How do we discover and justify axioms of mathematics? In view of the long history of the axiomatic method, it is rather embarrassing that we are still lacking a standard answer to this simple question. Since the axiom of choice is arguably one of the most frequently discussed famous axioms throughout the history of mathematics, Thomas Forster’s recent identification of the axiom as an inference to the best explanation provides us with a nice point of departure. I will argue that, (...) by separating sharply between abduction and IBE, we can give a convincing account of both the discovery and the justification of the axioms of mathematics. (shrink)

First of all I would like to describe inductive and abductive reasoning in the light of the agent–based framework to the aim of clarifying their fallacious character and the role of the so-called ideal systems (logical and computational). Then I will analyze some inductive and abductive types of reasoning that in the perspective of classical and informal logic are defined fallacies. I will describe how in an agent-based reasoning this kind of fallacious reasoning can in some cases be redefined and (...) considered as a good way of reasoning. Finally, I will illustrate how what I call manipulative abduction can be interpreted as a form of practical reasoning a better understanding of which can furnish a description of human beings as hybrid reasoners in so far they are users of ideal and computational agents. (shrink)

Peirce's "Neglected Argument" uses more or less standard logical vocabulary, such as "argument," "retroduction," "premise," "conclusion," and "hypothesis." There cannot be any doubt, however, that the musement process as he characterizes it must be regarded as a semiotic process—that is, one that relates a sign to an object by way of forming an interpretant. This assumption follows from the simple observation that, according to Peirce, all processes of thought are semiotically structured. What is more, Peirce quite often uses the term (...) 'argument' for a specific class of sign—namely, one that distinctly indicates1 or represents2 its conclusion. In addition, three years before his 1908... (shrink)

This book employs a new eco-cognitive model of abduction to underline the distributed and embodied nature of scientific cognition. Its main focus is on the knowledge-enhancing virtues of abduction and on the productive role of scientific models. What are the distinctive features that define the kind of knowledge produced by science? To provide an answer to this question, the book first addresses the ideas of Aristotle, who stressed the essential inferential and distributed role of external cognitive tools and epistemic mediators (...) in abductive cognition. This is analyzed in depth from both a naturalized logic and an ecology of cognition perspective. It is shown how the maximization of cognition, and of abducibility – two typical goals of science – are related to a number of fundamental aspects: the optimization of the eco-cognitive situatedness; the maximization of changeability for both the input and the output of the inferences involved; a high degree of information-sensitiveness; and the need to record the “past life” of abductive inferential practices. Lastly, the book explains how some impoverished epistemological niches – the result of a growing epistemic irresponsibility associated with the commodification and commercialization of science – are now seriously jeopardizing the flourishing development of human creative abduction. (shrink)

Theoretical and manipulative abduction conjectures and manipulations : the extra-theoretical dimension of scientific discovery. -- Non-explanatory and instrumental abduction : plausibility, implausibility, ignorance preservation. -- Semiotic brains and artificial minds : how brains make up material cognitive systems. -- Neuromultimodal abduction : pre-wired brains, embidiment, neurospaces. -- Animal abduction : from mindless organisms to srtifactual mediators. -- Abduction, affordances, and cognitive niches : sharing representations and creating chances through cognitive niche construction. -- Abduction in human and logical agents : hasty (...) generalizers, hybrid abducers, fallacies. -- Morphodynamical abduction : causation of hypotheses by attractors dynamics. (shrink)

While mechanics was developed under the idea of reciprocal action (interactions), electromagnetism, as we know it today, takes a form more akin to unilateral action. Interactions call for spatial relations, unilateral action calls for space, just one reference centre. In contrast, interactions are matters of relations that require at least two centres. The development of the relational electromagnetism encouraged by Gauss appears to stop around 1870 for reasons that are not completely clear but are certainly not solely scientific. By the (...) same time, Maxwell recognised the equivalence in formulae of his electromagnetism and the one advocated by Gauss and called for an explanation of why such theories so differently conceived have such a large part in common. In this work we reconstruct and update the relational electromagnetism up to the contributions of Lorentz guided by the non-arbitrariness principle (NAP) that requests arbitrary choices to be accompanied by groups of symmetries. We show that a-priori there must be two more symmetries in electromagnetism, one related to the breaking (in the description) of the relation source/detector and one relating all the perceptions of the same source by detectors moving with different (constant) relative velocities. We show that the idea of electromagnetic waves put forward in concept by Lorenz (1861-1863) before Maxwell (1865) and in formulae (1867) just after Maxwell, together with the ``least action principle'' proposed by Lorentz are enough to derive Maxwell's equations, the continuity equation and the Lorentz' force, and that there is a dual formulation in terms of fields of the receiver (as opposed to fields of the source). While Galilean transformations are associated with removing the arbitrariness implied in the election of a reference space, they will not explicitly appear in a formulation based upon a relational space although we occasionally mention their usefulness. In contrast, Lorentz' transformations will emerge in this formulation involving the relations between the perceived fields of different receivers. Moreover, the role of the full Poincaré-Lorentz group as a group of transformations of the perceived actions is elucidated. In summary, we answer Maxwell's philosophical question showing how the same theory in formulae can be abduced using different inferred entities. Each form of abduction implies as well an interpretation and a facilitation of the theoretical construction. This work relies heavily on logical concepts as abduction put forward by C. Peirce, needed for the construction of theories. (shrink)

Abduction was first introduced in the epistemological context of scientific discovery. It was more recently analyzed in artificial intelligence, especially with respect to diagnosis analysis or ordinary reasoning. These two fields share a common view of abduction as a general process of hypotheses formation. More precisely, abduction is conceived as a kind of reverse explanation where a hypothesis H can be abduced from events E if H is a good explanation of E. The paper surveys four known schemes for abduction (...) that can be used in both fields. Its first contribution is a taxonomy of these schemes according to a common semantic framework based on belief revision. Its second contribution is to produce, for each non-trivial scheme, a representation theorem linking its semantic framework to a set of postulates. Its third contribution is to present semantic and axiomatic arguments in favor of one of these schemes, ordered abduction, which has never been vindicated in the literature. (shrink)

In this paper we explore a generalization of traditional abduction which can simultaneously perform two different tasks: given an unprovable sequent Γ ⊢ G, find a sentence H such that Γ, H ⊢ G is provable ; given a provable sequent Γ ⊢ G, find a sentence H such that Γ ⊢ H and the proof of Γ, H ⊢ G is simpler than the proof of Γ ⊢ G . We argue that the two tasks should not be distinguished, (...) and present a general procedure for finding suitable hypotheses or lemmas. When the original sequent is provable, the abduced formula can be seen as a cut formula with respect to Gentzen's sequent calculus, so the abduction method is cut-based. Our method is based on the tableau-like system KE and we argue for its advantages over existing abduction methods based on traditional Smullyan-style Tableaux. (shrink)

This paper develops an inquiry about creativity through the philosophy of Charles S. Peirce. The author deals, first of all, with the general characteristics of the creative pheno - mena. Later, the notion of abduc tion is explai - ned, which constitutes for Peirce the engine of creativity. Th..

Diminishing awareness is a consequence of the information explosion: disciplines are becoming increasingly specialized; individuals and groups are becoming ever more insular. This paper considers how awareness can be enhanced via abductive knowledge discovery the goal of which is to produce suggestions which can span disparate islands of knowledge. Knowledge representation is motivated from a cognitive perspective. Words and concepts are represented as vectors in a high dimensional semantic space automatically derived from a text corpus. Information flow computation between vectors (...) is proposed as a means of suggesting potentially interesting implicit associations between concepts. Information flow is applied to computational scientific discovery by attempting to simulate Swanson's Raynaud-fish oil discovery in medical texts. Both automatic and semi-automatic attempts were studied and compared against suggestions computed via semantic association. Even though this work is preliminary and speculative in nature, there is some justification to believe that appropriate suggestions can be “abduced” from semantic space. (shrink)

O experimento mental como recurso filosófico não é raro ou mesmo recente – podemos pensar no gato de Schrödinger ou na alegoria platônica da caverna. Porém, é incomum que textos ancorados na Filosofia se proponham a analisar objetos ou debater propostas da literatura de ficção, e em especial, da ficção científica. Apressadamente tomada, a relação levantaria um descompasso entre a preocupação filosófica com realidade e verdade e a libertária licença poética da ficção. É como se imaginação filosófica e imaginação criativa (...) não pudessem coexistir. Advogamos justo o oposto disso. Acreditamos que esse descompasso não se sustenta para além da aparência, de uma imposição forçosamente rígida entre realidade e ficção como campos apartados. Este artigo pretende analisar a possibilidade de a ficção científica operar como ferramenta cognitiva capaz não só de simular, mas propor novas dinâmicas para o mundo presente, informando sobre o real. Aproximando o exercício de criar histórias do exercício de pensar realidades alternativas, a ficção científica abre espaço para o questionamento crítico e transformação de nossa própria realidade da vigília, deixando de ser um mero devaneio necessariamente desprovido de agência no mundo. Para tanto, faremos uso de certos aspectos da filosofia semiótica de Charles S. Peirce e de alguns ensaios de Ursula K. Le Guin acerca da ficção científica e da habilidade narrativa. Para Peirce, signos encadeiam-se ininterruptamente em semioses que participam tanto na compreensão do mundo quanto em sua intervenção. Ainda que o exercício da ficção científica possa parecer à primeira vista contraintuitivo ou antinatural, explorar mentalmente novas possibilidades pode render insights preciosos. Peirce institui e valoriza um terceiro modo de pensamento, diferente da lógica vertical da dedução e da indução: a abdução, operação do raciocínio que busca explicar fatos por meio de hipóteses. Poderíamos pensar que a ficção científica muitas vezes se vale de abduções na busca de vislumbrar uma compreensão mais profunda. Insights não simplesmente bons para examinar como seriam situações alternativas, fictícias, mas úteis na necessária tarefa de pôr-se em crítica e transformação contínua do mundo para um lugar melhor. De Ursula Le Guin, examinamos de que modo a habilidade – até onde sabemos – humana de narração fictícia pode ser uma tecnologia de transformação do que é o caso no presente real no qual convivemos. A autora faz uma analogia entre a capacidade de narrar e a cesta: ambas seriam umas das primeiras tecnologias evolutivas de nossa espécie. Cestas e bolsas, histórias e estórias, são artefatos semióticos que armazenam, transportam, reúnem, classificam, alimentam. A ficção como uma cesta e como um signo é uma proposta que alberga e põe em relação não só humanos, mas seres diversos, conectados em semioses mais ou menos próximas, mais ou menos dependentes, mais ou menos perceptíveis; mas nunca, irreais. (shrink)

Este artigo tem como objetivo rever a crítica que Peirce faz a uma definição de abdução como uma relação de probabilidade a partir das características. Parece consensual entre seus comentadores que, de fato, essa definição não se adequa ao conceito peirciano. Contudo, este artigo defende que não há uma desarmonia entre abdução e uma relação de probabilidade. Ao contrário, será defendido que, sendo a abdução composta de formação e seleção de hipóteses, essa relação de probabilidade poderia ter uma função na (...) parte de seleção de hipóteses. Para isso, será apresentada uma definição básica de abdução, seguida da proposta de relação de probabilidade entre características. As críticas a essa proposta serão apresentadas e será evidenciado que não se sustentam, abrindo, assim, a possibilidade da permanência dessa característica no conceito de abdução peirciana. (shrink)

There are various contexts in which it is not pertinent to generate and attend to all the classical consequences of a given premiss—or to trace all the premisses which classically entail a given consequence. Such contexts may involve limited resources of an agent or inferential engine, contextual relevance or irrelevance of certain consequences or premisses, modelling everyday human reasoning, the search for plausible abduced hypotheses or potential causes, etc. In this paper we propose and explicate one formal framework for a (...) whole spectrum of consequence relations, flexible enough to be tailored for choices from a variety of contexts. We do so by investigating semantic constraints on classical entailment which give rise to a family of infra-classical logics with appealing properties. More specifically, our infra-classical reasoning demands (beyond ${\alpha\models\beta}$ ) that Mod(β) does not run wild, but lies within the scope (whatever that may mean in some specific context) of Mod(α), and which can be described by a sentence ${\bullet\alpha}$ with ${\beta\models\bullet\alpha}$ . Besides being infra-classical, the resulting logic is also non-monotonic and allows for non-trivial reasoning in the presence of inconsistencies. (shrink)

This paper describes in some detail a pattern of justification which seems to be part of common sense logic and also part of the logic of scientific investigations. Calling this pattern “abduction,” the paper lays out an “abduction-prediction” model of scientific inference as an update to the traditional hypothetico-deductive model. According to this newer model, scientific theories receive their claims for acceptance and belief from the abductive arguments that support them, and the processes of scientific discovery aim to develop theories (...) with strong abductive support. It is suggested that the study of diagnosis presents a good opportunity for studying abduction under somewhat simpler and more reproducible conditions than occur in scientific discovery. A computer-based diagnostic system is described which provides a small-scale validation of the abduc-tion-prediction model by showing that a version of it can be made precise enough to be implemented and to perform correctly for diagnosis. (shrink)

Atocha Aliseda’s Abductive Reasoning (2006) gives a structural characterization of the “forward” explana-tory reasoning from a theory to observational data. This paper asks whether there are any interesting structural rules for the “backward” abductive reasoning from observations to explanatory theories. Ignoring statistical cases, a partial explication of abduction is converse deductive explanation: h is abducible from e iff h deductively explains e. This relation of abducibility trivially satisfies Converse Entailment (if h entails e, then h is abducible from e (...) ), but it does not generally satisfy Converse Consequence (if h is abducible from e and g entails h, then g is abducible from e ), since deductive explanation is not always transitive. (shrink)

En este breve comentario, discuto dos aspectos, en mi opinión esenciales, del reciente libro de Atocha Aliseda sobre el razonamiento abductivo (Abductive Reasoning). El primero tiene que ver con la clasificación de la abducción propuesta por Aliseda respecto al tipo de lógica que le subyace. Sobre esto, considero que la mejor opción sería tal vez excluir la abducción de tal clasificación. El segundo se refiere al mecanismo de búsqueda de hipótesis abductivas que nos ofrece Aliseda (el método computacional de los (...) árboles semánti-cos extendidos). Sugiero que queda por establecerse la realidad psicológica de tal mecanismo.I discuss, in this brief commentary, two relevant aspects of Atocha Aliseda’s recent book on abductive reasoning (Abduc-tive Reasoning). The first has to do with Aliseda’s proposed classification of abduction with respect to the sort of logic under-lying it. I contend that perhaps the best option is to exclude abduction from this classification. The second aspect concerns the search mechanism for abductive hypotheses offered by Aliseda (the computational method of extended semantic tableaux). I suggest that its psychological reality has yet to be established. (shrink)

After a brief comparison of Aliseda’s account with different approaches to abductive reasoning, I relate abduction, as studied by Aliseda, to idealization, a notion which also occupies a very important role in scientific change, as well as to different ways of dealing with the growth of scientific knowledge understood as a particular kind of non-monotonic process. A particularly interesting kind of abductive reasoning could be that of finding an appropriate concretization case for a theory, originally revealed as extraordinarily success-ful but (...) later discovered to be strictly false or only approximately or ideally true. I try to show this with the example of the Kepler-Newton relation. At the end of the paper, I give criteria in order to construe abduc-tive explanations in correspondence with a reasonable account of empirical progress. (shrink)

ABSTRACT One major problem in the process of knowledge assimilation is how to deal with inconsistency of new knowledge and the existing knowledge base. In this paper we present a formal, provably correct and yet computational methodology for assimilation of new knowledge into knowledge bases about actions and changes based on the slogan: what is believed is what is explained. Technically, we employ Gelfond and Lifschitz' action description language A to describe domains of actions. The knowledge bases on domains of (...) actions are defined and obtained by a new translation from domain descriptions in A into abductive normal logic programs, where a time dimension is incorporated. The knowledge bases are shown to be both sound and complete with respect to their domain descriptions. In particular, we propose a possible causes approach (PCA) to knowledge assimilation about evolving domains of actions, in contrast to Ginsberg's possible worlds approach (PWA) and Winslett's possible models approach (PMA). A possible cause of new knowledge consists of abduced occurrences of actions and value propositions about the initial state of the domain of actions, that would allow to derive the new knowledge. We show how to compute possible causes with abductive logic programming, and present some techniques to improve search efficiency. We use examples to compare our possible causes approach with syntax-based approaches, such as Ginsberg's possible worlds approach, and semantics-based approaches, such as Winslett's possible models approach, to belief revision/update. (shrink)

The naturalization of logic aims at a revision of mainstream logic. In this article, I contend it is an urgent task to be completed. This new project will permit a new collaboration between logic and cognitive science. This can be accomplished doing for logic what many decades ago Quine and other philosophers undertook in the case of epistemology. First of all, this article analyzes how the naturalization can be achieved thanks to some insights provided by the recent John Woods’ book (...) Errors of Reasoning: Naturalizing the Logic of Inference; important concepts that regard a naturalized logic are synthetically analyzed: errors, paradigm creep, third-way reasoning, consequence-having and consequence drawing, agent based reasoning. The article also takes advantage of my own studies, which are aimed both at exculpating the negative fallacious character of abduction and at illustrating the EC-model of it, I have recently proposed. Aiming at encouraging the project of naturalization of logic, the article specifically recommends the increase of logical research on abduction, and emphasizes how current philosophical and logical research on human inferences is indebted towards Charles Sanders Peirce, a philosopher whose importance and modernity are too often underestimated. The final part of the article will introduce an analysis of the importance of the so-called optimization of situatedness, a concept that is necessary to understand that maximization of “abducibility”, which characterizes modern science. (shrink)

I will analyse three fundamental ways of governing ignorance though abduction, which are essential from an eco-cognitive and eco-logical point of view, in which the central role in human cognition of natural and artefactual environment is taken into account. First of all, according to the so-called GW-schema, proposed by Gabbay and Woods, abduction presents an ignorance-preserving or (ignorance-mitigating) character: given the fact that the abduced hypotheses aim at becoming truths, the basic ignorance is neither solved nor left untouched. Second, I (...) will contend that abduction is not always ignorance preserving but also knowledge enhancing. Indeed, according to the eco-cognitive model of abduction, I myself have recently proposed, we can easily see that, occasionally, knowledge can be immediately increased (and ignorance ‘killed’) through abduction: in this perspective, abduction does not have to be rigidly conceptualized as an inference to the best explanation in the received sense, which is as an inference that, to grant truth, also takes advantage of an empirical evaluation phase or an inductive phase, as Peirce classified it. Finally, it is important to stress that abductive cognition is at the roots of two fundamental cognitive processes. On one side, abductive cognition constructs (and/or takes advantage of the exploitation of) embodiments, external representations, enactions, artefacts and props, which involve ignorant entities suitably transformed in cognitive representations and/or devices. On the other side, abductive cognition dominates those ‘special’ cognitive creative processes that lead to what I call the disseminated ‘computational domestication of ignorant entities’: I will illustrate the example of the recent unconventional computational domestication of ignorant entities, which creates novel cognitive embodiments (morphological computation). (shrink)