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Addiction in existential positive psychology (EPP, PP2.0): from a critique of the brain disease model towards a meaning-centered approach
(Taylor and Francis Group, Routledge, 2019-04-19) Carreño, David F.; Pérez Escobar, José Antonio; https://orcid.org/0000-0002-0688-6485; https://orcid.org/0000-0002-3728-6896
Addiction is widely considered to be a chronic brain disease. Under this view, neuroscientists have spent lots of resources to study the brain and identify pharmacological targets to palliate addiction. However, the brain disease model presents serious epistemological and practical limitations. Firstly, this article collects important critiques to the medical model and calls for a more pluralistic approach to addiction. Secondly, we discuss the problematic self-regulation of people with addiction from an existential positive perspective (also termed PP2.0). People with addiction, whether it is related to substance abuse, gambling, internet surfing, shopping or eating, usually manifest existential struggles that could account for the development and maintenance of their addiction. Relational problems, evasion of guilt and responsibility, and a lack of meaning in life have been evidenced in the literature. At the base of this psychological problem, there are both an inability to cope with the dark side of life and a maladaptive search for positive emotions that cannot be naturally obtained from meaningful social interactions. Finally, the meaning-centered approach (MCA) is proposed for addiction recovery. MCA helps clients find a purpose in life and integrate into society. This existential positive approach can be a fundamental complement for mainstream addiction treatments.
An algebraic view of super-Belnap logics. Studia Logica
(Springer Nature, 2017-07-28) Albuquerque, Hugo; Přenosil, Adam; Rivieccio, Umberto
The Belnap–Dunn logic (also known as First Degree Entailment, or FDE) is a well-known and well-studied four-valued logic, but until recently little has been known about its extensions, i.e. stronger logics in the same language, called super-Belnap logics here. We give an overview of several results on these logics which have been proved in recent works by Přenosil and Rivieccio. We present Hilbert-style axiomatizations, describe reduced matrix models, and give a description of the lattice of super-Belnap logics and its connections with graph theory. We adopt the point of view of Abstract Algebraic Logic, exploring applications of the general theory of algebraization of logics to the super-Belnap family. In this respect we establish a number of new results, including a description of the algebraic counterparts, Leibniz filters, and strong versions of super-Belnap logics, as well as the classification of these logics within the Leibniz and Frege hierarchies.
Bilattice Logic Properly Displayed
(Elsevier, 2019-05-15) Greco, Giuseppe; Fei Liang,; Palmigiano,Alessandra; Rivieccio, Umberto
We introduce a proper multi-type display calculus for bilattice logic (with conflation) for which we prove soundness, completeness, conservativity, standard subformula property and cut elimination. Our proposal builds on the product representation of bilattices and applies the guidelines of the multi-type methodology in the design of display calculi.
Characterizing finite-valuedness
(Elsevier, 2018-08-15) Caleiro, Carlos; Marcelino, Sérgio; Rivieccio, Umberto
We introduce properties of consequence relations that provide abstract counterparts of different notions of finite-valuedness in logic. In particular, we obtain characterizations of logics that are determined (i) by a single finite matrix, (ii) by a finite set of finite matrices, and (iii) by a set of n-generated matrices for some natural number n. A crucial role is played in our proofs by two closely related notions, local tabularity and local finiteness.
Compatibly involutive residuated lattices and the Nelson identity
(Springer Nature, 2018-11-03) Matthew Spinks; Rivieccio, Umberto; Nascimento, Thiago
Nelson’s constructive logic with strong negation N3 can be presented (to within definitional equivalence) as the axiomatic extension NInFL ew of the involutive full Lambek calculus with exchange and weakening by the Nelson axiom[Figure not available: see fulltext.] The algebraic counterpart of NInFL ew is the recently introduced class of Nelson residuated lattices. These are commutative integral bounded residuated lattices ⟨ A; ∧ , ∨ , ∗ , ⇒ , 0 , 1 ⟩ that: (i) are compatibly involutive in the sense that ∼ ∼ a= a for all a∈ A, where ∼ a: = a⇒ 0 , and (ii) satisfy the Nelson identity, namely the algebraic analogue of (Nelson ⊢ ), viz.(x⇒(x⇒y))∧(∼y⇒(∼y⇒∼x))≈x⇒y.The present paper focuses on the role played by the Nelson identity in the context of compatibly involutive commutative integral bounded residuated lattices. We present several characterisations of the identity (Nelson) in this setting, which variously permit us to comprehend its model-theoretic content from order-theoretic, syntactic, and congruence-theoretic perspectives. Notably, we show that a compatibly involutive commutative integral bounded residuated lattice A is a Nelson residuated lattice iff for all a, b∈ A, the congruence condition ΘA(0,a)=ΘA(0,b)andΘA(1,a)=ΘA(1,b)impliesa=bholds. This observation, together with others of the main results, opens the door to studying the characteristic property of Nelson residuated lattices (and hence Nelson’s constructive logic with strong negation) from a purely abstract perspective.
Diseases as social problems
(Springer Nature, 2024-02-02) Saborido Alejandro, Cristian; Zamora Bonilla, Jesús Pedro
In this paper we articulate a characterization of the concept of disease as a social problem. We argue that, from a social ontology point of view, diseases are problems that are identified and addressed within the framework of concrete social institutions and practices (those that shape medicine). This approach allows us to overcome the classical distinction between naturalist and normativist approaches in the philosophy of medicine, taking into account both the material and the symbolic factors that shape the categories and determine the practices of medicine.
Dualities for modal N4-lattices
(Oxford University Press, 2014-08) Jansana, Ramon; Rivieccio, Umberto
We introduce a new Priestley-style topological duality for N4-lattices, which are the algebraic counterpart of paraconsistent Nelson logic. Our duality differs from the existing one, due to S. Odintsov, in that we only rely on Esakia duality for Heyting algebras and not on the duality for De Morgan algebras of Cornish and Fowler. A major advantage of our approach is that we obtain a simple description for our topological structures, which allows us to extend the duality to other algebraic structures such as N4-lattices with monotonic modal operators, and also to provide a neighbourhood semantics for the non-normal modal logic corresponding to these algebras.
Four-valued modal logic: Kripke semantics and duality
(IEEE Xplore, 2017-02) Rivieccio, Umberto; Jung, Achim; Jansana, Ramon
We introduce a family of modal expansions of Belnap–Dunn four-valued logic and related systems, and interpret them in many-valued Kripke structures. Using algebraic logic techniques and topological duality for modal algebras, and generalizing the so-called twist-structure representation, we axiomatize by means of Hilbert-style calculi the least modal logic over the four-element Belnap lattice and some of its axiomatic extensions. We study the algebraic models of these systems, relating them to the algebraic semantics of classical multi-modal logic. This link allows us to prove that both local and global consequence of the least four-valued modal logic enjoy the finite model property and are therefore decidable.
Implicative twist-structures
(Springer Alemania, 2014-09-03) Rivieccio, Umberto
The twist-structure construction is used to represent algebras related to non-classical logics (e.g., Nelson algebras, bilattices) as a special kind of power of better-known algebraic structures (distributive lattices, Heyting algebras). We study a specific type of twist-structure (called implicative twist-structure) obtained as a power of a generalized Boolean algebra, focusing on the implication-negation fragment of the usual algebraic language of twist-structures. We prove that implicative twist-structures form a variety which is semisimple, congruence-distributive, finitely generated, and has equationally definable principal congruences. We characterize the congruences of each algebra in the variety in terms of the congruences of the associated generalized Boolean algebra. We classify and axiomatize the subvarieties of implicative twist-structures. We define a corresponding logic and prove that it is algebraizable with respect to our variety.
Inner harmony as an essential facet of well-being: a multinational study during the COVID-19 pandemic
(Frontiers Media, 2021-03-26) Carreño, David F.; Eisenbeck, Nikolett; Pérez Escobar, José Antonio; García Montes, José M.; https://orcid.org/0000-0002-0688-6485; https://orcid.org/0000-0002-3728-6896
This study aimed to explore the role of two models of well-being in the prediction of psychological distress during the COVID-19 pandemic, namely PERMA and mature happiness. According to PERMA, well-being is mainly composed of five elements: positive emotions, engagement, relationships, meaning in life, and achievement. Instead, mature happiness is understood as a positive mental state characterized by inner harmony, calmness, acceptance, contentment, and satisfaction with life. Rooted in existential positive psychology, this harmony-based happiness represents the result of living in balance between positive and negative aspects of one's life. We hypothesized that mature happiness would be a more prominent protective factor during the present pandemic than the PERMA composite. A total of 12,203 participants from 30 countries responded to an online survey including the Depression Anxiety Stress Scale (DASS-21), the PERMA-Profiler, and the Mature Happiness Scale-Revised (MHS-R). Confirmatory factor analyses indicated that PERMA and mature happiness were highly correlated, but nonetheless, they represented two separate factors. After controlling for demographic factors and country-level variables, both PERMA Well-being and MHS-R were negative predictors of psychological distress. Mature happiness was a better predictor of stress, anxiety, and general distress, while PERMA showed a higher prediction of depression. Mature happiness moderated the relation between the perceived noxious effects of the pandemic and all markers of distress (depression, anxiety, stress, and total DASS-21). Instead, PERMA acted as a moderator in the case of depression and stress. These findings indicate that inner harmony, according to the mature happiness theory, is an essential facet of well-being to be taken into consideration. The results of this study can also orient policies aimed to alleviate the negative effects of the pandemic on mental health through the promotion of well-being.
Meaning-centered coping in the era of COVID-19: direct and moderating effects on depression, anxiety, and stress
(Frontiers Media, 2021-03-17) Eisenbeck, Nikolett; Carreño, David F.; Pérez Escobar, José Antonio; https://orcid.org/0000-0002-0688-6485; https://orcid.org/0000-0002-3728-6896
The COVID-19 pandemic has subjected most of the world’s population to unprecedented situations, like national lockdowns, health hazards, social isolation and economic harm. Such a scenario calls for urgent measures not only to palliate it but also, to better cope with it. According to existential positive psychology, well-being does not simply represent a lack of stress and negative emotions but highlights their importance by incorporating an adaptive relationship with them. Thus, suffering can be mitigated (and transformed into growth) by, among other factors, adopting an attitude of positive reframing, maintaining hope, existential courage, life appreciation, engagement in meaningful activities, and prosociality. The conglomerate of these elements has been recently denominated as meaning-centered coping. In this study, we evaluated the protective role of this type of coping on mental health. A sample of 12,243 participants from 30 countries across all continents completed measures of Meaning-Centered Coping Scale (MCCS), depression, stress, anxiety and stressful COVID-19 related conditions they experienced. Results indicated that meaning-centered coping was strongly associated with diminished symptoms of stress, anxiety, and depression. Moreover, it moderated various relationships between vulnerability factors and markers of psychological distress, especially in the case of depression. These findings call for attention to meaning-centered coping approaches in the context of hardship, such as the current COVID-19 health crisis. In these difficult times, decision-makers and health organizations may integrate these approaches into their guidelines.
Modal twist-structures over residuated lattices
(Oxford University Press, 2014-06) Ono, Hiroakira; Rivieccio, Umberto
We introduce a class of algebras, called twist-structures, whose members are built as special squares of an arbitrary residuated lattice. We show how our construction relates to and encompasses results obtained by several authors on the algebraic semantics of non-classical logics. We define a logic that corresponds to our twist-structures and show how to expand it with modal operators, obtaining a paraconsistent many-valued modal logic that generalizes existing work on modal expansions of both Belnap–Dunn logic and paraconsistent Nelson logic.
Purifying applied mathematics and applying pure mathematics: how a late Wittgensteinian perspective sheds light onto the dichotomy
(Springer Nature, 2021-12-23) Pérez Escobar, José Antonio; Sarikaya, Deniz; https://orcid.org/0000-0002-3728-6896; https://orcid.org/0000-0001-8951-8161
In this work we argue that there is no strong demarcation between pure and applied mathematics. We show this first by stressing non-deductive components within pure mathematics, like axiomatization and theory-building in general. We also stress the “purer” components of applied mathematics, like the theory of the models that are concerned with practical purposes. We further show that some mathematical theories can be viewed through either a pure or applied lens. These different lenses are tied to different communities, which endorse different evaluative standards for theories. We evaluate the distinction between pure and applied mathematics from a late Wittgensteinian perspective. We note that the classical exegesis of the later Wittgenstein’s philosophy of mathematics, due to Maddy, leads to a clear-cut but misguided demarcation. We then turn our attention to a more niche interpretation of Wittgenstein by Dawson, which captures aspects of the aforementioned distinction more accurately. Building on this newer, maverick interpretation of the later Wittgenstein’s philosophy of mathematics, and endorsing an extended notion of meaning as use which includes social, mundane uses, we elaborate a fuzzy, but more realistic, demarcation. This demarcation, relying on family resemblance, is based on how direct and intended technical applications are, the kind of evaluative standards featured, and the range of rhetorical purposes at stake.
Showing mathematical flies the way out of foundational bottles: the later Wittgenstein as a forerunner of Lakatos and the philosophy of mathematical practice
(De Gruyter, 2022-01-12) Pérez Escobar, José Antonio; https://orcid.org/0000-0002-3728-6896
This work explores the later Wittgenstein’s philosophy of mathematics in relation to Lakatos’ philosophy of mathematics and the philosophy of mathematical practice. I argue that, while the philosophy of mathematical practice typically identifies Lakatos as its earliest of predecessors, the later Wittgenstein already developed key ideas for this community a few decades before. However, for a variety of reasons, most of this work on philosophy of mathematics has gone relatively unnoticed. Some of these ideas and their significance as precursors for the philosophy of mathematical practice will be presented here, including a brief reconstruction of Lakatos’ considerations on Euler’s conjecture for polyhedra from the lens of late Wittgensteinian philosophy. Overall, this article aims to challenge the received view of the history of the philosophy of mathematical practice and inspire further work in this community drawing from Wittgenstein’s late philosophy.
Three Roles of Empirical Information in Philosophy: Intuitions on Mathematics do Not Come for Free
(De Gruyter, 2021-11-02) Deborah Kant; Pérez Escobar, José Antonio; Deniz Sarikaya; https://orcid.org/0000-0002-5716-0924; https://orcid.org/0000-0002-3728-6896; https://orcid.org/0000-0001-8951-8161
This work gives a new argument for ‘Empirical Philosophy of Mathematical Practice’. It analyses different modalities on how empirical information can influence philosophical endeavours. We evoke the classical dichotomy between “armchair” philosophy and empirical/experimental philosophy, and claim that the latter should in turn be subdivided in three distinct styles: Apostate speculator, Informed analyst, and Freeway explorer. This is a shift of focus from the source of the information towards its use by philosophers. We present several examples from philosophy of mind/science and ethics on one side and a case study from philosophy of mathematics on the other. We argue that empirically informed philosophy of mathematics is different from the rest in a way that encourages a Freeway explorer approach, because intuitions about mathematical objects are often unavailable for non-mathematicians (since they are sometimes hard to grasp even for mathematicians). This consideration is supported by a case study in set theory.
Visual landmarks sharpen grid cell metric and confer context specificity to neurons of the medial entorhinal cortex
(eLife Sciences Publications, 2016-06-23) Pérez Escobar, José Antonio; https://orcid.org/0000-0002-3728-6896
Neurons of the medial entorhinal cortex (MEC) provide spatial representations critical for navigation. In this network, the periodic firing fields of grid cells act as a metric element for position. The location of the grid firing fields depends on interactions between self-motion information, geometrical properties of the environment and nonmetric contextual cues. Here, we test whether visual information, including nonmetric contextual cues, also regulates the firing rate of MEC neurons. Removal of visual landmarks caused a profound impairment in grid cell periodicity. Moreover, the speed code of MEC neurons changed in darkness and the activity of border cells became less confined to environmental boundaries. Half of the MEC neurons changed their firing rate in darkness. Manipulations of nonmetric visual cues that left the boundaries of a 1D environment in place caused rate changes in grid cells. These findings reveal context specificity in the rate code of MEC neurons.

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