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)

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 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. (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.

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)

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)

The most common definition of belief is taken from analytical philosophy, which understands it as a proposition that is considered as true. Such a broad definition is ambiguous for some fields of empirical research, like psychology, which deals with the mental state of the believer when holding the belief. This article aims to reach an operationalization of beliefs to pinpoint their distinctive features with respect to similar concepts. We summarize the most influential interpretations of belief in psychology and psychiatry, which (...) are mainly based on Immanuel Kant and analytical philosophy. We also expose the problem that arises from putting the mental states of beliefs, knowledge, opinions and preferences in the same bag. Our proposal is that a belief is: a proposition that is taken to be true; and which the subject is willing to hold even if irrefutable evidence were hypothetically argued against it. We introduce a narrower interpretation to reliably discriminate the mental state of believing, which is intended to be applied to empirical psychology, neuroscience, behavioral economics, sociology and related sciences. (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)

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)