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The history of the journal "Esercitazioni Matematiche" (1921-43) edited by the "Circolo Matematico di Catania" for university students is described. A selection of proposed problems with some of their solutions is reported. (Author)

This article explores what ‘plausible’ means in statements about legal evidence and shows that it is highly ambiguous. Twelve different meanings of ‘plausibility’ are identified and distinguished from each other by definitions. Contrary to what has been claimed by some evidence scholars (Allen and Pardo, 2019), the article shows that all uses of ‘plausibility’ can be captured in terms of probability. The author also shows that the exposed ambiguity is deeply problematic for legal practice and legal scholarship. The fundamental principle of justice that ‘like cases should be treated alike’ is endangered when the standard of proof is expressed in an ambiguous way, and the scientific testability of hypotheses about legal fact-finding is undermined when these hypotheses are formulated in ambiguous terms.

The paper explores the argumentation from probability in Cicero’s speech Pro Roscio comoedo, concerning the financial litigation between a famous Roman actor Quintus Roscius and an unknown businessman Fannius Chaerea. The Roman rhetorician had analysed the question of probability in his earlier dissertation De inventione, which influenced his art of persuasion. Because of lack of the strong proofs the arguments from probability played a great role in the defence of Roscius. Cicero used different types of likelihood arguments: syllogistic argument from probability, credibilia, incredibilia, verisimilia, as well as the arguments from ethos and kedros. He seems to be here aware of the Greek theory of argumentation present in the writings of Aristotle and Rhetorica ad Alexandrum. The Roman orator recalled often the truth and juxtaposed it with the probability. Cicero employed likelihood proofs in his speech, both in argumentation and in refutation.

The rationalization of expectation, here considered as ‘hope’ regarding a possible future, has been declined not with the aim of eliminating uncertainty about the future (which is assumed as an immanent and ineliminable feature of the World) but as aimed at defining a rational behavior in deliberation in conditions of uncertainty. A ‘freely’ rational behavior, in that supported by coherent arguments. This coherency does ensure the success of the action chosen by the deliberating subject, but rather makes this action acceptable by the reference community in the light of its consequences.

Modern science was historically built by avoiding a direct treatment of cause-effect relationship questions. Recent developments in mathematical, probabilistic and statistical sciences make possible to pursue a more direct approach in cause-effect relationships leading to effective and systematic investigations in a wide range of scientific research fields.

This paper follows the already existing literature to address three main pressing concerns that Romania is currently facing with respect to sustainable development and economic growth, which has likely been impeded as a direct consequence of the ongoing sanitary crisis. The research questions of this paper were asked with the consideration of finding possible solutions to the current developments. These questions were “How will the global health crisis project on Romania’s GDP growth in 2021 and going forward?”, “To what extent can Romania face its current challenges with respect to the budgetary pressures?”. The research itself was conducted using the R programming language with quantitative data, namely quarterly GDP starting from 2005 Q1 onwards and its main objective is to simulate Romania’s GDP to answer the aforementioned questions. Therefore, this research is empirical in the sense that it derives the simulated data from real data which was taken from Eurostat. The main findings of this research were that Romania’s GDP could grow by a mean 3.2% in 2021, which is more conservative than the existing institutional forecasts made by the European Commission, the International Monetary Fund, World Bank and the Romanian National Commission for Strategy and Forecasting, implying that the majority of the simulated outcomes have been in that respective range of values. Moreover, this research also finds that consumption is expected to increase by approximately 4.2% and that the budget deficit relative to GDP could go as low as to negative 7.8%. This paper creates value for future policymaking as it proposes solutions which could help Romania going forward. Thus, this paper creates value for not only the policymakers but the society as a whole.

Much has been written about the existence and formulation of different standards of proof, both in civil and criminal proceedings. However, one point on which it is worth deepening into is that of the normative anchor of those standards. The issue presents interesting and problematic trims while in the legislation the test standards are not always predetermined. The individualization and cognizability of the standard thus becomes a previous question on which it is necessary to reflect, before analyzing how a particular evidentiary standard is applied. The recognition of judicial standard before the jurisdictional decision favors legal certainty and allows the control of judicial decisions.

At the dawn of "metaclinical medicine" era, shared decision-making represents the overcoming of modern medicine guidelines and classical medicine experience. The patient's life plan, the doctor's health plan, the scientist's evidence-based plan, the administrator's plan and the beliefs of the society for healthcare options should be integrated into the shared decision-making process to avoid patient's unrealistic expectations, doctor's self-referential and defensive medicine, the science without compassion of the scientist, the administered medicine of the politician, the herd mentality of artificial intelligence. For a doctor who must evaluate according to science and conscience, it becomes difficult to make decisions about a patient who thinks that there can be "no decisions about me without me". It risks being a pure declamatory statement in the absence of clinical knowledge and the associated concept of probability. The idea of moving from informed consent to shared probability is convenient for both the doctor and the patient but not for litigation professionals. Even in metaclinical medicine, clinical decision support systems, if well governed, would facilitate the choice of the best treatment according to the definition of absolute risk reduction and the number of patients to be treated to avoid an event, leaving it up to the doctor-patient relationship the narrative and the choice of the most appropriate treatment, which also requires taking care of the emotional and compassionate aspects.

In «Naturalized Epistemology and the Law of Evidence Revisited», the original target article for the various refutations that I comment on here, I revisited through a slightly different lens the subject of the article that I coauthored with Brian Leiter close to twenty years ago. That article has prompted four responses from Professors Pardo, Spellman, Muffato, and Enoch. Professors Pardo and Spellman basically accept the implications of the original article and offer useful but friendly amendments. Prof. Muffato apparently does not want to dispute over my ground and so changes the subject, and in doing so offers a number of interesting points. Only the fourth, Prof. Enoch, has the same doubts about the utility of my original article as I do of the genre that gave rise to it. I can thus be quite brief in discussing professors Pardo, Spellman, and Muffato, but it will take bit more effort to lay out the limits of Prof. Enoch’s analysis.

In real life we have to deal with uncertainty, imprecision and vagueness. Many ideas were introduced and studied in detail to manage with these problems. Now we briefly expose the main formal concepts which describe non-ideal situations, i.e. Probability, Statistics and Fuzzy Logic. Probability has recent origins with respect to other branches of mathematics which have deep roots in the past, like geometry or algebra.We may say all this started with Antoine Gombaud, Chevalier de Méré (1607–1684), who asked Blaise Pascal (1623–1662) about gambling with dice. The correspondence between Pierre de Fermat and Blaise Pascal, which began in 1654, initially on these questions, led to the introduction of basic concepts, i.e. probability and expectation. Only in 1657, Christian Huygens in "De Ratiociniis in ludo aleae" proposed a first systematic study of the new branch of mathematics. However, the need of an axiomatic construction of the theory of probability arose to analyze more general and complex situations than gambling. A strong formalization was supplied by the monograph "Foundations of the theory of probability" (1933) by Andrey Nikolaevich Kolmogorov.Statistics represent the most popular application of probability theory, providing research tools in several areas, including physical and natural sciences, technology, psychology, economics and medicine. Statistics are the bridge that connects experimental data to the mathematical theory behind itself.Fuzzy logic, sometime confused with probability, wants to express and formalize all the sentences which are not true or false at all; the philosophical idea is that "everything is a matter of degree" (Zadeh). La logica della probabilità: un viaggio attraverso l’incertezza Nella vita reale ci si trova di fronte a molte situazioni caratterizzate da incertezza, imprecisione, vaghezza. Sono state introdotte diverse modellizzazioni per il trattamento di tali concetti e problemi. Ci proponiamo di esporre sinteticamente alcuni lineamenti fondamentali di Probabilità, Statistica e Fuzzy Logic.La probabilità ha origini recenti rispetto alle altre branche della matematica che hanno profonde radici nel passato, come la geometria o l’algebra.Possiamo dire che un passaggio iniziale importante si è avuto con Antoine Gombaud, Chevalier de Méré (1607-1684), che pose a Blaise Pascal (1623-1662) una questione riguardante il gioco dei dadi. La corrispondenza tra Pierre de Fermat e Blaise Pascal, che ha avuto inizio nel 1654, su questioni simili, ha portato all'introduzione di concetti di base, come probabilità e aspettativa. Successivamente Christian Huygens, in "De ludo Ratiociniis in aleae", ha proposto un primo studio sistematico della nuova branca della matematica. Tuttavia, la necessità di una costruzione assiomatica della teoria della probabilità sorse per l’esigenza di analizzare situazioni più generali e complesse rispetto al gioco d'azzardo. Una forte formalizzazione è stata fornita dalla monografia "Fondamenti della teoria della probabilità" (1933) di Andrey Nikolaevich Kolmogorov.La statistica rappresenta l'applicazione più popolare della teoria della probabilità, fornendo strumenti di ricerca in diversi settori, tra cui le scienze fisiche e naturali, la tecnologia, la psicologia, l'economia e la medicina. In un certo senso essa rappresenta il ponte che collega i dati sperimentali con la teoria matematica.La Logica Fuzzy, da non confondere con la probabilità, si occupa del trattamento formale delle proposizioni di cui non si può affermare senza ambiguità che siano vere o false; l'idea filosofica è che "tutto è una questione di gradualità" (Zadeh). Parole Chiave: Incertezza, Probabilità, Statistica, Fuzzy

In this paper I discuss the distribution of grammatical monosyllables in the iambic pentameter line. I show that in Milton's Paradise Lost, the word OF appears with greater than expected frequency at the beginning of the line; 27% of all instances of OF are in the first of the ten metrical positions, and 5% of all the lines begin with OF, making it the most frequent line-initial word. I suggest that this might reflect the way that Milton uses enjambment in the poem. It also means that OF may function as a clue to the beginning of the line, in the context of other evidence for lineation, essential if the audience is to establish the metrical form of the poem. In constrast, in the eighteenth century blank verse long poems of Thomson and Cowper, the word AND is relatively frequent at the beginning of the line. But Wordsworth uses both OF and AND as frequent line-initial words,(merging Milton's formal practice with the practice of other writers. The paper concludes by reflecting on the relation between statistical characteristics of text and probabilistic aspects of our knowledge of literary form.

Many authors have hoped to understand the indicative conditional construction in everyday language by means of what are usually called conditional probabilities. Other authors have hoped to make sense of conditional probabilities in terms of the absolute probabilities of conditional statements. Although all such hopes were disappointed by the triviality theorems of Lewis (1976), there have been copious subsequent attempts both to rescue CCCP (the conditional construal of conditional probability) and to extend and to intensify the arguments against it. In this paper it will be shown that triviality is avoidable if the probability function is replaced by an alternative generalization of the deducibility relation, the measure of deductive dependence of Miller and Popper (1986). It will be suggested further that this alternative way of orchestrating conditionals is nicely in harmony with the test proposed in Ramsey (1931), and also with the idea that it is not the truth value of a conditional statement that is of primary concern but its assertability or acceptability.

In probability and statistics courses, a popular method for the evaluation of the students is to assess them using multiple choice tests. The use of these tests allows to evaluate certain types of skills such as fast response, short-term memory, mental clarity and ability to compete. In our opinion, the verification through testing can certainly be useful for the analysis of certain aspects, and to speed up the process of assessment, but we should be aware of the limitations of such a standardized procedure and then exclude that the assessments of pupils, classes and schools can be reduced to processing of test results. To prove this thesis, this article argues in detail the main test limits, presents some recent models which have been proposed in the literature and suggests some alternative valuation methods. Quesiti e test di Probabilità e Statistica: un'analisi critica Nei corsi di Probabilità e Statistica, un metodo molto diffuso per la valutazione degli studenti consiste nel sottoporli a quiz a risposta multipla. L'uso di questi test permette di valutare alcuni tipi di abilità come la rapidità di risposta, la memoria a breve termine, la lucidità mentale e l'attitudine a gareggiare. A nostro parere, la verifica attraverso i test può essere sicuramente utile per l'analisi di alcuni aspetti e per velocizzare il percorso di valutazione ma si deve essere consapevoli dei limiti di una tale procedura standardizzata e quindi escludere che le valutazioni di alunni, classi e scuole possano essere ridotte a elaborazioni di risultati di test. A dimostrazione di questa tesi, questo articolo argomenta in dettaglio i limiti principali dei test, presenta alcuni recenti modelli proposti in letteratura e propone alcuni metodi di valutazione alternativi. Parole Chiave: item responce theory, valutazione, test, probabilità

While tobacco became more and more popular, there were always voices against it being considered immoral and harmful. However the intent of restraining his using has only made it more valuable and encouraged smuggling. Smoking is a risk factor for excitement state at young infants. Being a subject of actuality and of national interest, the authors have performed a study among the citizens of Bucharest, in order to sketch of the typical smoker profile. Smoking teenagers have to seek for medical care more often than non-smokers. As a final conclusion of this study we have to mention the fact that through a better campaign against smoking, sustained by the authorities, the number of smokers and smoking harmful effects could be significantly reduced.

Apresenta-se a interpretação oferecida por Bayle do ceticismo antigo: suas características, sua origem e a distinção entre pirrônicos e acadêmicos. Em seguida, discutem-se alguns aspectos importantes do ceticismo: sua concepção de ciência, sua conduta na vida prática e sua atitude em face da religião.The topic of this paper is Bayle´s interpretation of ancient scepticism: its characteristics, its origin and the distinction between pyrrhonism and academic scepticism. Some important aspects of scepticism are also discussed: its conception of science, its conduct in practical life and its attitude concerning religion.

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Heart failure with improved ejection fraction (HFimpEF) represents a nosological entity that has recently been recognized and has little evidence from the literature. Available data indicate an increasing incidence of this patient group, consistent with the progressive improvement and implementation of medical therapy of heart failure with reduced ejection fraction (HFrEF). Furthermore, it is important to underline that the therapy itself should not be suspended after ejection fraction recovery, to avoid the recurrence of worse systolic dysfunction and patient outcomes. Only recently a randomized clinical study has been published, which enrolled also this patient subgroup, the DELIVER trial. Other data will soon become available, given the interest of the scientific community for this subgroup of patients, whose best management remains controversial. Since many studies suggest that the probability of myocardial recovery in HFrEF patients might be as high as 40%, depending on the case series taken into account, whereas the time to recovery might even be 12 months, the appropriate timing of device implantation, such as the defibrillator, in this setting deserves careful consideration.

We believe that a high percentage of covid-19 infections could be due to the presence of false negative (FN) individuals on rapid swabs. To support this hypothesis and quantify their number, we performed simulations using Bayes' rule and various assumptions about the sensitivity, specificity of swabs and prevalence of infection. Imagining FNs in liberty, we then calculated the probability of encountering them in groups of people with a typical number of habitual sites, such as: bus, supermarket, theatre, etc. The probability of encountering FN from rapid tests was more than 3 times higher (345% change) that reported by the RT-PCR test.

The p-value has been widely criticized in the scientific literature for its naive use in classifying results as 'significant' and 'non significant'. Much has been written about it; for example, see the American Statistical Association position statement of march 2016. To date, few alternative measures have been suggested and few changes were observed in the scientific practice regarding the use of p-value despite general agreement on the critics raised on it. In this paper, we use an alternative measure to p-value. It consists in the probability of the direction of the effect, that is the strength of empirical evidence in favour of the alternative directional hypothesis. In the context of scientific research, reporting the probability of the direction of the effect is easier to understand. Moreover, it focuses on the effect in the study rather than on the value under the null hypothesis, which sometimes has little meaning or has been used opportunistically. The proposal is not intended as an alternative to using the confidence interval, but as a probabilistic metric to be used instead of the p-value when we refer to particular hypotheses to be tested.

Jean Baptiste Lamarck was the first scientist to deal thoroughly with meteorology and weather forecasts to grant it dignity of science that was lately granted to meteorology, at the end of the twentieth century. The present paper examines Lamarck's contribution, still of great topical interest for meteorology research today, concerning topics such as: the specification of the causes of atmospheric phenomena, the acquisition of experimental data, the issue of weather forecasts in the probabilistic form, their social utility, ways of communication and validation. In this study the author addresses the relevance of Lamarck's contributions considering them as a fundamental step in the history of meteorology. [ABSTRACT FROM AUTHOR]

Correct assessment of critical variables influencing public investment final outcome is often a crucial procedure, especially in cases where the dynamics of such variables cannot be controlled by public agents, because they mainly depend on choices and behaviors of other operators. This is a typical situation occurring in development project assessment, characterized by a high uncertainty degree and by a scarce availability of information in relation to the behaviour of aleatory variables influencing investment final outcome. In such cases, risk analysis by directly using Montecarlo method could be misleading: on the contrary, we think that such an evaluation should be preceded by uncertainty analysis, allowing to generate new useful information for subsequent risk assessment. In this context, the paper presents one possible evaluative pattern, especially suited for development projects assessment, allowing first to understand the leeways of uncertainty between which investment decision must be taken and, then, to estimate investment risk and to generate useful information to help Decision Maker defining the most suitable economic tools to mitigate it. The proposed evaluative pattern is composed by four steps, based on different techniques and sequentially articulated, so that each step generates new useful information for developing the following one. Such a scheme allows both to deepen the information produced by the evaluative process, and to guarantee more decisional transparency. [ABSTRACT FROM AUTHOR]

Objectives: The Probability of Causation (PC) was introduced to compensate objectively and more possible legally the U.S. diseased subjects involved in the nuclear armament activities., Methods: The methodology is related to the attributable risk concept, but it is widely different from it, since it doesn't evaluate the "attributablity" from a collective point of view, but from a "personalistic" point, that is from the particular exposure condition, from the specific physical parameters and from the biological individual features of the single exposed subject. So the PC become an evaluation of the harm probability "tailored" for "that" specific exposed person, on the basis of the epidemiological indications coming from an exposed group with very similar characteristics of the under investigation individual. This is clearly possible owing to the large and exhaustive amount of epidemiological studies in the specific field of radiation exposure. The process to reach the PC adoption took a long time, was plodding and politically thwarted and various reexaminations and bills during time were necessary to extended the laws to the different exposure categories., Results: Now in the U.S. three departments (Health, Energy and Labour) are involved in the evaluation processes; they gather the personal, dosimetric and clinical data and with a computer program (usable on line also) based on the updated knowledge, evaluate the eligibility for compensation on the basis of the "more likely than not" criterion., Conclusions: The method meets the interest and the favor at international level and organizations in prominent positions in the pacific use of nuclear energy and in the radiation protection fields, like: NCRP, IAEA, WHO, ILO,... fight for it use. Now many institutional organism and the more enlightened justice courts utilize the PC to settle cases (increasing in frequency) in work and health activities, for which more often compensation claims are dealing with., Competing Interests: The authors of this article have no conflict of interests to disclose., (Copyright© by Aracne Editrice, Roma, Italy.)

Objectives: L'applicazione del metodo della Probability of Causation (PC) è certamente ampio poiché è oggi lo strumento riconosciuto per la individuazione del nesso di causa non solo nelle richieste di indennizzo in ambito assicurativo (per il quale è stata utilizzato inizialmente) ma anche per dirimere contenziosi giuridici in ambito civilistico e penalistico., Methods: Thanks to the Italian Association of Medical Radiation Protection (AIRM), PC method has been recently proposed as an aid for the radiation protection occupational physician in medical assessments involving both the mandatory actions that, in case of suspicion of occupational disease, the physician needs to perform (report / complaint / reporting) and the expression of the fitness evaluation in case of return to work after cancer and clinical recovery., Results: For all these uses PC value, calculated through the method, should be used in a flexible manner, and thus lead to different decisions, "modulated" on the basis of purposes and listed contexts; and this not only within the legal framework, but also in the strictly professional one., Conclusions: According to different purposes, different PC values are proposed as a reference for the decisions to be taken., Competing Interests: The authors of this article have no conflict of interests to disclose., (Copyright© by Aracne Editrice, Roma, Italy.)