equivalences we draw some foundational/philosophical consequences. (shrink)

In this paper, we introduce the systems ns-ACA₀ and ns-WKL₀ of non-standard second-order arithmetic in which we can formalize non-standard arguments in ACA₀ and WKL₀, respectively. Then, we give direct transformations from non-standard proofs in ns-ACA₀ or ns-WKL₀ into proofs in ACA₀ or WKL₀.

The program of Reverse Mathematics (Simpson 2009) has provided us with the insight that most theorems of ordinary mathematics are either equivalent to one of a select few logical principles, or provable in a weak base theory. In this paper, we study the properties of the Dirac delta function (Dirac 1927; Schwartz 1951) in two settings of Reverse Mathematics. In particular, we consider the Dirac Delta Theorem, which formalizes the well-known property \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} (...) \begin{document}$${\int_\mathbb{R}f(x)\delta(x)\,dx=f(0)}$$\end{document} of the Dirac delta function. We show that the Dirac Delta Theorem is equivalent to weak König’s Lemma (see Yu and Simpson in Arch Math Log 30(3):171–180, 1990) in classical Reverse Mathematics. This further validates the status of WWKL0 as one of the ‘Big’ systems of Reverse Mathematics. In the context of ERNA’s Reverse Mathematics (Sanders in J Symb Log 76(2):637–664, 2011), we show that the Dirac Delta Theorem is equivalent to the Universal Transfer Principle. Since the Universal Transfer Principle corresponds to WKL, it seems that, in ERNA’s Reverse Mathematics, the principles corresponding to WKL and WWKL coincide. Hence, ERNA’s Reverse Mathematics is actually coarser than classical Reverse Mathematics, although the base theory has lower first-order strength. (shrink)

In this paper, we introduce a system of nonstandard second-order arithmetic $\mathsf{ns}$-$\mathsf{WWKL_0}$ which consists of $\mathsf{ns}$-$\mathsf{BASIC}$ plus Loeb measure property. Then we show that $\mathsf{ns}$-$\mathsf{WWKL_0}$ is a conservative extension of $\mathsf{WWKL_0}$ and we do Reverse Mathematics for this system.

Functional electrical stimulation (FES), a method for inducing muscle contraction, has been successfully used in gait rehabilitation for patients with deficits after neurological disorders and several clinical studies have found that it can improve gait function after stroke and spinal cord injury. However, FES gait training is not suitable for patients with walking difficulty, such as those with severe motor paralysis of the lower limbs. We have previously shown that action observation combined with motor imagery (AO + MI) of walking (...) induces walking-related cortical activity. Therefore, we combined FES, which alternately generates dorsiflexion and plantar flexion, with AO + MI as an alternative to gait training. The present study investigates the transient effects of 20-min of FES simultaneously with and without AO + MI of walking on corticospinal and spinal reflex excitability in able-bodied participants. We measured motor evoked potentials and Hoffmann-reflexes to assess corticospinal and spinal reflex excitability at rest before and after the 20-min FES with and without the AO + MI. Our results show that FES without AO + MI did not change excitability (p > 0.05), while FES with AO + MI facilitated corticospinal excitability (p < 0.05). This facilitation likely occurred due to the synchronization of sensory inputs from FES and cortical activity during AO + MI. Facilitation was observed only in the dorsiflexor but not the plantar flexor muscle (p < 0.05), suggesting muscle specificity of the facilitation. These results demonstrate the effectiveness of combining FES with AO + MI and pave the way for novel neurorehabilitation strategies for patients with neurological gait deficits. (shrink)

In this paper, we introduce systems of nonstandard second-order arithmetic which are conservative extensions of systems of second-order arithmetic. Within these systems, we do reverse mathematics for nonstandard analysis, and we can import techniques of nonstandard analysis into analysis in weak systems of second-order arithmetic. Then, we apply nonstandard techniques to a version of Riemannʼs mapping theorem, and show several different versions of Riemannʼs mapping theorem.

This research is motivated by the program of reverse mathematics and non-standard arguments in second-order arithmetic. Within a weak subsystem of second-order arithmetic ACA0, we investigate some aspects of non-standard analysis related to sequential compactness. Then, using arguments of non-standard analysis, we show the equivalence of the Riemann mapping theorem and ACA0 over WKL0. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim).

We show that many principles of first-order arithmetic, previously only known to lie strictly between [Formula: see text]-induction and [Formula: see text]-induction, are equivalent to the well-foundedness of [Formula: see text]. Among these principles are the iteration of partial functions of Hájek and Paris, the bounded monotone enumerations principle by Chong, Slaman, and Yang, the relativized Paris–Harrington principle for pairs, and the totality of the relativized Ackermann–Péter function. With this we show that the well-foundedness of [Formula: see text] is a (...) far more widespread than usually suspected. Further, we investigate the [Formula: see text]-iterated version of the bounded monotone iterations principle, and show that it is equivalent to the well-foundedness of the -height [Formula: see text]-tower [Formula: see text]. (shrink)

‘Substance’ (substantia, zelfstandigheid) is a key term of Spinoza’s philosophy. Like almost all of Spinoza’s philosophical vocabulary, Spinoza did not invent this term, which has a long history that can be traced back at least to Aristotle. Yet, Spinoza radicalized the traditional notion of substance and made a very powerful use of it by demonstrating – or at least attempting to demonstrate -- that there is only one, unique substance -- God (or Nature) -- and that all other things are (...) merely modes or states of God. Some of Spinoza’s readers understood these claims as committing him to the view that only God truly exists, and while this interpretation is not groundless, we will later see that this enticing and bold reading of Spinoza as an ‘acosmist’ comes at the expense of another audacious claim Spinoza advances, i.e., that God/Nature is absolutely and actually infinite. But before we reach this last conclusion, we have a long way to go. So, let me first provide an overview of our plan. In the first section of this paper we will examine Spinoza’s definitions of ‘substance’ and ‘God’ at the opening of his magnum opus, the Ethics. Following a preliminary clarification of these two terms and their relations to the other key terms defined at the beginning of the Ethics, we will briefly address the Aristotelian and Cartesian background of Spinoza’s discussion of substance. In the second section, we will study the properties of the fundamental binary relations pertaining to Spinoza’s substance: inherence, conception, and causation. The third section will be dedicated to a clarification of Spinoza’s claim that God, the unique substance, is absolutely infinite. This essential feature of Spinoza’s substance has been largely neglected in recent Anglo-American scholarship, a neglect which has brought about an unfortunate tendency to domesticate Spinoza’s metaphysics to more contemporary views. The fourth section will study the nature of Spinoza’s monism. It will discuss and criticize the interesting yet controversial views of the eminent Spinoza scholar, Martial Gueroult, about the plurality of substances in the beginning of the Ethics; address Spinoza’s claim in Letter 50 that, strictly speaking, it is improper to describe God as “one”; and, finally, evaluate Spinoza’s kind of monism against the distinction between existence and priority monism recently introduced into the contemporary philosophical literature. The fifth and final section will explain the nature, reality, and manner of existence of modes. We therefore have an ambitious plan; let’s get down to business. (shrink)

This research is motivated by the program of Reverse Mathematics. We investigate basic part of complex analysis within some weak subsystems of second order arithmetic, in order to determine what kind of set existence axioms are needed to prove theorems of basic analysis. We are especially concerned with Cauchy’s integral theorem. We show that a weak version of Cauchy’s integral theorem is proved in RCAo. Using this, we can prove that holomorphic functions are analytic in RCAo. On the other hand, (...) we show that a full version of Cauchy’s integral theorem cannot be proved in RCAo but is equivalent to weak König’s lemma over RCAo. (shrink)

Background There are several psychosocial and ethical issues surrounding the decision to be a living kidney donor. The present study aimed to determine the perceptions of psychosocial and ethical issues that living kidney donors may have, and analyze their psychological characteristics.Methods Face-to-face semi-structured interviews were conducted with 15 donors. Thematic analysis was then performed to categorize the thematic elements of the transcripts. All procedures were approved by the relevant review board.Results Four main categories were identified: Awareness of family dynamics, barriers (...) to a proper understanding, contrasting psychological effects of recipient presence in clinical practice, insufficient information explained in informed consent.Conclusion Donors felt that they took on the “role as a care giver” for the recipient and were less aware of themselves as patients. This is a new concept that has not been shown in previous studies. Donors exist within the recipient and family, and the range of their autonomy may go beyond the traditional concept of autonomy and be rooted in relational autonomy. This study suggested that medical treatment in the presence of the recipient promotes the relational autonomy of the donor. (shrink)

Introduction Social anxiety disorder (SAD) symptoms are maintained by cognitive biases, which are overestimations of the severity and likelihood of negative social events (cost/probability biases), and by sensitivity to rewards and punishments that are determined according to behavioral inhibition/behavioral activation systems (BIS/BAS). Cost/probability biases might activate the behavioral immune system and exacerbate the avoidance of social events. Earlier studies have proposed that low BIS or high BAS decrease SAD symptoms; BIS/BAS may even change the effects of cognitive biases on SAD (...) symptoms. Hence, the current study investigates the interaction effects of BIS/BAS and cost/probability biases on SAD symptoms. Method Seventy-six Japanese undergraduate students completed the Japanese version of the Liebowitz Social Anxiety Scale (LSAS), which comprises Fear and Avoidance subscales, the BIS/BAS Scale, and the Social Cost Probability Scale. Results A multiple regression analysis was performed to examine whether cost/probability biases, BIS/BAS, and their interactions affected SAD symptoms; following this, the main effects of cost bias and BIS were determined for LSAS-Fear (β =.64, p <.001; β =.33, p <.01) and LSAS-Avoidance (β =.49, p <.001; β =.35, p <.01). The interaction effect between cost bias and BAS was significant for LSAS-Avoidance (β = −.32, p <.05). Simple slope analysis showed that the slope of cost bias was significant for low-BAS individuals (β =.77, p <.001) but not for high-BAS individuals (β = −.21, n.s.). The interaction effect between probability bias and BAS was significant for LSAS-Avoidance (β =.40, p <.01) as well. Further, simple slope analysis revealed that the slope of probability bias was significant for low-BAS individuals (β = −.53, p <.05) but not for high-BAS individuals (β =.17, n.s.). Discussion The study found interesting results with respect to the avoidance of social events. Low-BAS individuals with high cost or low probability biases regarding social events may have a tendency to avoid social events. In contrast, if high-BAS individuals overestimate the cost of social events or underestimate the probability of social events, their anticipation of rewards might prevent them from avoiding social events. (shrink)

Disbelief, lies, and manipulations have been objects of scholarly consideration from widely different perspectives: historical, sociological, philosophical, ethical, logical, and pragmatic. In this paper, these notions are re-examined in the framework of a Transactional Discourse Model which operates in terms of the location and relocation of various knowledge items within two sets of knowledge, A and B, representing two interlocators A and B, and two of their subsets Ca and Cb, which constitute the sets of the matters of A's and (...) B's current concern. This approach reveals certain formal features shared by lies, disbelief, and manipulations that indicate that these three types of discourse behavior constitute a deviation from successful interpersonal communication as defined in the proposed model. The model, moreover, enables us to explicitly capture both the similarities and the differences of lies and manipulations with other pragmatic phenomena, such as jokes, impersonating, role-acting, memory failure, politeness expressions, and tact; the comparison suggests that certain modifications of Gricean conversational maxims may be in order. (shrink)

Maquiavelo y su tiempo.--Reacción de algunos escritores españoles de los siglos XVII y XVIII ante la doctrina de Maquiavelo.--El maquiavelismo y las prácticas de gobierno.

The potential to collect brain data more directly, with higher resolution, and in greater amounts has heightened worries about mental and brain privacy. In order to manage the risks to individuals posed by these privacy challenges, some have suggested codifying new privacy rights, including a right to “mental privacy.” In this paper, we consider these arguments and conclude that while neurotechnologies do raise significant privacy concerns, such concerns are—at least for now—no different from those raised by other well-understood data collection (...) technologies, such as gene sequencing tools and online surveillance. To better understand the privacy stakes of brain data, we suggest the use of a conceptual framework from information ethics, Helen Nissenbaum’s “contextual integrity” theory. To illustrate the importance of context, we examine neurotechnologies and the information flows they produce in three familiar contexts—healthcare and medical research, criminal justice, and consumer marketing. We argue that by emphasizing what is distinct about brain privacy issues, rather than what they share with other data privacy concerns, risks weakening broader efforts to enact more robust privacy law and policy. (shrink)

DICTIONARY OF SPANISH VERBS WITH THEIR ENGLISH EQUIVALENTS AND MODELS OF CONJUGATION/DICCIONARIO CON LOS VERBOS EN ESPAÑOL, SU TRADUCCIÓN AL INGLÉS Y CONJUGACIONES.