Cognitive Theory and Phenomenology in Arendt’s and Nussbaum’s Work on Narrative

In this essay I compare Nussbaum’s and Arendt’s approach to narrativity. The point of the comparison is to find out which approach is more adequate for practical philosophy: the approach influenced by cognitive theory (Nussbaum) or the one influenced by hermeneutic phenomenology (Arendt). I conclude that Nussbaum’s approach is flawed by methodological solipsism, which is due to her application of cognitive theory.

Rosenkranz’s Logic of Justification and Unprovability

Journal of Philosophical Logic - Rosenkranz has recently proposed a logic for propositional, non-factive, all-things-considered justification, which is based on a logic for the notion of being in a...     

Benedykt Bornstein’s Philosophy of Logic and Mathematics

The aim of this paper is to present and discuss main philosophical ideas concerning logic and mathematics of a significant but forgotten Polish philosopher Benedykt Bornstein. He received his doctoral degree with Kazimierz Twardowski but is not included into the Lvov–Warsaw School of Philosophy founded by the latter. His philosophical views were unique and quite different from the views of main representatives of Lvov–Warsaw School. We shall discuss Bornstein’s considerations on the philosophy of geometry, on the infinity, on the foundations of set theory and his polemics with Stanis?aw Le?niewski as well as his conception of a geometrization of logic, of the categorial logic and of the mathematics of quality.     

Frege’s Anti-Psychologism about Logic : the Relationship between Logic and Judgment

Philosophia - Frege is an anti-psychologist about logic who takes logic to be sharply distinguished from psychology. However, Frege also takes judgment, which seems to be a subject of psychology,...     

Carroll’s Regress and the Epistemology of Logic

On an internalist account of logical inference, we are warranted in drawing conclusions from accepted premises on the basis of our knowledge of logical laws. Lewis Carroll’s regress challenges internalism by purporting to show that this kind of warrant cannot ground the move from premises to conclusion. Carroll’s regress vindicates a repudiation of internalism and leads to the espousal of a standpoint that regards our inferential practice as not being grounded on our knowledge of logical laws. Such a standpoint can take two forms. One can adopt either a broadly externalist model of inference or a sceptical stance. I will attempt, in what follows, to defend a version of internalism which is not affected by the regress. The main strategy will be to show that externalism and scepticism are not satisfying standpoints to adopt with regard to our inferential practice, and then to suggest an internalist alternative.     

On Axiomatizing Shramko-Wansing’s Logic

This work treats the problem of axiomatizing the truth and falsity consequence relations, ⊨ _t and ⊨ _f , determined via truth and falsity orderings on the trilattice SIXTEEN ₃ (Shramko and Wansing, 2005). The approach is based on a representation of SIXTEEN ₃ as a twist-structure over the two-element Boolean algebra.     

Logic’s Tower of Babel

Late in his life, Jung speculated that the natural numbers, the integers, “contain the whole of mathematics and everything yet to be discovered in this field.” This article presents the attempts by mathematicians to address this question in their terms; that is, whether arithmetic (the mathematics of the natural numbers) was complete and consistent.

Early in the twentieth century, mathematicians began to seek a formalism that could provide a solid foundation for mathematics. The first important product of this new formalism was Giuseppe Peano’s Postulates: five axioms from which the full arithmetic of the natural numbers or integers (i.e., 0, 1, 2, 3, …) can be derived. Inspired by Peano’s achievement, philosopher and mathematician Bertrand Russell began a project to show that mathematics could be reduced to logic. His overweening aim was to eventually show that all science could be reduced to logic.

Logician Kurt Gödel realized that the goal of the formalists and logicians was impossible. He produced a logically impeccable proof that no system at least as complex as arithmetic could be proved both complete and consistent within the system. In essence, he proved that the core of mathematical discovery must be intuitive: direct perception of reality, which then clothes itself in mathematical garb. This accords closely with Jung’s own insight, which was based on the idea that each number is qualitatively different from every other number. To this day, Gödel’s proof stands unchallenged.     

Hintikka’s Independence-Friendly Logic Meets Nelson’s Realizability

Inspired by Hintikka’s ideas on constructivism, we are going to ‘effectivize’ the game-theoretic semantics (abbreviated GTS) for independence-friendly first-order logic (IF-FOL), but in a somewhat different way than he did in the monograph ‘The Principles of Mathematics Revisited’. First we show that Nelson’s realizability interpretation—which extends the famous Kleene’s realizability interpretation by adding ‘strong negation’—restricted to the implication-free first-order formulas can be viewed as an effective version of GTS for FOL. Then we propose a realizability interpretation for IF-FOL, inspired by the so-called ‘trump semantics’ which was discovered by Hodges, and show that this trump realizability interpretation can be viewed as an effective version of GTS for IF-FOL. Finally we prove that the trump realizability interpretation for IF-FOL appropriately generalises Nelson’s restricted realizability interpretation for the implication-free first-order formulas.     

Robert Rosen’s Work and Complex Systems Biology

Complex Systems Biology approaches are here considered from the viewpoint of Robert Rosen’s (M,R)-systems, Relational Biology and Quantum theory, as well as from the standpoint of computer modeling. Realizability and Entailment of (M,R)-systems are two key aspects that relate the abstract, mathematical world of organizational structure introduced by Rosen to the various physicochemical structures of complex biological systems. Their importance for understanding biological function and life itself, as well as for designing new strategies for treating diseases such as cancers, is pointed out. The roles played by multiple metastable states in the “continuous uphill flow of Life” supported through internal bioenergetic processes that are coupled to essential inflows are also discussed in relation to dynamic realizations of (M,R)-systems. Furthermore, the roles played by the underlying, many-valued, quantum logics and symbolic computations for ultra-complex biological systems are also briefly discussed.     

Positive Experiences at Work and Daily Recovery: Effects on Couple’s Well-Being

The present diary study investigates, at the within-person level, how job satisfaction mediates the relationship between self-rated job performance and recovery experiences (i.e., psychological detachment from work and relaxation) during off-job time. Furthermore, we explore the effects of these two recovery experiences on couple´s well-being. Data were collected from 145 dual-earner couples (N = 290 participants; N = 1450 occasions) with a daily diary design (five consecutive working days). Multilevel analyses showed that daily job performance positively predicted psychological detachment and relaxation, and that daily job satisfaction partially mediated this relationship. In addition, we found that psychological detachment and relaxation have positive effects on own and partner´s indicators of well-being (i.e., relationship satisfaction and positive emotions). The benefits of recovery go beyond the individual and affect their partner´s level of well-being.     

Proof vs Provability: On Brouwer’s Time Problem

Is a mathematical theorem proved because provable, or provable because proved? If Brouwer’s intuitionism is accepted, we’re committed, it seems, to the latter, which is highly problematic. Or so I will argue. This and other consequences of Brouwer’s attempt to found mathematics on the intuition of a move of time have heretofore been insufficiently appreciated. Whereas the mathematical anomalies of intuitionism have received enormous attention, too little time, I’ll try to show, has been devoted to some of the temporal anomalies that Brouwer has invited us to introduce into mathematics.     

Buridan’s Secular Demarcation of Logic

Philosophia - In his Tractatus de Consequentiis, the 14th century logician John Buridan states a theorem, which reads like a refutation of Aristotelian Syllogistics. Syllogistics in its usual form,...     

Peter McHugh’s Late Work

I focus on some of Peter McHugh’s most recent papers. This is work that is not yet widely known, some of which has not even been published as yet. I try to show that while the work does not in any way contradict his life-long commitments, it still has the capacity to be not at all predictable.     

Intuitionistic Epistemic Logic,Kripke Models and Fitch’s Paradox

The present work is motivated by two questions. (1) What should an intuitionistic epistemic logic look like? (2) How should one interpret the knowledge operator in a Kripke-model for it? In what follows we outline an answer to (2) and give a model-theoretic definition of the operator K. This will shed some light also on (1), since it turns out that K, defined as we do, fulfills the properties of a necessity operator for a normal modal logic. The interest of our construction also lies in a better insight into the intuitionistic solution to Fitch’s paradox, which is discussed in the third section. In particular we examine, in the light of our definition, DeVidi and Solomon’s proposal of formulating the verification thesis as \(\phi \rightarrow \neg \neg K\phi\). We show, as our main result, that this definition excapes the paradox, though it is validated only under restrictive conditions on the models.     

Work and Women’s Well-being: Religion and Age as Moderators

Religion has been found to moderate the stress–strain relationship. This moderator role, however, may be dependent on age. The present study tested for the three-way interaction between work experience, age, and religiosity in the prediction of women’s well-being, and predicted that work experience and religiosity will combine additively in older women, while in younger women religiosity is predicted to moderate the relationship between work experience and well-being. In a sample of 389 married Malay Muslim women, results of the regression analyses showed significant three-way interactions between work experience, age, and religiosity in the prediction of well-being (measured by distress symptoms and life satisfaction). While in younger women the results were in line with the predictions made, in the older women, both additive and moderator effects of religiosity were observed, depending on the well-being measures used. These results are discussed in relation to the literature on work and family, with specific reference to women’s age, religion, as well as the issue of stress–strain specificity.     

Chateaubriand’s Realist Conception of Logic

Axiomathes - I present the realist conception of logic supported by Oswaldo Chateaubriand which integrates ontological and epistemological aspects, opposing it to mathematical and linguistic...     

Children’s Life Satisfaction: The Roles of Mothers’ Work Engagement and Recovery from Work

The present study examines whether mothers’ positive work-related experiences, work engagement and recovery from work, are indirectly linked to their children’s life satisfaction via mothers’ perceived life satisfaction and closeness with their children. Theoretically the study is based on the spillover and crossover models of work–family interface with a particular focus on positive interface, as this is a gap in the existing research. The sample consisted of 671 Finnish mother–child dyads. Survey-based data were analyzed using structural equation modeling. The results showed that mothers’ work engagement and recovery from work were positively and indirectly associated with children’s life satisfaction via mothers’ life satisfaction and closeness with their children. The findings suggest that work-to-family crossover of positive work-related experiences does indeed occur from mothers to children. Employers should pay attention to mothers’ work engagement and recovery from work, because these positive work-related experiences are likely to promote mothers’ life satisfaction and a positive mother–child relationship which, in turn, may be reflected in children’s life satisfaction. Job resources and mental detachment from work while not working are vital for work engagement and recovery from work, and should be promoted.     

Compositionality,Relevance, and Peirce’s Logic of Existential Graphs

Charles S. Peirce’s pragmatist theory of logic teaches us to take the context of utterances as an indispensable logical notion without which there is no meaning. This is not a spat against compositionality per se , since it is possible to posit extra arguments to the meaning function that composes complex meaning. However, that method would be inappropriate for a realistic notion of the meaning of assertions. To accomplish a realistic notion of meaning (as opposed e.g. to algebraic meaning), Sperber and Wilson’s Relevance Theory (RT) may be applied in the spirit of Peirce’s Pragmatic Maxim (PM): the weighing of information depends on (i) the practical consequences of accommodating the chosen piece of information introduced in communication, and (ii) what will ensue in actually using that piece in further cycles of discourse. Peirce’s unpublished papers suggest a relevance-like approach to meaning. Contextual features influenced his logic of Existential Graphs (EG). Arguments are presented pro and con the view in which EGs endorse non-compositionality of meaning.     

Giles’s Game and the Proof Theory of Łukasiewicz Logic

In the 1970s, Robin Giles introduced a game combining Lorenzen-style dialogue rules with a simple scheme for betting on the truth of atomic statements, and showed that the existence of winning strategies for the game corresponds to the validity of formulas in Łukasiewicz logic. In this paper, it is shown that ‘disjunctive strategies’ for Giles’s game, combining ordinary strategies for all instances of the game played on the same formula, may be interpreted as derivations in a corresponding proof system. In particular, such strategies mirror derivations in a hypersequent calculus developed in recent work on the proof theory of Łukasiewicz logic. Presented by Daniele Mundici