Книга предназначена для студентов, преподавателей и научных сотрудников высших учебных заведений, занимающихся вопросами педагогики и психологии.

The Quantified argument calculus (Quarc) has received a lot of attention recently as an interesting system of quantified logic which eschews the use of variables and unrestricted quantification, but nonetheless achieves results similar to the Predicate calculus (PC) by employing quantifiers applied directly to predicates instead. Despite this noted similarity, the issue of the relationship between Quarc and PC has so far not been definitively resolved. We address this question in the present paper, and then expand upon that result. Utilizing (...) recent developments in structural proof theory, we develop a G3-style sequent calculus for Quarc and briefly demonstrate its structural properties. We put these properties to use immediately to construct direct proofs of the meta-theoretical properties of the system. We then incorporate an abstract (and, as we shall see, logical) predicate into the system in a way that preserves all the structural properties. This allows us to identify a system of Quarc which is deductively equivalent to PC, and also yields a constructive method of demonstrating the Craig interpolation theorem (which speaks in favor of the aforementioned predicate being logical). We further generalize this extension to develop a bivalent system of Quarc with defining clauses that still maintains all the desirable properties of a good proof system. (shrink)

This article investigates the proof theory of the Quantified Argument Calculus as developed and systematically studied by Hanoch Ben-Yami [3, 4]. Ben-Yami makes use of natural deduction, we, however, have chosen a sequent calculus presentation, which allows for the proofs of a multitude of significant meta-theoretic results with minor modifications to the Gentzen’s original framework, i.e., LK. As will be made clear in course of the article LK-Quarc will enjoy cut elimination and its corollaries.

Free logics is a family of first-order logics which came about as a result of examining the existence assumptions of classical logic. What those assumptions are varies, but the central ones are that the domain of interpretation is not empty, every name denotes exactly one object in the domain and the quantifiers have existential import. Free logics usually reject the claim that names need to denote in, and of the systems considered in this paper, the positive free logic concedes that (...) some atomic formulas containing non-denoting names are true, while negative free logic rejects even the latter claim. Inclusive logics, which reject, are likewise considered. These logics have complex and varied axiomatizations and semantics, and the goal of this paper is to present an orderly examination of the various systems and their mutual relations. This is done by first offering a formalization, using sequent calculi which possess all the desired structural properties of a good proof system, including admissibility of contraction and cut, while streamlining free logics in a way no other approach has. We then present a simple and unified system of abstract semantics, which allows for a straightforward demonstration of the meta-theoretical properties, and offers insights into the relationship between different logics. The final part of this paper is dedicated to extending the system with modalities by using a labeled sequent calculus, and here we are again able to map out the different approaches and their mutual relations using the same framework. (shrink)

This note is a generalization and improved interpretation of the main result of Karni and Schmeidler. A decision-maker is supposed to possess a preference relation on acts and another preference relation on state-prize lotteries, both of which are assumed to satisfy the von Neumann–Morgenstern axioms. In addition, the two preference relations restricted to a state of nature are assumed to agree. We show that these axioms are necessary and sufficient for the existence of subjective expected utility over acts with state-dependent (...) utility functions and a subjective probability measure. This subjective probability measure is unique when conditioned on the set of states of nature in which not all the prizes are equally desirable. (shrink)

This is a study of all the recent literature on william james written from a phenomenological perspective with the purpose of showing that william james made fundamental contributions to the phenomenological theory of the intentionality of consciousness, To the phenomenological theory of self-Identity, And to the phenomenological conception of noetic freedom as the basic concept of ethical theory.

All of the major themes of Edmund Husserl's phenomenology, from the Logical Investigations to The Crisis of the European Sciences, are investigated from a critical point of view by James M. Edie. The philosophy of logic is considered insofar as it relates to the phenomenological and transcendental foundation of logic itself. Transcendental logic is studied with reference to both the formal logic of Aristotle and Leibniz and the dialectical logic of Hegel. Edie considers Husserl's theories of meaning and reference, intentionality, (...) the distinction between perceptual and eidetic intuition, the notion of the ideality of meaning, the laws of objectivity in general, and formal and material ontology, as well as Husserl's reinterpretation of the apriori. (shrink)

The teachings of Islam and the Indonesian constitution clearly prohibit interfaith marriage. However, some Muslim communities in North Sulawesi as a minority group have entered into interfaith marriages. Therefore, this study aims to analyze the phenomenon of interreligious marriage in North Sulawesi and the achievement of minority fiqh objectives in interfaith families. This research is a field research that uses qualitative methods with a phenomenological approach. Data collection was conducted through interviews with informants consisting of 5 interfaith marriage actors, 1 (...) village official, and 1 religious leader. The results showed that the main motivation for interfaith couples to marry is mutual love. They also tend to get support from their respective extended families so that the marriage runs relatively smoothly and safely. The objectives of minority fiqh are achieved in interfaith marriages in the multicultural society of North Sulawesi. Minority fiqh can be an approach in interfaith marriages in multicultural societies where Muslims are a minority, without losing their Islamic essence, it is based on the fiqh rule that changes in law can occur due to changes in times and places. Minority jurisprudence can be an alternative basis for the sustainability of interfaith families in North Sulawesi that are able to maintain their Islamic identity while still respecting their partner's beliefs. (shrink)

Provides an overview of the complex history of the secular tradition of science and its interactions with religions and spiritual traditions.

Judgments of the rationality of beliefs must take the costs of acquiring and possessing beliefs into consideration. In that case, certain false beliefs, especially those that are associated with the benefits of a cohesive community, can be seen to be useful for an agent and perhaps instrumentally rational to hold. A distinction should be made between excusable misbeliefs, which a rational agent should tolerate, and misbeliefs that are defensible in their own right because they confer benefits on the agent. Likely (...) candidates for such misbeliefs are to be found in the realm of nationalism and religion, where the possession costs of true beliefs are high, and where collective beliefs in falsehoods may allow for a cohesive community. We discuss the paradoxes of reflective awareness involved in the idea of deliberately embracing falsehoods. More rigorous, fully reflective concepts of rationality would still disallow false beliefs, but such demanding versions of rationality would commit agents to pay large costs, thereby weakening the motivation for acquiring true beliefs. (shrink)

This chapter contains sections titled: Scientific Reasons Motivated by Morality? The Science of Religion Notes.

Background: Food biofortification practices in agricultural sectors involve the process of employing biotechnology to enhance the nutritional content of crops during their growth process. Biofortification makes foods even more nutritious and highly functional for addressing malnutrition among children. These practices in farming industries need guidance and legal support from various national policies to support high-quality supplies of school meals fully. Aim: This study aims to analyze the association between various national policies and the implementation of food biofortification practices in agricultural (...) sectors among countries implementing school meal programs. Methods: The Bayesian Mindsponge Framework, combining the reasoning strengths of Mindsponge Theory and inference advantages of Bayesian analysis, was employed on a dataset of 126 government representatives who manage large-scale school meal programs in 126 different countries. Results: Findings showed that food safety policy was positively associated with food biofortification practices in agricultural sectors among countries implementing school meal programs. In contrast, nutrition policy had a significant negative association with these practices. Additionally, policies of school feeding, health, agriculture, and the private sector had unclear associations with food biofortification. Conclusions: Findings underscore the strong position of food safety policy in guiding food biofortification practices in agricultural sectors among countries implementing school meal programs. There is a need to re-assess the implemented nutrition policy due to its significant negative association with these practices. Enhancing and strengthening the policies of school feeding, health, agriculture, and the private sector may increase their potencies in giving positive impacts on food biofortification practices in agricultural sectors to ensure high-quality school meal supplies. (shrink)

Background: Microbiome biomarker discovery for patient diagnosis, prognosis, and risk evaluation is attracting broad interest. Selected groups of microbial features provide signatures that characterize host disease states such as cancer or cardio-metabolic diseases. Yet, the current predictive models stemming from machine learning still behave as black boxes and seldom generalize well. Their interpretation is challenging for physicians and biologists, which makes them difficult to trust and use routinely in the physician-patient decision-making process. Novel methods that provide interpretability and biological insight (...) are needed. Here, we introduce "predomics", an original machine learning approach inspired by microbial ecosystem interactions that is tailored for metagenomics data. It discovers accurate predictive signatures and provides unprecedented interpretability. The decision provided by the predictive model is based on a simple, yet powerful score computed by adding, subtracting, or dividing cumulative abundance of microbiome measurements. -/- Results: Tested on >100 datasets, we demonstrate that predomics models are simple and highly interpretable. Even with such simplicity, they are at least as accurate as state-of-the-art methods. The family of best models, discovered during the learning process, offers the ability to distil biological information and to decipher the predictability signatures of the studied condition. In a proof-of-concept experiment, we successfully predicted body corpulence and metabolic improvement after bariatric surgery using pre-surgery microbiome data. -/- Conclusions: Predomics is a new algorithm that helps in providing reliable and trustworthy diagnostic decisions in the microbiome field. Predomics is in accord with societal and legal requirements that plead for an explainable artificial intelligence approach in the medical field. (shrink)

Certain enterprises at the fringes of science, such as intelligent design creationism, claim to identify phenomena that go beyond not just our present physics but any possible physical explanation. Asking what it would take for such a claim to succeed, we introduce a version of physicalism that formulates the proposition that all available data sets are best explained by combinations of “chance and necessity”—algorithmic rules and randomness. Physicalism would then be violated by the existence of oracles that produce certain kinds (...) of noncomputable functions. Examining how a candidate for such an oracle would be evaluated leads to questions that do not admit an easy resolution. Since we lack any plausible candidate for any such oracle, however, chance-and-necessity physicalism appears very likely to be correct. (shrink)

This paper extends the investigations into logical properties of the quantified argument calculus (Quarc) by suggesting a series of proper subsystems which, although retaining the entire vocabulary of Quarc, restrict quantification in such a way as to make the result decidable. The proof of decidability is via a procedure that prunes the infinite branches of a derivation tree in what is a syntactic counterpart of semantic filtration. We demonstrate an application of one of these systems by showing that Aristotle’s assertoric (...) syllogistic is embeddable within, thus also providing another method of showing its decidability. (shrink)

Gödel's Theorem is often used in arguments against machine intelligence, suggesting humans are not bound by the rules of any formal system. However, Gödelian arguments can be used to support AI, provided we extend our notion of computation to include devices incorporating random number generators. A complete description scheme can be given for integer functions, by which nonalgorithmic functions are shown to be partly random. Not being restricted to algorithms can be accounted for by the availability of an arbitrary random (...) function. Humans, then, might not be rule-bound, but Gödelian arguments also suggest how the relevant sort of nonalgorithmicity may be trivially made available to machines. (shrink)

Free logics are a family of first-order logics which came about as a result of examining the existence assumptions of classical logic (Hintikka _The Journal of Philosophy_, _56_, 125–137 1959 ; Lambert _Notre Dame Journal of Formal Logic_, _8_, 133–144 1967, 1997, 2001 ). What those assumptions are varies, but the central ones are that (i) the domain of interpretation is not empty, (ii) every name denotes exactly one object in the domain and (iii) the quantifiers have existential import. Free (...) logics reject the claim that names need to denote in (ii). _Positive_ free logic concedes that some atomic formulas containing non-denoting names (including self-identity) are true, _negative_ free logic treats them as uniformly false, and _neutral_ free logic as taking a third value. There has been a renewed interest in analyzing proof theory of free logic in recent years, based on intuitionistic logic in Maffezioli and Orlandelli (_Bulletin of the Section of Logic_, _48_(2), 137–158 2019 ) as well as classical logic in Pavlović and Gratzl (_Journal of Philosophical Logic_, _50_, 117–148 2021 ), there for the positive and negative variants. While the latter streamlines the presentation of free logics and offers a more unified approach to the variants under consideration, it does not cover neutral free logic, since there is some lack of both clear formal intuitions on the semantic status of formulas with empty names, as well as a satisfying account of the conditional in this context. We discuss extending the results to this third major variant of free logics. We present a series of G3 sequent calculi adapted from Fjellstad (_Studia Logica_, _105_(1), 93–119 2017, _Journal of Applied Non-Classical Logics_, _30_(3), 272–289 2020 ), which possess all the desired structural properties of a good proof system, including admissibility of contraction and all versions of the cut rule. At the same time, we maintain the unified approach to free logics and moreover argue that greater clarity of intuitions is achieved once neutral free logic is conceptualized as consisting of two sub-varieties. (shrink)