Modality, Potentiality and Contradiction in Quantum Mechanics

In [11], Newton da Costa together with the author of this paper argued in favor of the possibility to consider quantum superpositions in terms of a paraconsistent approach. We claimed that, even though most interpretations of quantum mechanics (QM) attempt to escape contradictions, there are many hints that indicate it could be worth while to engage in a research of this kind. Recently, Arenhart and Krause [1, 2, 3] have raised several arguments against this approach and claimed that, taking into account the square of opposition, quantum superpositions are better understood in terms of contrariety propositions rather than contradictory propositions. In [17] we defended the Paraconsistent Approach to Quantum Superpositions (PAQS) and provided arguments in favor of its development. In the present paper we attempt to analyze the meanings of modality, potentiality and contradiction in QM, and provide further arguments of why the PAQS is better suited, than the Contrariety Approach to Quantum Superpositions (CAQS) proposed by Arenhart and Krause, to face the interpretational questions that quantum technology is forcing us to consider.Comment: Published in: New Directions in Paraconsistent Logic, J-Y B\'eziau M. Chakraborty & S. Dutta (Eds.), Springer, in press. arXiv admin note: text overlap with arXiv:1404.518

Inadequacy of Modal Logic in Quantum Settings

We test the principles of classical modal logic in fully quantum settings. Modal logic models our reasoning in multi-agent problems, and allows us to solve puzzles like the muddy children paradox. The Frauchiger-Renner thought experiment highlighted fundamental problems in applying classical reasoning when quantum agents are involved; we take it as a guiding example to test the axioms of classical modal logic. In doing so, we find a problem in the original formulation of the Frauchiger-Renner theorem: a missing assumption about unitarity of evolution is necessary to derive a contradiction and prove the theorem. Adding this assumption clarifies how different interpretations of quantum theory fit in, i.e., which properties they violate. Finally, we show how most of the axioms of classical modal logic break down in quantum settings, and attempt to generalize them. Namely, we introduce constructions of trust and context, which highlight the importance of an exact structure of trust relations between agents. We propose a challenge to the community: to find conditions for the validity of trust relations, strong enough to exorcise the paradox and weak enough to still recover classical logic.Comment: In Proceedings QPL 2018, arXiv:1901.0947

Multi-Criteria Assignment Techniques in Multi- Dimensional Neutrosophic Soft Set Theory

In this paper, we have introduced a new concept of multi-dimensional neutrosophic soft sets together with various operations, properties and theorems on them. Then we have proposed an algorithm named 2-DNS based on our proposed two-dimensional neutrosophic soft set for solving neutrosophic multi-criteria assignment problems with multiple decision makers

Dialectical Multivalued Logic and Probabilistic Theory

There are two probabilistic algebras: one for classical probability and the other for quantum mechanics. Naturally, it is the relation to the object that decides, as in the case of logic, which algebra is to be used. From a paraconsistent multivalued logic therefore, one can derive a probability theory, adding the correspondence between truth value and fortuity

Theology Under Siege: Reflections of a Troubled Philosopher and a Believer

The transposition of the theological expression into the framework of epistemology suggested by the contemporary philosophy of science is a long-desired project. The presented article offers an overview of the different epistemological and methodological issues that arise when this expression is carried out in the common sense paradigm. It turns that once the necessary change into the mode of knowledge acquisition of contemporary science is made, one can significantly improve theology’s both methodological and conceptual foundations. In particular, this concerns the use of abstract concepts to better penetrate the intricacies of the Divine nature as well as the non-classical logics to improve theology’s inferential basis. The resulting question of the contextuality of theology, namely, its dependence on the conceptual framework and the picture of the world, is also surveyed. Consequently, theology can be perceived as a lexically open project. In conclusion it is argued that while the contemporary theology should retain its common sense exposition for the pastoral and catechetical purposes that allows for the efficient transmission of faith through intuitive knowledge, the state-of-the-art theological research must reach out to to abstract conceptual frameworks to assure the depth of its penetrative insight.The transposition of the theological expression into the framework of epistemology suggested by the contemporary philosophy of science is a long-desired project. The presented article offers an overview of the different epistemological and methodological issues that arise when this expression is carried out in the common sense paradigm. It turns that once the necessary change into the mode of knowledge acquisition of contemporary science is made, one can significantly improve theology’s both methodological and conceptual foundations. In particular, this concerns the use of abstract concepts to better penetrate the intricacies of the Divine nature as well as the non-classical logics to improve theology’s inferential basis. The resulting question of the contextuality of theology, namely, its dependence on the conceptual framework and the picture of the world, is also surveyed. Consequently, theology can be perceived as a lexically open project. In conclusion it is argued that while the contemporary theology should retain its common sense exposition for the pastoral and catechetical purposes that allows for the efficient transmission of faith through intuitive knowledge, the state-of-the-art theological research must reach out to to abstract conceptual frameworks to assure the depth of its penetrative insight

Algunas preguntas difíciles para el racionalismo crítico

“Lo que distingue a la ciencia de todos los demás esfuerzos humanos es que las consideraciones acerca del  mundo que nuestras mejores ciencias maduras proporcionan están fuertemente apoyadas en la evidencia y  esta evidencia nos da la razón más fuerte para creer en ellas”. Esto fue lo que se dijo al anunciar inicialmente  una conferencia sobre la inducción en una célebre sede de estudios británica en 2007. Esto demuestra  cuánto le cuesta todavía a los racionalistas críticos dar a conocer el mensaje de la Lógica de la investigación  científica, respecto a lo que la evidencia empírica es capaz de hacer y lo que hace. Este artículo no se centra  en estas tareas de divulgación a las que se enfrentan los racionalistas críticos, pero si en algunos problemas  lógicos internos. Aunque estamos justamente orgullosos de tener la única casa en el barrio que es  lógicamente impermeable, debemos ser conscientes de que no todo al interior está en un orden impecable.  Hay críticas que aún no han sido satisfechas adecuadamente, al igual que preguntas que aún no han sido  contestadas de manera adecuada. Cada una de las seis dificultades a tratar surge de las soluciones  ejemplares de Popper a los problemas de la demarcación y la inducción. Estas soluciones se refieren a la  gestión de las contradicciones; la aproximación a la verdad; la corroboración de las hipótesis falsadas; la  toma de decisiones bajo la incertidumbre; el papel de la evidencia en el derecho; y la representación del  contenido lógico. En ninguna de estas áreas el racionalismo crítico todavía no ofrece, en mi opinión, una  respuesta comparable en claridad a las soluciones de los problemas de la demarcación y la inducción. Esta es una selección personal, por lo que no se sugiere que no haya otras preguntas difíciles por delante. Sin  embargo, en sólo uno o dos casos ofreceré algo parecido auna solución.    "What distinguishes science from all other human endeavours is that the accounts of the world that our best, mature sciences deliver are strongly supported by evidence and this evidence gives us the strongest reason  to believe them". That anyway is what is said at the beginning of the advertisement for a conference on  induction at a celebrated British seat of learning in 2007. It shows how much critical rationalists still have to  do to make known the message of Logik der Forschung concerning what empirical evidence is able to do and  what it does. This paper will focus not on these tasks of popularization faced by critical rationalists, but on  some logical problems internal to critical rationalism. Although we are rightly proud of having the only house in the neighbourhood that is logically watertight, we should be aware that not everything inside is in  impeccable order. There are criticisms that have not yet been adequately met, and questions that have not  yet been adequately answered. Each of the six difficulties to be discussed arises from Popper’s exemplary  solutions to the problems of demarcation and induction. They concern the management of contradictions;  approximation to truth; the corroboration of already falsified hypotheses; decision making under  uncertainty; the role of evidence in the law; and the representation of logical content. In none of these areas  does critical rationalism yet offer, to my mind, an account comparable in clarity to its solutions to the  problems of demarcation and induction. This is a personal selection, and it is not suggested that there are  not other hard questions ahead. In only one or two cases shall I offer anything like a solution

Logical theory revision through data underdetermination: an anti-exceptionalist exercise

The anti-exceptionalist debate brought into play the problem of what are the relevant data for logical theories and how such data affects the validities accepted by a logical theory. In the present paper, I depart from Laudan's reticulated model of science to analyze one aspect of this problem, namely of the role of logical data within the process of revision of logical theories. For this, I argue that the ubiquitous nature of logical data is responsible for the proliferation of several distinct methodologies for logical theories. The resulting picture is coherent with the Laudanean view that agreement and disagreement between scientific theories take place at different levels. From this perspective, one is able to articulate other kinds of divergence that considers not only the inferential aspects of a given logical theory, but also the epistemic aims and the methodological choices that drive its development

The Spirit (of our Time) is and is not a Bone.

Slavoj Žižek and Graham Priest are two philosphers who have a unique place within respectively postmodernist and formal-logic philosophy. They both defend Hegelianism within the two domains that could historically be characterized a anti-Hegelian. We characterize their formal Hegelianism through respectively the style form of chiasm and the inclosure schema. In addition to this, we make concrete the two movements in which they are situated on the basis of two prominent philosophers: Jacques Derrida and Bertrand Russell. We outline the two Hegelians#39; criticism of these figures and in this way we come to a refinement of the analogy and difference between the them. Finally, we explain how they could be considered in relation to their movements in general