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In this paper the authors provide an epistemological view on the old controversial random-necessity. It has been considered that either one or the other form part of the structure of reality. Chance and indeterminism are nothing but a disorderly efficiency of contingency in the production of events, phenomena, processes, i.e., in its causality, in the broadest sense of the word. Such production may be observed in natural and artificial processes or in human social processes (in history, economics, society, politics, etc.). Here we touch the object par excellence of all scientific research whether natural or human. In this work, is presented a hypothesis whose practical result satisfies the Hegelian dialectic, with the consequent implication of their mutual reciprocal integration. Producing abstractions, without which, there is no thought or knowledge of any kind, from the concrete, that is, the real problem, which in this case is a given Ontological System or Reality. [ABSTRACT FROM AUTHOR]

In this paper, the authors try to clarify the relations between Meinong's and Russell's thoughts on the ontological ideas of existence. The Meinongian theory on non-existent objects does not in itself violate the principle of non-contradiction, since the problem that this hypothesis offers to the theory of definite descriptions is not so much a logical problem as an ontological problem. To demonstrate this we will establish what we believe are the two main theses basic to the theory of descriptions: the epistemological thesis and logical thesis. [ABSTRACT FROM AUTHOR]

Deep disagreement is characterized as being a disagreement in which the interlocutors are unable to reach a common agreement or position on the problem under discussion. However, deep disagreement can be solved irrationally, that is, through fallacious persuasive techniques. One of the objectives of this work is to investigate the debate on deep disagreement in both dialectical and epistemic contexts, and to provide some elements that would allow the concept to be better encompassed in some theoretical framework suitable for analysis. As a hypothesis of this work, it is argued that there is no disagreement between logics, but disagreement between agents or subjects. A structure of belief systems is exposed based on the substantive beliefs that lead by inference to the derived beliefs. Mathematical and epistemological development of a theory of deep disagreement is based on the topological structure of belief systems. [ABSTRACT FROM AUTHOR]

In Ontology, quality determines beings. The quality-quantity bipolarity reveals that a conceptual logical comprehension that can include negation must be a dialectical logic. Quality is a precise characteristic of something (or a subject predicate) capable of augmentation or diminution while remaining identical through differences or quantitative changes. Thus, quality and in opposition quantity are inextricably linked, giving definition to each other, so constituting a logical bipolarity. The theory is that a magnitude G is never separated from secondary qualities α and β, and therefore, a measure depends on a concrete quality Gα or Gβ, that is to say on one pole of a logical bi-pole. However, the particular number, the unit, that expresses the result of a measure is the quality G alone. Examples drawn from physical and chemical experiments illustrate these ideas and elaborate the structure of the concept of opposition between the secondary qualities α and β of a magnitude G. [ABSTRACT FROM AUTHOR]

The concept of God is studied using the ontological argument of Anselm of Canterbury that proves God's existence using a syllogism based on ontology. Unlike metaphysical arguments that demonstrate the existence of God through the study of being and its attributes, the ontological argument aims to reach this same goal based on a concept of God by means of the idea of an entity "greater than anything that can be conceived". Descartes' influence highlighted some of the philosophical difficulties with the inherent dualism implicit in ontology. Logic does not say whether ideas are true or false, as Logic is concerned with right or wrong inference. We take a non-dualist approach in contrast to some of the approaches reviewed. To investigate belief and faith, a modal logical formalization is used, especially modal logic S5, which we find appropriate for presenting arguments. While mathematics and logic can convince, they do not help one to believe in God. This can make us think that reason is not enough to accept God, one must have faith to have access to Him. The relation between reason and faith needs clarification, and the ontological argument requires an unsustainable dualism. [ABSTRACT FROM AUTHOR]

Suppes proposes an analysis of the structure and identity of empirical theories with his model-theoretical approach and undertakes effective reconstructions of theories in diverse disciplinary fields. Here the authors analyse the results of these examinations under the optics of questions concerning the assumed ontological commitments, and for how they satisfy economic and other criteria. [ABSTRACT FROM AUTHOR]

If the words in Spinoza's Ethics are considered as symbols, then certain words in the definitions of the Ethics can be replaced with symbols from set theory and we can reexamine Spinoza's first definitions within a logical–mathematical frame. The authors believe that, some aspects of Spinoza's work can be explained and illustrated through mathematics. A semantic relation between the definitions of the philosopher and set theory is presented. It is explained each chosen symbol. The ontological argument is developed through modal logic. And finally, we present some conclusions drawn from this work. [ABSTRACT FROM AUTHOR]

In this paper the authors develop a logic of concepts within a mathematical linguistic theory. In the set of concepts defined in a belief system, the order relationship and Boolean algebra of the concepts are considered. This study is designed to obtain a tool, which is the metatheoretical base of this type of theory. [ABSTRACT FROM AUTHOR]

In this paper, the authors attempt to prove there is a relationship between Borges' "Argumentum ornithologicum" and Anselm's argument "Argumentum ontologicum". We suggest Borges, using the image of a flock of birds, with oriental reminiscences, half joking, half serious attempts to prove the existence of God. We demonstrate the fallacies incurred by Borges and why his "Argumentum" has no place within the traditional set of ontological arguments. However, it would easy to forget that Borges' claim is not philosophical, nor theological, nor apologetic, but rather ironic or paradoxical. [ABSTRACT FROM AUTHOR]

Infinity is not an easy concept. A number of difficulties that people cope with when dealing with problems related to infinity include its abstract nature, understanding infinity as an ongoing, never ending process, understanding infinity as a set of an infinite number of elements and appreciating well-known paradoxes. Infinity can be understood in several ways with often incompatible meanings, and can involve value judgments or assumptions that are neither explicit nor desired. To usher in its definition, we distinguish several aspects, teleological, artistic (Escher); some definitive, some potential, and others actual. This article also deals with some still unresolved aspects of the concept of infinity. [ABSTRACT FROM AUTHOR]

Infinity is not an easy concept. A number of difficulties that people cope with when dealing with problems related to infinity include its abstract nature: understanding of infinity as a never-ending process, understanding infinity as a set of an infinite number of elements, and understanding some well-known paradoxes. Infinity can be understood in a number of ways, some of which are incompatible, and can involve value judgments or assumptions that are neither explicit nor desired. In its definition, we distinguish several aspects, teleological, artistic (Escher 2000), some essential, some potential, and others actual. Cantor's work on set theory is linked to infinity and has implications for belief in God. [ABSTRACT FROM AUTHOR]

Using language requires simultaneously verifying communication and the linguistic message of the speaker. There is, therefore, an emphasis on understanding, which is contained in the linguistic message. Understanding goes beyond what is said, and includes the immediate connotations, that is, semantics in the strict sense. Language must, therefore, be interpreted, though it is indeed transferred by the immediate meanings of the linguistic code. In the present article, the authors approached some of these issues from the point of view of the hermeneutics of spoken or written language, as a double proposal (ostensive and estimative) of the subject in relation to his/her reality. [ABSTRACT FROM AUTHOR]

Mythical and religious belief systems in a social context can be regarded as a conglomeration of sacrosanct rites, which revolve around substantive values that involve an element of faith. Moreover, we can conclude that ideologies, myths and beliefs can all be analyzed in terms of systems within a cultural context. The significance of being able to define ideologies, myths and beliefs as systems is that they can figure in cultural explanations. This, in turn, means that such systems can figure in logic-mathematical analyses. © 2013 Wiley Periodicals, Inc. Complexity 19: 50-62, 2013 [ABSTRACT FROM AUTHOR]

On the second page, i.e. page 148, of our article Usó-Doménech and Nescolarde-Selva ([2]), the first sentence of section 1 should be changed into the following sentence "Belief systems have the following properties (Abelson, [1]), and through them social significance." Correction to: Found Sci (2016) 21:147-152 https://doi.org/10.1007/s10699-015-9409-z In the originally published version of our article Usó-Doménech and Nescolarde-Selva ([2]), the authors wish to recognize an earlier work on "Belief and Knowledge Systems", namely Abelson ([1]). On the first page, i.e. page 147, of our article Usó-Doménech and Nescolarde-Selva ([2]), the first sentence of the second paragraph should be changed into the following sentence "The use of the term "belief system" (Abelson, [1]) can be highly confusing.". [Extracted from the article]