A simple complete axiomatic system is presented for the many-valued propositional logic based on the conjunction interpreted as product, the coresponding implication (Goguen's implication) and the corresponding negation (Gödel's negation). Algebraic proof methods are used. The meaning for fuzzy logic (in the narrow sense) is shortly discussed.

Structural completeness properties are investigated for a range of popular t-norm based fuzzy logics—including Łukasiewicz Logic, Gödel Logic, Product Logic, and Hájek's Basic Logic—and their fragments. General methods are defined and used to establish these properties or exhibit their failure, solving a number of open problems.

Nammalvar, a Tamil poet who lived in IX-X centuries, is revered as one of the great mystics of India. His four poetic works are equated with the sacred hymns and are part of the ritual worship in the temples of South India. Artistic images of Nammalvar formed the basis of the philosophy of Vishishta-Advaita several centuries later. The poem “Thiruviruttam” is considered as his early work, where he combines the canons of ancient Tamil poetry and his devoted love for Vishnu-Tirumal. (...) The study presents a religious and philosophical interpretation of the poem. The secret of the poem is its dualism: external beauty and sacred meaning. There is a spiritual meaning in symbols of Tamil poetry. Nammalvar takes canons of his predecessors, poets of the Sangam era. However, he fills one with new content. The author compares ancient Tamil poetry and the work of Nammalvar. The plot describes the love between God and the soul. The poet reveals several types of bhakti or devoted love. The description of bhakti subsequently formed the basis for the classification of souls in the philosophy of vishishta-advaita. Bhakti leads to the transition to Vaikuntha or the heaven city. Sri Vaishnavism teachers turned the description of relationship soul-Vishnu into a spiritual practice. The artistic images of Nammalvar are compared with Hindu concepts such as transcendence, darshan, divine grace and moksha. In South India “Thiruviruttam” is considered the Tamil Rig Veda. Poem is performed at home, in the temple, during festive processes. It helps to find the roots of Vaishnavism and understand its poetic origin. (shrink)

This paper is a contribution to the study of the rôle of disjunction inAlgebraic Logic. Several kinds of (generalized) disjunctions, usually defined using a suitable variant of the proof by cases property, were introduced and extensively studied in the literature mainly in the context of finitary logics. The goals of this paper are to extend these results to all logics, to systematize the multitude of notions of disjunction (both those already considered in the literature and those introduced in this paper), (...) and to show several interesting applications allowed by the presence of a suitable disjunction in a given logic. (shrink)

Shows how different forms of skepticism can lead to remarkably different moral and political implications.

In this position paper we present a logical framework for modelling reasoning with graded predicates. We distinguish several types of graded predicates and discuss their ubiquity in rational interaction and the logical challenges they pose. We present mathematical fuzzy logic as a set of logical tools that can be used to model reasoning with graded predicates, and discuss a philosophical account of vagueness that makes use of these tools. This approach is then generalized to other kinds of graded predicates. Finally, (...) we propose a general research program towards a logic-based account of reasoning with graded predicates. (shrink)

Some aspects of vagueness as presented in Shapiro’s book Vagueness in Context [23] are analyzed from the point of fuzzy logic. Presented are some generalizations of Shapiro’s formal apparatus.

We are thankful to Gerhard Schurz for his response (Schurz 2023) to our paper (Spelda et al. 2023). Spelda et al. (2023) shows how a variant of no-regret learning called meta-induction (Schurz 2008; 2019) can be used for optimal selection from available political alternatives and, as a result, also for increasing voter competence that has come under attack from mis/disinformation. Since our paper takes a first step in applying meta-induction to long-standing issues in Democratic Theory (e.g., the usefulness of jury (...) theorems for justifying democracy), we are grateful to Gerhard Schurz for highlighting some of the conditions that need to be met for the development of practical applications. (shrink)

In the last few decades many formal systems of fuzzy logics have been developed. Since the main differences between fuzzy and classical logics lie at the propositional level, the fuzzy predicate logics have developed more slowly (compared to the propositional ones). In this text we aim to promote interest in fuzzy predicate logics by contributing to the model theory of fuzzy predicate logics. First, we generalize the completeness theorem, then we use it to get results on conservative extensions of theories (...) and on witnessed models. (shrink)

This paper addresses the ontological status of the body in the context of bodily practices in body-oriented disciplines, such as sport training, dance, and physiotherapy. Following Descartes’, Huss...

В книге исследуется острая проблема совместной эволюции (коэволюции) Человека и Природы, условий выживания людей и окружающей среды, перспективы развития ноосферы – биосферы и Разума.

Voprosy filosofii is publishing V. I. Danilov-Danil'ian's article "Is the ‘Coevolution of Nature and Society’ Possible?" in which he discusses at the same time the problems of sustainable development. It is a well-written, sharp polemic directed against my use of the concept "coevolution of nature and society." The article is reads easily and contains many interesting ideas. I believe it will spark the reader's interest, especially as it contains a number of debatable assertions, and may be regarded as the opening (...) of a debate on the problem of the coevolution of nature and society. A number of my works on this issue have been published and the fullest exposition of my position is contained in the monograph Sovremmenyi ratsionalizm, published in 1995. (shrink)

This article provides an analysis—within the framework of Radical Construction Grammar—of how become developed into a copula ‘become’ out of an original sense ‘arrive’, and wax, originally ‘grow’, also came to be used as a copula ‘become’. Importantly, it explains why these verbs successfully became fully productive copulas in a very short period of time. It is argued that this happened after a pre-copular stage had reached a cognitive threshold value. The occurrence of this threshold is related to the fact (...) that the copular constructions featuring become and wax were not the end result of a single diachronic lineage of constructions (i.e. one construction developed out of another one, one at a time). Instead, the copularization of these verbs was the result of an interaction between lineages of constructions, belonging to two groups: (i) constructions involving become or wax, which gradually changed and interacted with each other; (ii) constructions involving already existing copulas, notably weorđan ‘become’, which provided a generally productive analog upon which the newly emerging copulas could graft. Generally, the article calls attention to the importance of multiple source constructions and thresholds in understanding grammaticalization processes and productivity. (shrink)

This paper empirically examines how consumers react when a company marks a product with a gay label. The company under scrutiny is one of the largest video game developers in the world, and the labeled product is a popular video game character. We use a regression discontinuity design to exploit the quasi-experimental setting. The main finding was significant drop in demand for this character and a return to previous levels after approximately 3 months. Possible mechanisms and dynamics were explored by (...) analyzing demand for other characters and by surveying consumers. The results are consistent after performing robustness checks based on grid search, subsampling, and placebo tests. (shrink)

Linear arithmetics are extensions of Presburger arithmetic () by one or more unary functions, each intended as multiplication by a fixed element (scalar), and containing the full induction schemes for their respective languages. In this paper, we construct a model of the 2‐linear arithmetic (linear arithmetic with two scalars) in which an infinitely long initial segment of “Peano multiplication” on is ‐definable. This shows, in particular, that is not model complete in contrast to theories and that are known to satisfy (...) quantifier elimination up to disjunctions of primitive positive formulas. As an application, we show that, as a discretely ordered module over the discretely ordered ring generated by the two scalars, does not have the NIP, answering negatively a question of Chernikov and Hils. (shrink)

Uniform infinite bases are defined for the single-conclusion and multiple-conclusion admissible rules of the implication–negation fragments of intuitionistic logic and its consistent axiomatic extensions . A Kripke semantics characterization is given for the structurally complete implication–negation fragments of intermediate logics, and it is shown that the admissible rules of this fragment of form a PSPACE-complete set and have no finite basis.

This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and Δ-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics–namely the class of algebras defined over the real unit (...) interval, the rational unit interval, the hyperreals , the strict hyperreals and finite chains, respectively–and we survey the known completeness methods and results for prominent logics. We also obtain new interesting relations between the real, rational and hyperreal semantics, and good characterizations for the completeness with respect to the semantics of finite chains. Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are proved. (shrink)

Dave Ripley has recently argued against the plausibility of multiset consequence relations and of contraction-free approaches to paradox. For Ripley, who endorses a nontransitive theory, the best arguments that buttress transitivity also push for contraction—whence it is wiser for the substructural logician to go nontransitive from the start. One of Ripley’s allegations is especially insidious, since it assumes the form of a trivialisation result: it is shown that if a multiset consequence relation can be associated to a closure operator in (...) the expected way, then it necessarily contracts. We counter Ripley’s objection by presenting an approach to multiset consequence that escapes this trap. This approach is multiple-conclusioned in a heterodox way, for multiple succedents are given a conjunctive, rather than a disjunctive reading. Finally, we address a further objection by French and Ripley to the effect that the informational interpretation of sequents in linear logic does not motivate cut. (shrink)

The article is a critical systematic presentation of R. M. Hare's ethical concepts and doctrine as outlined in his books The Language of Morals (1952) and Freedom and Reason (1963). The theory merits attention for many reasons, yet it appears to suffer from some weaknesses; the chief among them being the lack of explanation for the source of binding force of moral principles.

This article identifies the assumption of responsibility as a basic need of human beings and applies the concept specifically to older people with dementia or Alzheimer's disease. It suggests a two‐level concept of responsibility, based on the approach of discourse ethicist Karl‐Otto Apel, as a promising approach to recognizing human diversity while at the same time respecting people's equal rights to participate in discourse. This concept can serve as a theoretical starting point for the construction of individually adapted types of (...) responsibility. Furthermore, the article describes practical ideas (primarily the practice of doll therapy) that can enable people with dementia or Alzheimer's disease to assume responsibility. Direct communication and a reflective, sensitive consideration of each individual case are identified as important prerequisites for the inclusion of elderly people with dementia. (shrink)

[Anthony Kenny: Thomas on the Human Spirit].

The paper explores the notion of communicative success as a match between the speaker's communicative intention and the audience's interpretation. The first part argues that it cannot be generalized to all kinds of communication. The second part characterizes various types of relations between the speaker's and the audience's beliefs on which this kind of communicative success can be based. It shows that the requirements concerning agreement between these beliefs are rather modest.

The paper discusses one of the central problems of contemporary formal semantics — counterexamples to the predictions of the theory of binding (due to N. Chomsky). In particular, the author addresses cases of the so-called coreferential readings of reflexive pronouns which are standardly predicted to receive only the bound reading. The author examines theories of T. Reinhart and I. Heim and suggests an extension ofthe latter theory in order to enable it to account for the aforementioned readings of reflexive pronouns.