In this article I analyze the Peirce’s concepts of abduction, insight, logica utens and logica docens in order to propose, finally, a vision in which “genuine” abductions are generated only after an exercise in logica docens. These “genuine” abductions are characterized in contrast to those generated by means of logica utens.

In the first section, our anonymous author discusses sophistria as an art. Like other authors who wrote sophistria, the author first shows that sophistria is a demonstrative science, not indeed in the sense that one is taught how to make sophistical arguments, but a science in the sense that knowledge about sophistical arguments is taught through demonstrations. In the subsequent questions on this topic, he makes a number of distinctions, for example, between a new and an old division of sophistrie, (...) between sophistria utens and docens, and between scientia realis and scientia rationis, ultimately identifying the science in question as a scientia rationis. He ends this section by identifying the ways in which the four causes pertain to this science. Unfortunately, a number of lines are missing in these questions, making it impossible to identify some of the author’s arguments which lead him to some of his positions. For example, in question 5, which asks whether the division of sophistrie into an older part and a newer part is suitable, only two arguments to the opposite are given; in question 6, which asks about the distinction between utens and docens, nothing but the question has survived, while in question 7, which asks whether the new logic of sophistria is distinct from the other parts, only one opposing argument is given. (shrink)

We investigate the formal cause of diagrams, initially realizing that diagrams have no obvious form. It is argued their form is to mimic expert perspectives. This perspective provides a organizational structure that represents the relations important in understanding the worldly situation. We then shift to a study of how we are to understand an expert perspective. Using the distinction between intuitive and formal logic, logica utens versus logica docens, we identify games of habituation: games of focus and (...) distraction. The skills required for games of focus and distraction are phenomenological in regulating the way we see, i.e., how we approach and analyze different situations. This unique phenomenological skill is characteristic of diagrammatic reasoning. (shrink)

The Adoption Problem (AP) was a postponed issue for some years (Kripke, 2024; Padró, 2015; Birman, 2024). This problem highlights certain difficulties surrounding the adoption of rules of inference: If anti-exceptionalism is wrong, is it possible to adopt an alternative logic? What is the point of the revision of logic in epistemology? During 2022 Kripke, Padró and Barrio held seminars on AP. The latter two edited the first thematic section on this subject in the journal Análisis Filosófico. It contains “What (...) the Adoption Problem Does Not Show” by Camilo Fiore, subject of this critical note, in which Fiore holds two theses: 1) AP is compatible with the thesis that logica utens is revisable; 2) to assess whether an agent can revise their logic, it is best to consider a different definition of adoption, e.g. weak adoption, according to which Universal Instantiation and Modus Ponens are sometimes adoptable. It then states that (1) and (2) are independent. In this article I will criticize the independence between (1) and (2). To this end, I will point out that thesis (1) and (2) are supported by the examples of Carrie and Barry, respectively, and that the type of logical revision involved in both is the same and local. Therefore, (1) and (2) are not independent. Next, I argue that it is impossible to satisfy another kind of logical revision, e.g. global revision. Therefore, the interdependence between (1) and (2) is not due to the examples proposed. (shrink)

In medieval writers an important distinction was drawn between two applications of the term ‘logica’: there was logica utens, the practice of thinking logically about this or that subject-matter, and there was logica docens, the construction of logical theory. Of course the English word ‘logic’ and its derivative ‘logical’ have a corresponding twofold meaning, and we ignore the distinction at the risk of serious confusion. ‘Logical thought’ may mean thinking that is being commended as orderly, consistent, (...) and consequent, whatever its subject-matter; or it may mean the thinking of logicians about logic, which alas has not always exhibited these virtues. Similarly for ‘teaching logic’: there is trying to get people, by precept and example, to be orderly, consistent, and consequent in their thinking, and there is the endeavour to train logicians for the next generation. In any respectable philosophy department there will be someone teaching logic in the first sense; in my own university there are very many first-year undergraduates who do a course called Reason and Argument with this aim. But we hold that the teacher of such logica utens must himself have a sufficient skill in logica docens if he is to do his job properly; and we undertake the further task of training people in logical theory so that some of them, who have sufficient native ability and motivation, may take up the torch from their teachers. (shrink)

The abductive stage of logical investigation benefits from direct contact with objects of thought, especially material objects in aggregates. The ubiquity of collecting activity and collections of non-utilitarian material objects in ancient as well as contemporary settings, with increasingly deliberate attention to material objects as implements of thought, demonstrates these benefits. This essay focuses on the logica utens of collecting and the role of collections in detection and discovery.

This article is focused on the concept of logic in Avicenna’s Isagoge, a text which had great impact both on Arabic and Western thought. Its main section is devoted to an investigation of Avicenna’s clarification of the nature of logic, its proper subject matter as well as its place within the canon of the philosophical sciences. In this connection, special attention is given to Avicenna’s use of the concepts ‘art’ and ‘science’. Significantly, he regards logic as both a science and (...) an art, and argues that in the latter sense, logic is an instrument for the philosophical sciences. Because Avicenna’s Isagoge was read in the Latin West for several centuries, his ideas on the nature of logic played a prominent role in the debates at medieval universities and hence were a likely source of the distinction between ‘logica utens’ and ‘logica docens’. (shrink)

The second chapter spells out Buridan’s conception of logic as a practical science, teaching us, as logica docens, to heed the valid rules of reasoning embedded in our logical practice, logica utens. The chapter also deals with the particular difficulties of Buridan’s approach, considering his idea of the radical conventionality of written and spoken languages, consisting of token-symbols that owe their meaningfulness to the natural representational system of the human mind. This is the fundamental idea that naturally (...) leads to the nominalist conception of a mental language. On this conception, mental language itself is a compositional semantic system of naturally representative token-symbols, the singular mental acts of singular human minds. (shrink)

Responding to the paradox of inference and the related problems in philosophy of logic, this paper argues for the necessity of distinguishing between two different objects of justification: logica utens and logica docens. Then, equipped with Peirce’s critical common-sensist conception of logica utens and his classification of sciences, I propose a diagnosis of and a solution to the problem of justification of logic. I argue that this alternative approach successfully avoids circularity in which most attempts (...) in philosophy of logic have been inescapably trapped. I also anticipate and respond to possible objections to taking a Peircean turn in justifying logic. (shrink)

The pragmatic conception of truth, anticipated by Henry David Thoreau and developed by C.S. Peirce and subsequent pragmatists, is proposed as a useful analogy for characterising 'sustainability.' Peirce's definitions of 'truth' provides an attractive approach to sustainability because (a) it re-focuses discussions of truth and objectivity from a search for 'correspondence' to an 'external world' (the 'conform' approach) to a more forward-looking ('transform') approach; and (b) it emphasises the crucial role of an evolving, questioning community in the conduct of inquiry. (...) Any successful definition of sustainability must share these characteristics with Peircean truth. While Peirce and John Dewey never reconciled their disagreements regarding the nature and task of 'inquiry', a pragmatist resolution of their differences is offered, arguing that we need both a logic of management sciences (logica utens) and a logic of pure science (logica docens), which (perhaps among other differences) respond very differently to uncertainty. It is shown that adaptive management – can be understood as a first approximation of a logica utens for social learning in pursuit of solutions to environmental problems, and it is suggested that a pragmatist, transform approach to inquiry such as Dewey's may provide a way around the 'fact-value' gulf. (shrink)

This paper considers Peirce's striking remarks about mathematics in a little-known review of Spinoza's Ethics within the larger context of his philosophy of mathematics. It argues that, for Peirce, true mathematical reasoning is always at the vanguard of thought, and resists logical demonstration. Through diagrammatic thought and her pre-theoretical innate faculty of logica utens, the great mathematician is able to see a theorem as true long before the logical apparatus necessary to demonstrate its truth exists. For Peirce, true (...) (theoremic) mathematical thought is in some sense pre-logical, and thus, the logical demonstration of this thought in the form of mathematical proofs is in fact "merely a veil over the living thought.". (shrink)

El problema de la adopción (Padró, 2015), según el cual es imposible adoptar una lógica, sugiere la idea de que la práctica de inferir es conceptualmente prioritaria a la lógica entendida como teoría. Este problema representa un desafío para la concepción antiexcepcionalista de la lógica, que entiende a los principios lógicos como meras hipótesis o como creencias sujetas a revisión. Desde nuestra perspectiva, el principal problema de esta concepción ha sido dejar abierta la pregunta sobre la naturaleza de la práctica (...) de inferir. Sin embargo, nos parece completamente posible responder esta pregunta dentro del marco teórico antiexcepcionalista. En este trabajo desarrollamos una concepción naturalista de la práctica de inferir que viene a llenar el vacío dejado por el antiexcepcionalismo tradicional; y a su vez responde al desafío lanzado por el problema de la adopción. (shrink)

Saul Kripke proposed a skeptical challenge that Romina Padró defended and popularized by the name of the Adoption Problem. The challenge is that, given a certain definition of adoption, there are some logical principles that cannot be adopted—paradigmatic cases being Universal Instantiation and Modus Ponens. Kripke has used the Adoption Problem to argue that there is an important sense in which logic is not revisable. In this essay, I defend two independent claims. First, that the Adoption Problem does not entail (...) that logic is never revisable in the sense that Kripke addresses. Second, that, to assess whether an agent can revise their logic in the sense that Kripke addresses, it is best to consider a different definition of adoption, according to which Universal Instantiation and Modus Ponens are sometimes adoptable. (shrink)

En el presente trabajo se muestra cómo la colonialidad cultural surge, se desarrolla y se mantiene como derivación, parte y premisa de la lógica del capital. En tanto lógica cultural nacida con el capitalismo y mantenida hasta hoy, la colonialidad estuvo asociada, primero, a la acumulación originaria del capital y, después, a su reproducción ampliada. El trabajo también indaga en las relaciones entre colonialidad, por una parte, y poder, colonialismo y eurocentrismo, por otra.

Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. Despite these studies, a comprehensive survey of the topic is currently lacking, and the theory of Nelson algebras remains largely unknown to most logicians. This paper aims to fill this gap by focussing on the essential developments in the field over the past two decades. Additionally, we explore generalisations of Nelson algebras, such as N4-lattices which (...) correspond to the paraconsistent version of Nelson's logic, as well as their applications to other areas of interest to logicians, such as duality and rough set theory. A general representation theorem states that each Nelson algebra is isomorphic to a subalgebra of a rough set-based Nelson algebra induced by a quasiorder. Furthermore, a formula is a theorem of Nelson logic if and only if it is valid in every finite Nelson algebra induced by a quasiorder. (shrink)

As proposições condicionais receberam atenção teórica concentrada, embora intermitente, desde a Antiguidade. A atenção durante últimos quarenta anos tem sido intensa. Nesse artigo, apresentaremos os principais desenvolvimentos da análise lógica acerca das proposições condicionais e discutiremos como elas desempenham papel central em muitas teorias filosóficas. Na primeira parte dessas observações introdutórias, mostraremos como os antigos, principalmente as escolas megárica e estoica, envolveram-se com a questão dos condicionais e quão importante isso foi para os posteriores desenvolvimentos da análise lógica dos condicionais (...) no medievo e na Idade Moderna. Por fim, apresentaremos, já na contemporaneidade, C. I. Lewis expondo sua teoria da implicação estrita em franca oposição à doutrina da implicação que ele julgava errada. Espera-se que este trabalho sirva como a apresentação panorâmica de um campo que em lógica ainda é muito frutífero e fecundo para aprofundamentos e novas ideias. (shrink)

En este trabajo planteo la pregunta de si la lógica de Aristóteles es o no una lógica formal. Respondo que, aunque las doctrinas contenidas en el Organon inauguren, efectivamente, la lógica formal, hay también buenas razones para pensar que Aristóteles no creía que la lógica fuese una disciplina que pudiera prescindir por completo del contenido. In this paper I discuss the question of whether Aristotle’s logic is a formal logic or not. I answer that, although the doctrines contained in the (...) Organon inaugurate indeed formal logic, there are also good reasons to think that Aristotle did not believe that logic was a discipline that ought to prescind completely from content. (shrink)

Este é um conto sobre visão, pensamento e contradição, bem como sobre o papel que desempenham na primeira metade da Ciência da Lógica de Hegel. A Lógica começa com uma descida, nesse caso, uma queda do Ser ao Nada. Posteriormente, aproximadamente na metade de cada texto, há um certo paradoxo em que tudo está em jogo, a categoria da contradição. Nesse exato momento, o pensamento ao mesmo tempo falha e é renovado em um viés especulativo. Nessa seção, nos debruçamos sobre (...) algumas das interpretações influentes do uso hegeliano da contradição. Para isso, voltamo-nos a uma curiosa obra de arte, Pleiades, de James Turrell, como um exemplo estético dessa primeira queda. Progrediremos, então, através do texto com pensamento e visão como nosso duplo norteador em um passo relativamente rápido, sem desacelerar até encontrarmos a história de Hegel da contradição, onde mostro a natureza explosiva da contradição. Isso nos permitirá ver como Hegel invoca o poder da contradição para gerar a segunda metade da história da Ciência da Lógica. Eu começo com a descida do Ser ao Nada, o momento em que a escuridão emerge. (shrink)

We understand by data analysis the full set of methods which are used to point out the structural relations between certain objects and the characteristics observed in them. In the case where these characteristics admit a process of dichotomy, the relations can be expressed in terms of propositional logic.In the present paper, we endeavour to make clear the opposition between the problems of propositional logic and those of certain model utilised in data analysis: in propositional logic, we look for a (...) solution verified by a given set of propositions; as long as we are concerned with data analysis, we look for a solution in terms of propositions which include as proper parts the observed objects.Finally, we draw the main lines of two very used methods which can be relevant with the aid of computer: the factor analysis and the automatic classification (cluster analysis). (shrink)