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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., Author(s): J. L. Usó-Doménech [sup.1] , J. A. Nescolarde-Selva [sup.1] , H. Gash [sup.2] Author Affiliations: (1) grid.5268.9, 0000 0001 2168 1800, Department of Applied Mathematics, University of Alicante, , [...]

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 [alpha] and [beta], and therefore, a measure depends on a concrete quality G[alpha] or G[beta], 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 [alpha] and [beta] of a magnitude G., Author(s): J. L. Usó-Doménech [sup.1] , J. A. Nescolarde-Selva [sup.1] , H. Gash [sup.2] Author Affiliations: (1) grid.5268.9, 0000 0001 2168 1800, Department of Applied Mathematics, University of Alicante, , [...]

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., Author(s): J. Nescolarde-Selva [sup.1] , J. L. Usó-Doménech [sup.1] , H. Gash [sup.2] Author Affiliations: (1) grid.5268.9, 0000 0001 2168 1800, Department of Applied Mathematics, University of Alicante, , Alicante, [...]

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., Author(s): J. L. Usó-Doménech [sup.1], J. A. Nescolarde-Selva [sup.1], H. Gash [sup.2] Author Affiliations: (1) grid.5268.9, 0000 0001 2168 1800, Department of Applied Mathematics, University of Alicante, , Alicante, Spain [...]

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., Author(s): J. L. Usó-Doménech [sup.1] , J. A. Nescolarde-Selva [sup.1] , Hugh Gash [sup.2] Author Affiliations: (1) grid.5268.9, 0000 0001 2168 1800, Department of Applied Mathematics, University of Alicante, , [...]

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., Author(s): J. L. Usó-Doménech [sup.1] , J. A. Nescolarde-Selva [sup.1] Author Affiliations: (1) grid.5268.9, 0000 0001 2168 1800, Department of Applied Mathematics, University of Alicante, , Alicante, Spain Introduction The [...]

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., Author(s): J. L. Usó-Doménech [sup.1] , J. A. Nescolarde-Selva [sup.1] , H. Gash [sup.2] Author Affiliations: (1) grid.5268.9, 0000 0001 2168 1800, Department of Applied Mathematics, University of Alicante, , [...]

In order to establish patterns of materialization of the beliefs we are going to consider that these have defined mathematical structures. It will allow us to understand better processes of the textual, architectonic, normative, educative, etc., materialization of an ideology. The materialization is the conversion by means of certain mathematical correspondences, of an abstract set whose elements are beliefs or ideas, in an impure set whose elements are material or energetic. Text is a materialization of ideology and it is any representation of the Reality represented by symbolic means. In all text T we can observe diverse topological structures: Metric Textual Space, Textual Topology and a Textual Lattice., Author(s): J. Nescolarde-Selva[sup.1] , J. L. Uso-Domenech[sup.1] Author Affiliations: J. Nescolarde-Selva graduated in Mathematics from the University of Havana (Cuba) in 1999. He won the award: Gold Title at the [...]

Author(s): J. L. Uso-Domenech[sup.1] , J. Nescolarde-Selva[sup.1] Author Affiliations: J. L. Uso-Domenech graduated in Sciences in 1968 and Doctor in Mathematics by the University of Valencia (Spain) in 1991. Since [...]

Reality contains information (significant) that becomes significances in the mind of the observer. Language is the human instrument to understand reality. But is it possible to attain this reality? Is there an absolute reality, as certain philosophical schools tell us? The reality that we perceive, is it just a fragmented reality of which we are part? The work that the authors present is an attempt to address this question from an epistemological, linguistic and logical-mathematical point of view. Keywords Connotative significance * Denotative significance * Knowledge * Language * Mathematical things * Paradigm * Reality * Significant * Sintagm, 1 Introduction Our starting point is the recognition of Reality that is beyond us, but we can get in touch in different ways. We have two great tools to access [...]