By justification we understand what makes a belief epistemologically viable: generally this is considered knowledge that is true. The problem is defining this with a higher degree of precision because this is where different conflicting conceptions appear. On the one hand, we can understand justification as what makes it reasonable to acquire or maintain a belief; on the other, it is what increases the probability that the belief is true. This work tries to prove that beliefs depend on other beliefs (...) that are epistemically justified and that such beliefs are the result of (i.e., they arise from) our privileged intuition of reality. For this, we examine the concept of epistemic regress. Epistemic reasons authorize a proposition P to be the conclusion of an argument in which such reasons function as premises and are vulnerable to epistemic regress. The three most important approaches to epistemic regress are Infinitism, Coherentism and Foundationalism. (shrink)

In beliefs we live, we move and we are [...] the beliefs constitute the base of our life, the land on which we live [...] All our conduct, including the intellectual life, depends on the system of our authentic beliefs. In them [...] lies latent, as implications of whatever specifically we do or we think [...] the man, at heart, is believing or, which is equal, the deepest stratum of our life, the spirit that maintains and carries all the others, (...) is formed by beliefs...We know that the human being is a social animal. This is a common fact. Moreover, the human being is defined as a rational being. It is clear and nobody can deny that human creations include logic, mathematics, philosophy, science, and jurisprudence. These are all products of rationality or abstract thought. Nevertheless, human sociability goes further that the sociability of an animal herd. Societies were founded, cohere, develop, degenerate and die based on their belief systems. Reason cannot prove the .. (shrink)

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 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. (shrink)

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. (shrink)

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.

This reply to Gash’s (Found Sci 2014) commentary on Nescolarde-Selva and Usó-Doménech (Found Sci 2014b) answers the questions raised and at the same time opens up new questions.

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. (shrink)

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. (shrink)

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.

Impure systems contain Objects and Subjects: Subjects are human beings. We can distinguish a person as an observer (subjectively outside the system) and that by definition is the Subject himself, and part of the system. In this case he acquires the category of object. Objects (relative beings) are significances, which are the consequence of perceptual beliefs on the part of the Subject about material or energetic objects (absolute beings) with certain characteristics.The IS (Impure System) approach is as follows: Objects are (...) perceptual significances (relative beings) of material or energetic objects (absolute beings). The set of these objects will form an impure set of the first order. The existing relations between these relative objects will be of two classes: transactions of matter and/or energy and inferential relations. Transactions can have alethic modality: necessity, possibility, impossibility and contingency. Ontic existence of possibility entails that inferential relations have Deontic modality: obligation, permission, prohibition, faculty and analogy. We distinguished between theorems (natural laws) and norms (ethical, legislative and customary rules of conduct). (shrink)

Reality contains information 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.

This reply to Gash’s (Found Sci 2013) commentary on Nescolarde-Selva and Usó-Doménech (Found Sci 2013) answers the three questions raised and at the same time opens up new questions.

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. (shrink)

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. 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. (shrink)

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. (shrink)

Human language has the characteristic of being open and in some cases polysemic. The word “infinite” is used often in common speech and more frequently in literary language, but rarely with its precise meaning. In this way the concepts can be used in a vague way but an argument can still be structured so that the central idea is understood and is shared with to the partners. At the same time no precise definition is given to the concepts used and (...) each partner makes his own reading of the text based on previous experience and cultural background. In a language dictionary the first meaning of “infinite” agrees with the etymology: what has no end. We apply the word infinite most often and incorrectly as a synonym for “very large” or something that we do not perceive its completion. In this context, the infinite mentioned in dictionaries refers to the idea or notion of the “immeasurably large” although this is open to what the individual’s means by “immeasurably great.” Based on this linguistic imprecision, the authors present a non Cantorian theory of the potential and actual infinite. For this we have introduced a new concept: the homogon that is the whole set that does not fall within the definition of sets established by Cantor. (shrink)

Palabras claves. Métodos estadísticos, pruebas de hipótesisResumen. Se presentan de forma simple, breve y por medios de los ejemplos prácticos, los métodos estadísticos que sirven para demostrar la representatividad de una, dos o varias muestras basada en los parámetros poblacionales . Se indican la manera de reducir el tamaño del error experimental para aclarar el efecto significativo de los grupos o muestras bajo el interés . Además, se demuestran la forma de eliminar el efecto de las variables auxiliares o colaterales (...) causante del ruido o error en la estadística . También se nota el uso del modelo ANOVA Anidada para indicar la forma de segmentar la ANOVA en varias partes y de esta manera poder contestar preguntas más complejas. Finalmente, se describen e explican la forma de optimizar los recursos en la conducción de los experimentos y descubrir el efecto de la interacción entre las variables .Keywords. Hypothesis testing, statistical methods. Statistical methods that serve to represent, based upon population parameters of mean and variance, for one, tow or various samples taken from study populations are discussed. Ways to reduce the amount of experimental error in order to clarify the real effect of the treatments are demonstrated . The use of Covariance Analysis to show the pure effect of treatment free from the effect of collateral variables is also indicated. Nested ANOVA that allows division of ANOVA in several parts in order to answer complex questions is described and explained. Finally, the utility of Factorial Analysis for optimization of resource use as well as the illustration of interaction effects are noted and analyzed. (shrink)

In the Reality we know, we cannot say if something is infinite whether we are doing Physics, Biology, Sociology or Economics. This means we have to be careful using this concept. Infinite structures do not exist in the physical world as far as we know. So what do mathematicians mean when they assert the existence of ω? There is no universally accepted philosophy of mathematics but the most common belief is that mathematics touches on another worldly absolute truth. Many mathematicians (...) believe that mathematics involves a special perception of an idealized world of absolute truth. This comes in part from the recognition that our knowledge of the physical world is imperfect and falls short of what we can apprehend with mathematical thinking. The objective of this paper is to present an epistemological rather than an historical vision of the mathematical concept of infinity that examines the dialectic between the actual and potential infinity. (shrink)

The liar paradox is a famous and ancient paradox related to logic and philosophy. It shows it is perfectly possible to construct sentences that are correct grammatically and semantically but that cannot be true or false in the traditional sense. In this paper the authors show four approaches to interpreting paradoxes that illustrate the influence of: the levels of language, their belonging to indeterminate compatible propositions or indeterminate propositions, being based on universal antinomy and the theory of dialetheism.

sBuilding models as a practical aspect of ecological theory has as a principal purpose the determination of relations in formal language. In this paper, the authors provide a formalization of ecological models based on impure systems theory. Impure systems contain objects and subjects: subjects are human beings. We can distinguish a person as an observer that by definition is the subject himself and part of the system. In this case he acquires the category of object. Objects are significances, which are (...) the consequence of perceptual beliefs on the part of the subject about material or energetic objects with certain characteristics. The impure system approach is as follows: objects are perceptual significances of material or energetic objects. The set of these objects will form an impure set of the first order. The existing relations between these relative objects will be of two classes: transactions of matter and/or energy and inferential relations. Transactions can have alethic modality: necessity, possibility, impossibility and contingency. In this work we define measures which let us choose the more suitable variables to relate both the model with the ecosystem and with different models. In this way we define different comparison indexes. (shrink)

A semiotic theory of systems derived from language would have the purpose of classifying all the systems of linguistic expression: philosophy, ideology, myth, poetry, art, as much as the dream, lapsus, and free association in a pluridimensional matrix that will interact with many diversified fields. In each one of these discourses it is necessary to consider a plurality of questions, the essence of which will only be comprehensible by the totality; it will be necessary to ask, in the first place, (...) what will be the purpose of this language, what function does it fulfill and for which reason has it been constructed. The concept of World vision (WV) is introduced and its relation with Generalized Collective Conscience (GCC) and Particularized Collective Conscience. Culture implies a particular WV. Culture creates GCC. The semantic field is a structure that formalizes the units of a certain culture constituting a portion of the vision of the Reality that owns this culture. An ecological case is explained. (shrink)

This paper refers to a subjective approach to Ecosystems, referred to as Impure Systems to capture a set of fundamental properties. There are four main phenomenological components: directionality, intensity, connection energy and volume. A fundamental question in this approach to Impure Systems is the intensity or forces of a relation. Concepts as the system volume, and propose a system thermodynamic theory based in the Law of Zipf and the temperature of information are introduced. It hints at the possibility of adapting (...) the fractal theory by introducing the fractal dimension of the system. (shrink)

Originally published in Proceedings of the British Academy 60 (1974), 339-359.