Ricardo Peraça Cavassane

Neste artigo, exploramos o uso de role-playing games (RPGs) no ensino de lógica, como parte da disciplina de Filosofia, no Ensino Médio, como ferramentas que propiciem a aplicação de metodologias de ensino lúdicas, interativas e inclusivas. Após discutirmos a aplicação de RPGs como ferramentas educacionais, bem como a aplicação de metodologias lúdicas no ensino de lógica, apresentamos O Legado dos Lógicos, um RPG desenvolvido para auxiliar na introdução e no ensino de lógica proposicional clássica (LPC). Neste jogo, tanto os conceitos mais básicos da LPC, tais como proposição, conectivo lógico, valor de verdade e argumento, bem como noções mais avançadas, tais como tautologia e contradição, consequência e equivalência lógica e até mesmo falácia lógica, são apresentados aos jogadores, através, respectivamente, da mecânica principal de um RPG, que permite que os jogadores assumam o controle da narrativa, e de enigmas lógicos, possibilitando aos jogadores aprender lógica por meio da sua própria aplicação.

By discussing Wittgenstein’s views on negation, inference, tautology, contradiction, consistency, and inconsistency, we analyze, in the early, middle, and late periods of his philosophical career, the status of the ex falso sequitur quodlibet, which states that from the false any formula can be demonstrated, or ex contradictione sequitur quodlibet, which states that, from a contradiction, any formula can be demonstrated. We also discuss the status of the necessarium ex quodlibet sequitur, or necessarium sequitur ad quodlibet, which states that a necessity can be demonstrated from any formula. We conclude that, while the ex falso and the necessarium ex are tautologies in the logic of the Tractatus and of his initial transitional period, they do not allow one to deduce anything from a contradiction or to deduce a necessity from anything; and, therefore, triviality is not entailed by the presence of contradictions. However, for most of his intermediary period, as well as in his late philosophy, the ex falso may or may not entail trivialization, for pragmatic reasons. Based on this, we investigate the presence of relevance and paraconsistency in Wittgenstein’s approach to logic.

The so-called “hallucinations” of chatbots based on Large Language Models, like ChatGPT, are often defined as false or nonsensical outputs. We employ formal theories of truth, specifically Tarski’s semantic theory of truth and da Costa’s theory of quasi-truth, to provide clear criteria for determining if an output by a chatbot based on an LLM can be considered true or false, quasi-true or quasi-false, or neither. By doing so, we offer a clearer characterization of the problem of hallucinations in chatbots based on LLMs, more specifically regarding the Natural Language Generation task of Generative Question Answering. We conclude that hallucinations are inherent to the current LLM architectures and that a definitive solution to this problem would require the development of significantly more advanced models, capable of establishing not only probabilistic, but also logical relations between tokens and their grounded semantic counterparts.

A despeito das mudanças que o pensamento de Wittgenstein sofre ao longo de sua obra, a filosofia é continuamente compreendida como uma atividade de elucidação da linguagem e de dissolução de confusões surgidas do mal uso da mesma. No contexto de seus escritos de juventude, nos quais a linguagem pode expressar apenas estados de coisas contingentes, proposições que pretendam expressar necessidades, tais como os juízos de valor absolutos da ética normativa, são contrassensos e, assim, cabe à filosofia (logo, também à ética) apenas elucidar a linguagem a fim de eliminar tais contrassensos. Nossa proposta é compreender o que a ética enquanto elucidação significaria no contexto dos escritos de maturidade de Wittgenstein.

In this article, we discuss the ubiquity of Big Data and machine learning in society and propose that it evinces the need of further investigation of their fundamental limitations. We extend the “too much information tends to behave like very little information” phenomenon to formal knowledge about lawlike universes and arbitrary collections of computably generated datasets. This gives rise to the simplicity bubble problem, which refers to a learning algorithm equipped with a formal theory that can be deceived by a dataset to find a locally optimal model which it deems to be the global one. In the context of lawlike (computable) universes and formal learning systems, we show that there is a ceiling above which formal knowledge cannot further decrease the probability of zemblanitous findings, should the randomly generated data made available to the formal learning system be sufficiently large in comparison to their joint complexity. Zemblanity, the opposite of serendipity, is defined by an undesirable but expected finding that reveals an underlying problem or negative consequence in a given model or theory, which is in principle predictable in case the formal theory contains sufficient information. We also argue that this is an epistemological limitation that may generate unpredictable problems in digitally intermediated societies.

Inspired by the early Wittgenstein’s concept of nonsense (meaning that which lies beyond the limits of language), we define two different, yet complementary, types of nonsense: formal nonsense and pragmatic nonsense. The simpler notion of formal nonsense is initially defined within Tarski’s semantic theory of truth; the notion of pragmatic nonsense, by its turn, is formulated within the context of the theory of pragmatic truth, also known as quasi-truth, as formalized by da Costa and his collaborators. While an expression will be considered formally nonsensical if the formal criteria required for the assignment of any truth-value (whether true, false, pragmatically true, or pragmatically false) to such sentence are not met, a (well-formed) formula will be considered pragmatically nonsensical if the pragmatic criteria (inscribed within the context of scientific practice) required for the assignment of any truth-value to such sentence are not met. Thus, in the context of the theory of pragmatic truth, any (well-formed) formula of a formal language interpreted on a simple pragmatic structure will be considered pragmatically nonsensical if the set of primary sentences of such structure is not well-built, that is, if it does not include the relevant observational data and/or theoretical results, or if it does include sentences that are inconsistent with such data.

In this paper we investigate if sentences presented as the result of the application of statistical models and artificial intelligence to large volumes of data – the so-called ‘Big Data’ – can be characterized as semantically true, or as quasi-true, or even if such sentences can only be characterized as probably quasi-false and, in a certain way, post-true; that is, if, in the context of Big Data, the representation of a data domain can be configured as a total structure, or as a partial structure provided with a set of sentences assumed to be true, or if such representation cannot be configured as a partial structure provided with a set of sentences assumed to be true.