Catalin Barboianu

Contemporary philosophical accounts of the applicability of mathematics in physical sciences and the empirical world are based on formalized relations between the mathematical structures and the physical systems they are supposed to represent within the models. Such relations were constructed both to ensure an adequate representation and to allow a justification of the validity of the mathematical models as means of scientific inference. This article puts in evidence the various circularities (logical, epistemic, and of definition) that are present in these formal constructions and discusses them as an argument for the alternative semantic and propositional-structure accounts of the applicability of mathematics.

Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of the knowledge attached to mathematical models of games of chance and the act of modeling, arguing that such knowledge holds potential in the prevention and cognitive treatment of excessive gambling, and I propose further research in this direction.

Problemele filosofie sensibile pe care le pune aplicabilitatea matematicii în ştiinţe şi viaţa de zi cu zi au conturat, pe un fond interdisciplinar, o nouă “ramură” a filosofiei ştiinţei, anume filosofia aplicabilităţii matematicii. Aplicarea cu succes a matematicii de-a lungul istoriei ştiinţei necesită reprezentare, încadrare, explicaţie, dar şi o justificare de ordin metateoretic a aplicabilităţii. Între rolurile matematicii în practica ştiinţifică, rolul constitutiv teoriilor ştiinţifice este cel a cărui analiză poate contribui esenţial la această justificare. În lucrarea de faţă, am analizat acest rol constitutiv prin prisma relaţiilor sale cu celelalte roluri importante ale matematicii (descriptiv-semantic-reprezentaţional, inferenţial-explicativ-predictiv), încercând să surprind motivaţia primară a acestui rol relativ la ideea de structură matematică şi epistemică, componente esenţiale ale ştiinţei structurale matematizate.

Lucrarea tratează unul dintre “misterele” filosofiei analitice şi ale raţionalităţii însăşi, anume aplicabilitatea matematicii în ştiinţe şi în investigarea matematică a realităţii înconjurătoare, a cărei filosofie este dezvoltată în jurul sintagmei – de acum paradigmatice – ‘eficacitatea iraţională a matematicii’, aparţinând fizicianului Eugene Wigner, problemă filosofică etichetată în literatură drept “puzzle-ul lui Wigner”. Odată intraţi în profunzimea acestei probleme, investigaţia nu trebuie limitată la căutarea unor răspunsuri explicative la întrebări precum “Ce este de fapt aplicabilitatea matematicii?”, “Cum explicăm prezenţa în natură a conceptelor matematice simple şi complexe?” sau “Cum explicăm rata de succes uriaşă a aplicaţiilor matematice, care presupun modele aproximativ false ale unei realităţi idealizate?”, ci extinsă în plan metateoretic către căutarea unei justificări teoretice a utilizării metodei matematice în practica ştiinţifică, independent de succesul acestei metode. Aceste întrebări şi probleme sunt abordate în detaliu în lucrarea de faţă. Lucrarea, care va continua cu un al doilea titlu, dedicat modelelor teoretice ale aplicabilităţii şi alternativelor structurale ale acestora, se adresează în special – dar nu exclusiv – matematicienilor, fizicienilor, filosofilor ştiinţei, filosofilor limbajului şi epistemologilor, dar şi studenţilor acestor discipline.

The classical (set-theoretic) concept of structure has become essential for every contemporary account of a scientific theory, but also for the metatheoretical accounts dealing with the adequacy of such theories and their methods. In the latter category of accounts, and in particular, the structural metamodels designed for the applicability of mathematics have struggled over the last decade to justify the use of mathematical models in sciences beyond their 'indispensability' in terms of either method or concepts/entities. In this paper, I argue that these metamodels employ structures of different natures and epistemologies, and this diversity does pose a serious problem to the intended justification.

The near-miss has been considered an important factor of reinforcement in gambling behavior, and previous research has focused more on its industry-related causes and effects and less on the gaming phenomenon itself. The near-miss has usually been associated with the games of slots and scratch cards, due to the special characteristics of these games, which include the possibility of pre-manipulation of award symbols in order to increase the frequency of these “engineered” near-misses. In this paper, we argue that starting from an elementary mathematical description of the classical (by pure chance) near-miss, generalizable to any game, and focusing equally on the epistemology of its constitutive concepts and their mathematical description, we can identify more precisely the fallacious elements of the near-miss cognitive effects and the inadequate perception and representation of the observational-intentional “I was that close.” This approach further suggests a strategy of using non-standard mathematical knowledge of an epistemological type in problem-gambling prevention and cognitive therapies.