The central limit theorem has been found to apply to random vectors in complex Hilbert space. This amounts to sufficient reason to study the complex–valued Gaussian, looking for relevance to quantum mechanics. Here we show that the Gaussian, with all terms fully complex, acting as a propagator, leads to Schrödinger’s non-relativistic equation including scalar and vector potentials, assuming only that the norm is conserved. No physical laws need to be postulated a priori. It thereby presents as a process (...) of irregular motion analogous to the real random walk but executed under the rules of the complex number system. There is a standard view that Schrödinger’s equation is deterministic, whereas wavefunction “collapse” is probabilistic —we have now a demonstrated linkage to the central limit theorem, indicating a stochastic picture at the foundation of Schrödinger’s equation itself. It may be an example of Wheeler’s “It from bit” with “No underlying law”. Reasons for the primary role of \ are open to discussion. The present derivation is compared with recent reconstructions of the quantum formalism, which have the aim of rationalizing its obscurities. (shrink)

We review studies of an evolution operator ℒ for a discrete Langevin equation with a strongly hyperbolic classical dynamics and a Gaussian noise. The leading eigenvalue of ℒ yields a physically measurable property of the dynamical system, the escape rate from the repeller. The spectrum of the evolution operator ℒ in the weak noise limit can be computed in several ways. A method using a local matrix representation of the operator allows to push the corrections to the escape rate (...) up to order eight in the noise expansion parameter. These corrections then appear to form a divergent series. Actually, via a cumulant expansion, they relate to analogous divergent series for other quantities, the traces of the evolution operators ℒn. Using an integral representation of the evolution operator ℒ, we then investigate the high order corrections to the latter traces. Their asymptotic behavior is found to be controlled by sub-dominant saddle points previously neglected in the perturbative expansion, and to be ultimately described by a kind of trace formula. (shrink)

Concern about air-quality in urban areas has led to the implementation of Low Emission Zones as one of many other initiatives to control it. Recently in Spain, the enactment of a law made this mandatory for cities with a population larger than 50k inhabitants. The delimitation of these areas is not without controversy because of possible negative economic and social impacts. Therefore, clear assessments of how these initiatives decrease pollutant concentrations are to be provided. Madrid Central is a major initiative (...) of Madrid city council for reducing motor traffic and the associated air pollution in the city centre. This Low Emission Zone starts at the end of 2018, but the first fully-operational period corresponds to the second quarter of 2019. In this work, a methodology based on the Gaussian Process to analyse the evolution of Nitrogen Dioxide inside Madrid Central is undertaken. A Gaussian Process is a stochastic process suitable for interpretable model selection and predictions. Due to its probabilistic nature it provides error estimation at predictions. After the activation of Madrid Central, a relevant reduction of Nitrogen Dioxide has been observed. However, the role of the meteorology during this period must be ascertained to correctly evaluate the role of the activation of the Low Emission Zone against a prone weather. In this work, a model based on the Gaussian Process is trained with meteorological information to predict the concentration of Nitrogen Dioxide at Madrid Central, $[NO_{2}]$. This probabilistic description allows extracting statistical information on the reduction affected by the meteorological scenario and separately by the Madrid Central activation. (shrink)

In this paper, we propose an adaptive Gaussian incremental expectation stadium parameter estimation algorithm for sports video analysis and prediction through the study and analysis of sports videos. The features with more discriminative power are selected from the set of positive and negative templates using a feature selection mechanism, and a sparse discriminative model is constructed by combining a confidence value metric strategy. The sparse generative model is constructed by combining L1 regularization and subspace representation, which retains sufficient representational (...) power while dealing with outliers. To overcome the shortcomings of the traditional multiplicative fusion mechanism, this paper proposes an adaptive selection mechanism based on Euclidean distance, which aims to detect deteriorating models in time during the dynamic tracking process and adopt corresponding strategies to construct more reasonable likelihood functions. Based on the Bayesian citation framework, the adaptive selection mechanism is used to combine the sparse discriminative model and the sparse generative model. Also, different online updating strategies are adopted for the template set and Principal Component Analysis subspace to alleviate the drift problem while ensuring that the algorithm can adapt to the changes of target appearance in the dynamic tracking environment. Through quantitative and qualitative evaluation of the experimental results, it is verified that the algorithm proposed in this paper has stronger robustness compared with other classical algorithms. Our proposed visual object tracking algorithm not only outperforms existing visual object tracking algorithms in terms of accuracy, success rate, accuracy, and robustness but also achieve the performance required for real-time tracking in terms of execution speed on the central processing unit. This paper provides an in-depth analysis and discussion of the adaptive Gaussian incremental expectation stadium parameter estimation algorithm for sports video analysis. Using a variety of county-level algorithms for analysis and multiple solutions to improve the accuracy of the results, we obtain a more efficient and accurate algorithm. (shrink)

In this article, we extend the Bayesian nonparametric regression method Gaussian Process Regression to the analysis of longitudinal panel data. We call this new approach Gaussian Process Panel Modeling (GPPM). GPPM provides great flexibility because of the large number of models it can represent. It allows classical statistical inference as well as machine learning inspired predictive modeling. GPPM offers frequentist and Bayesian inference without the need to resort to Markov chain Monte Carlo-based approximations, which makes the approach exact (...) and fast. GPPMs are defined using the kernel-language, which can express many traditional modeling approaches for longitudinal data, such as linear structural equation models, multilevel models, or state-space models but also various commonly used machine learning approaches. As a result, GPPM is uniquely able to represent hybrid models combining traditional parametric longitudinal models and nonparametric machine learning models. In the present paper, we introduce GPPM and illustrate its utility through theoretical arguments as well as simulated and empirical data. (shrink)

Effective feature representation is the key to success of machine learning applications. Recently, many feature learning models have been proposed. Among these models, the Gaussian process latent variable model for nonlinear feature learning has received much attention because of its superior performance. However, most of the existing GPLVMs are mainly designed for classification and regression tasks, thus cannot be used in data clustering task. To address this issue and extend the application scope, this paper proposes a novel GPLVM for (...) clustering. Specifically, by combining GPLVM with the subspace clustering method, our C-GPLVM can obtain more representative latent variable for clustering. Moreover, it can directly predict the new samples by introducing a back constraint in the model, thus being more suitable for big data learning tasks such as analysis of chaotic time series and so on. In the experiment, we compare it with the related GPLVMs and clustering algorithms. The experimental results show that the proposed model not only inherits the feature learning ability of GPLVM but also has superior clustering accuracy. (shrink)

An intervention may have an effect on units other than those to which it was administered. This phenomenon is called interference and it usually goes unmodeled. In this paper, we propose to combine Lauritzen-Wermuth-Frydenberg and Andersson-Madigan-Perlman chain graphs to create a new class of causal models that can represent both interference and non-interference relationships for Gaussian distributions. Specifically, we define the new class of models, introduce global and local and pairwise Markov properties for them, and prove their equivalence. We (...) also propose an algorithm for maximum likelihood parameter estimation for the new models, and report experimental results. Finally, we show how to compute the effects of interventions in the new models. (shrink)

In the data collection phase, the digital images are captured using sensors that often contaminated by noise (undesired random signal). In digital image processing task, enhancing the image quality and reducing the noise is a central process. Image denoising effectively preserves the image edges to a higher extend in the flat regions. Several adaptive filters (median filter, Gaussian filter, fuzzy filter, etc.) have been utilized to improve the smoothness of digital image, but these filters failed to preserve the image (...) edges while removing noise. In this paper, a modified fuzzy set filter has been proposed to eliminate noise for restoring the digital image. Usually in fuzzy set filter, sixteen fuzzy rules are generated to find the noisy pixels in the digital image. In modified fuzzy set filter, a set of twenty-four fuzzy rules are generated with additional four pixel locations for determining the noisy pixels in the digital image. The additional eight fuzzy rules ease the process of finding the image pixels,whether it required averaging or not. In this scenario, the input digital images were collected from the underwater photography fish dataset. The efficiency of the modified fuzzy set filter was evaluated by varying degrees of Gaussian noise (0.01, 0.03, and 0.1 levels of Gaussian noise). For performance evaluation, Structural Similarity (SSIM), Mean Structural Similarity (MSSIM), Mean Square Error (MSE), Normalized Mean Square Error (NMSE), Universal Image Quality Index (UIQI), Peak Signal to Noise Ratio (PSNR), and Visual Information Fidelity (VIF) were used. The experimental results showed that the modified fuzzy set filter improved PSNR value up to 2-3 dB, MSSIM up to 0.12-0.03, and NMSE value up to 0.38-0.1 compared to the traditional filtering techniques. (shrink)

This study aims to identify the necessary strategies for the development of a sustainable financial system. For this purpose, a novel approach could be provided for soft computing with Gaussian-based fuzzy DEMATEL approach to understand the significant levels and impact-relation degrees of these criteria. For robustness check, this evaluation has also been performed for triangular and trapezoidal fuzzy sets. There are many novelties of this study. Firstly, computer science has a significant role in the decision-making process. Another specificity is (...) that the use of Gaussian numbers with fuzzy numbers is a new area. In addition, interval type-2 fuzzy sets also provide a significant advantage in decision-making under uncertainty. The results demonstrate that the size of the alternative financing, investment in efficient projects, and effective advertisement/promotions are the most important items to affect the performance of alternative banking system of emerging economies. Hence, it is recommended that the new banking applications should be applied by the state or the state can provide some incentives for foreign banks to invest in emerging economies, such as tax reduction. Another important point is that the financial intermediations should generate a component financial analysis team to examine the financial reports of the companies in detail so that the financial credibility of these companies can be evaluated more effectively. (shrink)

Exploratory analyses are an important first step in psychological research, particularly in problem-based research where various variables are often included from multiple theoretical perspectives not studied together in combination before. Notably, exploratory analyses aim to give first insights into how items and variables included in a study relate to each other. Typically, exploratory analyses involve computing bivariate correlations between items and variables and presenting them in a table. While this is suitable for relatively small data sets, such tables can easily (...) become overwhelming when datasets contain a broad set of variables from multiple theories. We propose the Gaussian graphical model as a novel exploratory analyses tool and present a systematic roadmap to apply this model to explore relationships between items and variables in environmental psychology research. We demonstrate the use and value of the Gaussian graphical model to study relationships between a broad set of items and variables that are expected to explain the effectiveness of community energy initiatives in promoting sustainable energy behaviors. (shrink)

A vehicle-commodity matching problem is presented for service providers to reduce the cost of the logistics system. The vehicle classification model is built as a Gaussian mixture model, and the expectation-maximization algorithm is designed to solve the parameter estimation of GMM. A nonlinear mixed-integer programming model is constructed to minimize the total cost of VCMP. The matching process between vehicle and commodity is realized by GMM-EM, as a preprocessing of the solution. The design of the vehicle-commodity matching platform for (...) VCMP is designed to reduce and eliminate the information asymmetry between supply and demand so that the order allocation can work at the right time and the right place and use the optimal solution of vehicle-commodity matching. Furthermore, the numerical experiment of an e-commerce supply chain proves that a hybrid evolutionary algorithm is superior to the traditional method, which provides a decision-making reference for e-commerce VCMP. (shrink)

Trajectories along which phase-space points of the Wigner distribution function move are computed for a Gaussian wave packet moving under the influence of a weak perturbative potential. The potentials considered are a potential step, a potential barrier, and a periodic potential. Trajectories computed exhibit the complex, nonlocal nature of quantum dynamics. It is seen that quantum interference, which takes place in the time development of the wave packet, is taken care of in a simple way by the Wigner trajectory (...) method presented here. (shrink)

In this article, we propose a new method to learn the underlying acyclic mixed graph of a linear non-Gaussian structural equation model with given observational data. We build on an algorithm proposed by Wang and Drton, and we show that one can augment the hidden variable structure of the recovered model by learning multidirected edges rather than only directed and bidirected ones. Multidirected edges appear when more than two of the observed variables have a hidden common cause. We detect (...) the presence of such hidden causes by looking at higher order cumulants and exploiting the multi-trek rule. Our method recovers the correct structure when the underlying graph is a bow-free acyclic mixed graph with potential multidirected edges. (shrink)

The results of a previous study (Craig & Lipp, 2018) into the effects of multiple social category cues (face race and face sex) on facial emotion recognition indicate that face sex dominates face race, and moreover, participant sex differences contribute little to the observed effects. Here, I modelled the same dataset (https://osf.io/rsmxb/) using the ex-Gaussian, a distribution that is 1) well suited to RT data and 2) separates slow from relatively fast influences. Corroborating recent results (Tipples, 2022) current results (...) show larger effects of face sex (for the faces of White individuals) for female participants. Further novel interaction effects were revealed. For example, results support a different time course for the influence of face sex on expression for the faces of Black compared to White individuals. (shrink)

Mathematicians use the word ‘deep’ to convey a high appreciation of a concept, theorem, or proof. This paper investigates the extent to which the term can be said to have an objective character by examining its first use in mathematics. It was a consequence of Gauss's work on number theory and the agreement among his successors that specific parts of Gauss's work were deep, on grounds that indicate that depth was a structural feature of mathematics for them. In contrast, French (...) mathematicians had a less structural, more problem-oriented approach to mathematics and did not speak of depth so readily. (shrink)

Acoustic emission technique is a common approach to identify the damage of the refractories; however, there is a complex problem since there are as many as fifteen involved parameters, which calls for effective data processing and classification algorithms to reduce the level of complexity. In this paper, experiments involving three-point bending tests of refractories were conducted and AE signals were collected. A new data processing method of merging the similar parameters in the description of the damage and reducing the dimension (...) was developed. By means of the principle component analysis for dimension reduction, the fifteen related parameters can be reduced to two parameters. The parameters were the linear combinations of the fifteen original parameters and taken as the indexes for damage classification. Based on the proposed approach, the Gaussian mixture model was integrated with the Bayesian information criterion to group the AE signals into two damage categories, which accounted for 99% of all damage. Electronic microscope scanning of the refractories verified the two types of damage. (shrink)

Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This equality is motivated by generality of deductions. Characterizations are given for pairs of isomorphic formulae, which lead to decision procedures for this isomorphism.

ObjectiveThere is little literature on the validity of kurtosis-adjusted noise energy metrics in human studies. Therefore, this study aimed to validate the application of cumulative noise exposure adjusted by kurtosis in evaluating occupational hearing loss associated with non-Gaussian noise among manufacturing workers.MethodsA cross-sectional survey was conducted on 1,558 manufacturing workers exposed to noise from five industries to collect noise exposure and hearing loss data. Both CNE and kurtosis-adjusted CNE were collapsed into 2-dB∙year bins, and the mean noise-induced permanent threshold (...) shifts at 3, 4, and 6 kHz in each bin were calculated. The contributions of CNE and CNE′ to noise-induced hearing loss were compared using the multiple linear regression. The degree of overlap of two linear regression equations was used to evaluate the validity of the CNE′ using a stratified analysis based on age and sex.ResultsMultiple linear regression models showed that after kurtosis adjustment, the standardized regression coefficient of CNE increased from 0.230 to 0.255, and R2 increased from 0.147 to 0.153. The linear relationship between NIPTS346 and CNE′ or CNE showed that the regression line of non-Gaussian noise was closer to that of Gaussian noise when using CNE′ than using CNE. The mean difference in NIPTS346 between the equations of non-Gaussian noise and Gaussian noise was significantly reduced from 4.32 to 1.63 dB HL after kurtosis adjustment. Through a stratified analysis, these significant decreases were observed in male and female workers, and workers aged ≥30 years old.ConclusionAs a noise exposure metric combining noise energy and temporal characteristics, the kurtosis-adjusted-CNE metric was more effective than CNE alone in assessing occupational hearing loss among manufacturing workers in non-Gaussian noise environment. However, more studies are needed to verify the validity of the kurtosis-adjusted-CNE metric. (shrink)

Quantum frameworks for modeling competitive ecological systems and self-organizing structures have been investigated under multiple perspectives yielded by quantum mechanics. These comprise the description of the phase-space prey–predator competition dynamics in the framework of the Weyl–Wigner quantum mechanics. In this case, from the classical dynamics described by the Lotka–Volterra (LV) Hamiltonian, quantum states convoluted by statistical gaussian ensembles can be analytically evaluated. Quantum modifications on the patterns of equilibrium and stability of the prey–predator dynamics can then be identified. These (...) include quantum distortions over the equilibrium point drivers of the LV dynamics which are quantified through the Wigner current fluxes obtained from an onset Hamiltonian background. In addition, for gaussian ensembles highly localized around the equilibrium point, stability properties are shown to be affected by emergent topological quantum domains which, in some cases, could lead either to extinction and revival scenarios or to the perpetual coexistence of both prey and predator agents identified as quantum observables in microscopic systems. Conclusively, quantum and gaussian statistical driving parameters are shown to affect the stability criteria and the time evolution pattern for such microbiological-like communities. (shrink)

Konrad Lorenz, an ethologist, proposed that certain physical elements are perceived as cute and induce caretaking behavior in other individuals, with the evolutionary function of enhancing offspring survival. He called these features Kindchenschema, baby schema. According to his introspection, these include a large forehead, chubby round features, and chubby cheeks. Previous studies are limited to examining the effects of these facial features on perceived cuteness. However, other morphological factors may be related to perceived cuteness. This study uses Bayesian optimization, one (...) of the global sequential optimization methods for estimating unknown functions, to search for facial morphological features that enhance the perceptions of facial cuteness. We applied Bayesian optimization incorporating Gaussian process ordinal regression, which allows an estimation of the latent cuteness function based on evaluations using the Likert scale. A total of 96 preschool children provided the facial images used in this study. We summarized the facial shape variations using methodologies of geometric morphometrics and principal component analysis up to the third principal component, which we refer to as the face space. A total of 40 participants evaluated the images created by warping the average facial texture of the children's faces with randomly generated parameters in the face space. Facial traits related to perceived cuteness were estimated based on the averaged cuteness function. Perceived cuteness was linked to the relative lower position of facial components and narrower jawline but not to the forehead height. (shrink)

Understanding and solving the psychological health problems of college students have become a focus of social attention. Complex networks have become important tools to study the factors affecting psychological health, and the Gaussian graphical model is often used to estimate psychological networks. However, previous studies leave some gaps to overcome, including the following aspects. When studying networks of subpopulations, the estimation neglects the intrinsic relationships among subpopulations, leading to a large difference between the estimated network and the real network. (...) Because of the high cost, previous psychological surveys often have a small sample size, and the psychological description is insufficient. Here, the intrinsic connections among multiple tasks are used, and multitask machine learning is applied to develop a multitask Gaussian graphical model. The psychological networks of the population and subpopulations are estimated based on psychological questionnaire data. This study is the first to apply a psychological network to such a large-scale college student psychological analysis, and we obtain some interesting results. The model presented here is a dynamic model based on complex networks which predicts individual behavior and provides insight into the intrinsic links among various symptoms. (shrink)

This paper presents an in-depth analysis of tennis match scene classification using an adaptive Gaussian mixture model parameter estimation simulation algorithm. We divided the main components of semantic analysis into type of motion, distance of motion, speed of motion, and landing area of the tennis ball. Firstly, for the problem that both people and tennis balls in the video frames of tennis matches from the surveillance viewpoint are very small, we propose an adaptive Gaussian mixture model parameter estimation (...) algorithm, which has good accuracy and speed on small targets. Secondly, in this paper, we design a sports player tracking algorithm based on role division and continuously lock the target player to be tracked and output the player region. At the same time, based on the displacement information of the key points of the player’s body and the system running time, the distance and speed of the player’s movement are obtained. Then, for the problem that tennis balls are small and difficult to capture in high-speed motion, this paper designs a prior knowledge-based algorithm for predicting tennis ball motion and landing area to derive the landing area of tennis balls. Finally, this paper implements a prototype system for semantic analysis of real-time video of tennis matches and tests and analyzes the performance indexes of the system, and the results show that the system has good performance in real-time, accuracy, and stability. (shrink)

In order to solve the shortcomings of particle swarm optimization in solving multiobjective optimization problems, an improved multiobjective particle swarm optimization algorithm is proposed. In this study, the competitive strategy was introduced into the construction process of Pareto external archives to speed up the search process of nondominated solutions, thereby increasing the speed of the establishment of Pareto external archives. In addition, the descending order of crowding distance method is used to limit the size of external archives and dynamically adjust (...) particle parameters; in order to solve the problem of insufficient population diversity in the later stage of algorithm iteration, time-varying Gaussian mutation strategy is used to mutate the particles in external archives to improve diversity. The simulation experiment results show that the improved algorithm has better convergence and stability than the other compared algorithms. (shrink)

Kant’s most prominent formulation of the Categorical Imperative, known as the Formula of Universal Law (FUL), is generally thought to demand that one act only on maxims that one can will as universal laws without this generating a contradiction. Kant's view is standardly summarized as requiring the 'universalizability' of one's maxims and described in terms of the distinction between 'contradictions in conception' and 'contradictions in the will'. Focusing on the underappreciated significance of the simultaneity condition included in the FUL, (...) I argue, by contrast, that the principle is better read as requiring that one be able to will two things simultaneously without self-contradiction, namely, that a maxim be one's own and that it be a universal law. This amounts to a new interpretation of the FUL with significant interpretive and philosophical advantages. (shrink)

Proof-theoretic semantics (P-tS) is the paradigm of semantics in which meaning in logic is based on proof (as opposed to truth). A particular instance of P-tS for intuitionistic propositional logic (IPL) is its base-extension semantics (B-eS). This semantics is given by a relation called support, explaining the meaning of the logical constants, which is parameterized by systems of rules called bases that provide the semantics of atomic propositions. In this paper, we interpret bases as collections of definite formulae and use (...) the operational view of them as provided by uniform proof-search—the proof-theoretic foundation of logic programming (LP)—to establish the completeness of IPL for the B-eS. This perspective allows negation, a subtle issue in P-tS, to be understood in terms of the negation-as-failure protocol in LP. Specifically, while the denial of a proposition is traditionally understood as the assertion of its negation, in B-eS we may understand the denial of a proposition as the failure to find a proof of it. In this way, assertion and denial are both prime concepts in P-tS. (shrink)

Breastfeeding is analogous to pregnancy as an experience, in its exclusiveness to women, and in its cost and the effects it has on equitable share of labor. Therefore, the history of formula feeding provides useful insights into the future of full ectogenesis, which could evolve into a more severe version of what formula feeding is today: simplify life for some women and provide couples with a more equitable share of work at the cost of stigma, guilt and a (...) daily diet of studies purporting to show the benefits of natural pregnancy. Making pregnancy an optional route to motherhood would make women's life trajectory more similar to men's and thus put pressure on women to compete with men on the ground shaped by men's preferences. Despite being a treasured experience of many women today, bearing children could become the luxury of the few, the province of the very poor and a choice working women will pay a high price for as women who choose pregnancy become stigmatized as self-indulgent or unprofessional and penalized for it in the workplace. At the same time, scarce societal resources that could be used to support pregnant women and working mothers would instead be directed toward proving to women or even forcing them to gestate children "the right way." While not necessarily threatening on its own, when added to formula feeding, IVF, stem-cell produced ova and sex robots, full ectogenesis could diminish men's stake in women's wellbeing and even existence. (shrink)

The Barcan formula (BF) is commonly paraphrased as the schematic conditional that if it is possible that there be a phi then something or other is possibly a phi. It is validated by the most straightforward systems of quantified modal logic. It is also widely considered to pose a threat to the commonsensical metaphysical view that there are no non-actual (or ‘merely possible’) things. I show how BF can be cleared of such a charge by construing it as a (...) bridge principle connecting modality de dicto and modality de re while retaining a Russellian robust sense of reality in modal matters. (shrink)

This paper provides a methodologically original construction of Kant’s “Formula of Universal Law” . A formal structure consisting of possible worlds and games—a “game frame”—is used to implement Kant’s concept of a maxim and to define the two tests FUL comprises: the “contradiction in conception” and “contradiction in the will” tests. The paper makes two contributions. Firstly, the model provides a formal account of the variables that are built into FUL: agents, maxims, intentions, actions, and outcomes. This establishes a (...) clear benchmark for understanding how the mechanics of FUL actually work. Secondly, the analysis of the resulting framework sheds new light on discussions about the implications of FUL. On the basis of this, we suggest a move to “comprehensive Kantianism’, which is the application of FUL to systems of maxims rather than to isolated maxims. (shrink)

We generalize and extend the class of Sahlqvist formulae in arbitrary polyadic modal languages, to the class of so called inductive formulae. To introduce them we use a representation of modal polyadic languages in a combinatorial style and thus, in particular, develop what we believe to be a better syntactic approach to elementary canonical formulae altogether. By generalizing the method of minimal valuations à la Sahlqvist–van Benthem and the topological approach of Sambin and Vaccaro we prove that all inductive formulae (...) are elementary canonical and thus extend Sahlqvist’s theorem over them. In particular, we give a simple example of an inductive formula which is not frame-equivalent to any Sahlqvist formula. Then, after a deeper analysis of the inductive formulae as set-theoretic operators in descriptive and Kripke frames, we establish a somewhat stronger model-theoretic characterization of these formulae in terms of a suitable equivalence to syntactically simpler formulae in the extension of the language with reversive modalities. Lastly, we study and characterize the elementary canonical formulae in reversive languages with nominals, where the relevant notion of persistence is with respect to discrete frames. (shrink)

Ritualistic formulae and acts pervade the political, legal, societal and religious life of the ancient world. In many instances there are striking similarities between the formulae of the Greco-Roman world and those of the Near East. Often illumination exists from one to the other. Here I wish to notice a few passages in Greek drama where I think such illumination is possible.

A Fórmula Porchat — ou seja, a intuição de um conflito das filosofias de caráter indecidível – possui papel tanto propedêutico quanto compulsório para um tratamento não dogmático da história dos sistemas filosóficos. Ao mesmo tempo em que reconhece tal papel, o presente artigo pretende indicar o caráter problemático da correspondência entre “conflito das filosofias” e “indecidibilidade filosófica”. Para tal, sustenta que o sentimento de indecidibilidade filosófica tem como referência impensada uma nostalgia da decidibilidade. O artigo sugere, ainda, o abandono (...) do tema da indecidibilidade, como um falso problema filosófico, e sustenta a necessidade de considerar os efeitos da prática filosófica sobre a configuração da vida comum e de tomar tais efeitos como formas de decidibilidade. Para tal é necessário considerar a atividade filosófica como inscrita no campo maior da manufatura da experiência humana. (shrink)

Kantians are increasingly deserting the universal law formula in favor of the humanity formula. The former, they argue, is open to various decisive objections; the two are not equivalent; and it is only by appealing to the humanity formula that Kant can reliably generate substantive implications from his theory of an acceptable sort. These assessments of the universal law formula, which clash starkly with Kant's own assessment of it, are based on various widely accepted interpretative assumptions. (...) These assumptions, it is argued in this article, depend on misleading translations of key terms; selective attention to Kant's concrete examples; not taking seriously Kant's theoretical claims about the relations among his various ideas; and a failure to take into account Kant's idiosyncratic definitions of key concepts. The article seeks to right these interpretative wrongs, and finds that the universal law formula is not open to many of the standard objections. (shrink)

Ancient Greek mathematics developed the original feature of being deductive mathematics. This article attempts to give a explanation f or this achievement. The focus is on the use of a fixed system of linguistic formulae in Greek mathematical texts. It is shown that the structure of this system was especially adapted for the easy computation of operations of substitution on such formulae, that is, of replacing one element in a fixed formula by another, and it is further argued that (...) such operations of substitution were the main logical tool required by Greek mathematical deduction. The conclusion explains why, assuming the validity of the description above, this historical level is the best explanatory level for the phenomenon of Greek mathematical deduction. (shrink)

The formula of universal law (FUL) is a natural starting point for philosophers interested in a Kantian perspective on the morality of abortion. I argue, however, that FUL does not yield much in the way of promising or substantive conclusions regarding the morality of abortion. I first reveal how two philosophers' (Hare's and Gensler's) attempts to use Kantian considerations of universality and prescriptivity fail to provide analyses of abortion that are either compelling or true to Kant=s understanding of FUL. (...) I then turn to some recent interpretations of Kant=s FUL contradiction in conception (CC) and contradiction in will (CW) tests. I argue that none of the interpretations of the CC testBincluding the practical interpretation favored by KorsgaardBdoes much to reveal moral problems with maxims of abortion. The CW test (as developed by Herman) is more helpful. Nevertheless, I argue that neither by considering abortion maxims as a subset of maxims of convenience killing, nor by considering such maxims as maxims of refusing to aid, can the CW test generate a general prohibition of abortion. At best, the CW test illuminates the abortion issue because by forcing us to think about how killing a fetus differs from killing other human beings, what attitudes we may reasonably have toward a fetus, and whether Kant's moral theory must be amended to do justice to the problem of abortion. But to pursue these questions, we must look beyond FUL; Kant’s formula of humanity and doctrine of virtue may well have more to offer. (shrink)

In two recent articles I have argued that Kant’s legal and political philosophy can shed new light on his much-contested account of moral autonomy and that important changes in his political theory help to explain why in his later work the Formula of Autonomy disappears. In the present essay, I respond to comments by Sorin Baiasu and Marie Newhouse, who argue that the changes in Kant’s political theory fail to explain the disappearance of the Formula of Autonomy, since (...) in both phases Kant held that laws are given by the people’s representatives. I offer additional support for my original argument by developing a more detailed account of Kant’s conception of the relation between the legislating representatives and the people they are taken to represent. I argue that Kant’s conception of the proper representation relation changed, and that it changed so fundamentally that the analogy at the basis of the Formula of Autonomy was no longer apt, thus providing a plausible explanation for its disappearance. I also address several related comments and propose an explanation for why Kant dropped the very idea of autonomy as a property of the will. (shrink)

This is a survey article in which I explore some important recent work on the topic in question, Kant’s formula of the end in itself (or “formula of humanity”). I first provide an overview of the formulation, including what the formula seems roughly to be saying, and what Kant’s main argument for it seems to be. I then call the reader’s attention to a variety of questions one might have about the import of and argument for this (...) formula, alluding to some of the works in which philosophers have recently raised or tried to answer these questions. Then, for the bulk of the paper, I focus my discussion on two issues of contention: the identity of the “end in itself” that the formula refers to, and the relation between the value of the end in itself and the value of other ends. I do not attempt to argue for a particular position of my own regarding these issues. Instead, I explain a number of the more interesting or influential recent attempts to answer these questions, compare these approaches in various ways, draw implications from them, and raise concerns about some of them. I also suggest that an important link connects the question about the identity of the end in itself and the question about the relation between the value of the end in itself in relation to the value of other ends: How one answers these questions commits one to a position on the thorny issue of whether, how, and how fully, autonomy is manifested through empirical (not simply pure) practical reason. (shrink)

In The Formula, Luke Dormehl takes readers inside the world of numbers, asking how we came to believe in the all-conquering power of algorithms; introducing the mathematicians, artificial intelligence experts and Silicon Valley entrepreneurs who are shaping this brave new world, and ultimately asking how we survive in an era where numbers can sometimes seem to create as many problems as they solve.