The motivation behind the collection of papers presented in this THEORIA forum on Abductive reasoning is my book Abductive Reasoning: Logical Investigations into the Processes of Discovery and Explanation. These contributions raise fundamental questions. One of them concerns the conjectural character of abduction. The choice of a logical framework for abduction is also discussed in detail, both its inferential aspect and search strategies. Abduction is also analyzed as inference to the best explanation, as well as a process of epistemic change, both of which chal-lenge the argument-like format of abduction. Finally, the psychological question of whether humans reason abduc-tively according to the models proposed is also addressed. I offer a brief summary of my book and then comment on and respond to several challenges that were posed to my work by the contributors to this issue.

Abduction is a typical theme where logic and philosophy of science meet today: occasionally, with computer science as a go-between. This is just one instance of a broader study of ‘styles of reasoning’, dating back to Bolzano and Peirce. The resulting concern with ‘logical architecture’ moves us closer to cognitive science, and the dynamics of reasoning intertwined with learning and belief revision. The crucial process of self-correction involved here is usually triggered by others, and hence a shared target of logic and philoso-phy of science should be the phenomenon of ‘intelligent interaction’ between rational agents.

In her book Abductive Reasoning Atocha Aliseda (2006) stresses the attention to the logical models of abduction, centering on the semantic tableaux as a method for extending and improving both the whole cognitive/philosophical view on it and on other more restricted logical approaches. I will provide further insight on two aspects. The first is re-lated to the importance of increasing logical knowledge on abduction: Aliseda clearly shows how the logical study on abduction in turn helps us to extend and modernize the classical and received idea of logic. The second refers to some ideas coming from the so-called distributed cognition and concerns the role of logical models as forms of cognitive exter-nalizations of preexistent in-formal human reasoning performances. The logical externalization in objective systems, communicable and sharable, is able to grant stable perspectives endowed with symbolic, abstract, and rigorous cogni-tive features. I will also emphasize that Aliseda especially stresses that this character of stability and objectivity of logical achievements are not usually present in models of abduction that are merely cognitive and epistemological, and of ex-treme importance from the computational point of view.

Abduction can be intended as a special kind of deductive consequence. In fact a general trend is to consider it as a backward deduction with some additional conditions. However, there can be more than one kind of deduction, so that any definition of abduction must take that into account. From a logical perspec-tive the problem is precisely the formalization of conditions when the deductive consequence is fixed. In this paper, we adopt Makinson’s method to define new consequence relations, hence abduction is defined as a reverse relation corresponding to each one of such relations.

In this paper, we present a goal-directed proof procedure for abductive reasoning. This procedure will be compared with Aliseda’s approach based on semantic tableaux. We begin with some comments on Aliseda’s algorithms for computing conjunctive abductions and show that they do not entirely live up to their aims. Next we give a concise account of goal-directed proofs and we show that abductive explanations are a natural spin-off of these proofs. Finally, we show that the goal-directed procedure solves the problems we encountered in Aliseda’s algorithms.

This is an examination of similarities and differences between two recent models of abductive reasoning. The one is developed in Atocha Aliseda’s Abductive Reasoning: Logical Investigations into the Processes of Discovery and Evaluation (2006). The other is advanced by Dov Gabbay and the present author in their The Reach of Abduction: Insight and Trial (2005). A principal difference between the two approaches is that in the Gabbay-Woods model, but not in the Aliseda model, abductive inference is ignorance-preserving. A further differ-ence is that Aliseda reconstructs the abduction relation in a semantic tableaux environment, whereas the Woods-Gabbay model, while less systematic, is more general. Of particular note is the connection between abduction and legal reasoning.

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.

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.

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.

Aliseda’s Abductive Reasoning is focused on the logical problem of abduction. My paper, in contrast, deals with the epistemic problems raised by this sort of inference. I analyze the relation between abduction and inference to the best explanation (IBE). Firstly a heuristic and a normative interpretation of IBE are distin-guished. The epistemic problem is particularly pressing for the latter interpretation, since it is devoid of content without specific epistemic criteria for separating acceptable explanations from those which are not. Then I discuss two different normative interpretations of IBE. I. Niiniliuoto favours a “probabilistic-confirmational” translation of explanatory merit while S. Psillos thinks that the insight of IBE is lost in a pure probabilistic format. My conclusion is that Aliseda’s theory of abduction fits better with a heuristic ac-count of IBE.

Este comentario se centra en el primer capítulo de Abductive Reasoning (2006), donde Aliseda ofrece nuevas herramien-tas conceptuales para examinar los modelos metodológicos que trazan una distinción de contextos en la investigación científica. Elucidamos la posición de Popper frente al problema del descubrimiento y distinguimos dos sentidos en que deliberadamente utiliza ‘discovery’ en su LSD (1959), distinción que permite reforzar la heterodoxa interpretación que hace Aliseda de la metodología popperiana. Por último, nos detenemos en la comparación entre Popper y Simon frente a la “lógica del descubrimiento”, ya que condensa las razones por las que Aliseda considera que la dicotomía descubrimiento-justificación está destinada al fracaso.This brief commentary focuses on the first chapter of Abductive Reasoning (2006), where Aliseda offers new conceptual tools for examining the methodological models in which a distinction between contexts of scientific research is traced. In particular, we analyze Popper’s position with respect to the problem of discovery and distinguish two different senses in which he deliberately uses the term ‘discovery’ in LSD (1959); this, in turn, lends support to Aliseda’s heterodox interpretation of the Popperian methodology. Last, we examine the comparison the author makes between Popper and Simon as it contains the primary reasons for asserting that the discovery-justification dichotomy is doomed to failure.

Assuming, with Hasok Chang, that the history and philosophy of science can contribute to scientific knowledge, particularly when it is a matter of disposing of groundless or useless notions, I examine the case of the luminiferous ether, and seek to ascertain what factors may have kept it alive until 1905, when Einstein declared it superfluous.

En este artículo, me propongo exponer algunas dificultades relacionadas con la posibilidad de que la Teoría de Modelos pueda constituirse en una Teoría General de la Interpretación. Específicamente la idea que sostengo es que lo que nos muestra la Paradoja de Orayen es que las interpretaciones no pueden ser ni conjuntos ni objetos. Por eso, una elucidación del concepto intuitivo de interpretación, que apele a este tipo de entidades, está condenada al fracaso. De manera secundaria, muestro que no hay algún supuesto conjuntista que sea imprescindible para que surja la mencionada paradoja: sólo se necesita que las interpretaciones sean objetos. Voy a argumentar que si las interpretaciones son objetos, tal como lo supone la posibilidad de cuantificar sobre las mismas para poder dar una caracterización satisfactoria de consecuencia lógica, la au-toaplicación (como un caso de aplicación de los recursos semánticos de la teoría de modelos para encontrar una interpretación con máxima generalidad) es imposible. Finalmente, discuto cada una de las dos soluciones que el propio Orayen imaginó frente a su paradoja, y muestro que cada una posee diferentes dificultades.In this paper, I intend to present some problems to construe the Model Theory as a Theory of Interpretation. Specifically, I am going to defend that, according to the Paradox of Orayen, interpretations can not be neither set nor object. Thus, an explication of the intuitive concept of interpretation that appeals to these types of entities will be condemned to failure. Secondary, I will show that there is not any like-set assumption indispensable to get rise to that paradox: only all is needed is the assumption that interpretations are objects. I am going to argue that if interpretations are objects, as it is assumed by the possibility of quantifying over interpretations in order to offer an satisfactory characterization of logical consequence, self-application (as a case of application of semantics resources of the Model Theory for finding a interpretation with absolute generality) is not possible. Eventually, I will discuss both of the solutions provided by Orayen to his paradox and I will support that both have different difficulties.

This paper is an examination and evaluation of McDowell’s criticisms of Davidson’s views on conceptual schemes and empiricism. I will argue that McDowell does not understand the real nature of Davidson’s arguments against the scheme-content dualism and that his new empiricist proposal fails to solve all the problems that old empiricism has traditionally raised. This is so because Davidson does not try to reject only a certain conception of experience by rejecting the dualism of scheme and content, but a way of thinking about meaning and knowledge that assumes a dualism that cannot be maintained.

La tesis central de este artículo es que la argumentación por analogía consiste en la transferencia de un argumento de un dominio a otro con la pretensión de que el argumento término será bueno si lo es el argumento fuente. El examen de algunos argumentos filosóficos tradicionalmente considerados analógicos lleva a distinguir dos tipos de transferencia analógica. Cuando la transferencia se justifica con un principio abductivo como a casos similares, explicaciones similares, el argumento término es más débil que el argumento fuente, pero cuando se aduce que en los dos dominios valen las mismas razones, la fuerza de los dos argu-mentos es proporcional.I contend that analogical argumentations transfer an argument from one domain to another, intending that the target argument will be good if the source argument is good. After analysis of some philosophical arguments traditionally taken to be analogical, I conclude that there are two kinds of analogical transfer. When some abductive principle like similar cases should have similar explanations is used, the target argument is weaker than the source argument; when it is claimed that the same reasons hold in both domains the strength of both arguments is proportional.

Aquí lo que me interesa es, primero, distinguir dos problemas de justificación con respecto a la inferencia inductiva: por un lado, el de una justificación persuasiva de este tipo de inferencia y, por otro lado, el de una justificación explicativa de tal inferencia. En segundo lugar, intento mostrar que el argumento de Ramsey-de Finetti a favor de las reglas inductivas de la lógica bayesiana no es capaz de proporcionar una justifi-cación persuasiva de estas reglas. Finalmente, propongo una justificación explicativa para las reglas de condicionalización bayesianas en términos de un argumento trascendental de inspiración kantiana y de estilo davidsoniano.Here, I am interested, firstly, in distinguishing two justification problems concerning inductive inference: on the one hand, the problem of a persuasive justification of induction and, on the other, the problem of an explicative justification of this sort of inference. Secondly, I intend to show that Ramsey-de Finetti’s argument in favor of Bayesian inductive rules cannot provide a persuasive justification for these rules. Finally, I propose an explicative justification for Bayesian conditionalization rules in terms of a transcendental argument of Kantian inspiration and Davidsonian style.

El corpuscularismo sirvió a los físicos del XVII para matematizar la naturaleza al considerarla un conjunto de sistemas mecánicos. Pero la discontinuidad del atomismo chocaba con la continuidad de las magnitudes básicas, espacio y el tiempo, y derivadas. En su madurez, Galileo fundió física y matemáticas propo-niendo componer tanto los cuerpos como las magnitudes continuas a base de átomos inextensos (indivisibles). En el proceso inició el análisis de las propiedades de los conjuntos infinitos, pero no logró elaborar un cálculo que le permitiese computar diferentes movimientos acelerados, mientras que en física no resolvió en problema fundamental de la condensación y la rarefacción.Seventeenth century atomism envisioned Nature as a set of mechanical systems to be treated mathematically. But the basic discontinuity of atomic theory of matter appeared inconsistent with the essential continuous character of geometrical magnitudes. In his old age Galileo devised a way to unify mathematics and physics via composing matter and continuous magnitudes out of an infinity of indivisible (atomic) units. Even though he forwarded the analysis of infinite sets, he couldn’t establish a calculus to compute and compare different accelerated motions. In physics he never solved the basic problem of condensation and rarefaction of substances. But the side results were interesting and even fascinating.

La tesis principal de este ensayo estipula que el determinismo causal es una propiedad de la naturaleza y el primer principio de la inteligibilidad natural. Se expresa, por ejemplo, en la frase de Lucrecio: “Nada surge de la nada ni va hacia la nada”. Todo lo que existe es efecto de una red de causas y es a su vez causa de otras cosas. Se sigue que la teoría científica orientada hacia la inteligibilidad —diferente de la ciencia positi-vista y pragmática— es la búsqueda de determinismo causal. El desarrollo de esta tesis utiliza como hilo conductor el pensamiento de René Thom. Esto significa que el determinismo causal se examina en su rela-ción con (I) la estabilidad y la inestabilidad, (II) el desafío de la mecánica cuántica, (III) las raíces aporéticas de la ciencia tal como la dualidad determinismo-indeterminismo, y finalmente (IV) en su relación con el método para ponerlo de manifiesto, es decir la reducción de lo posible —estrategia que es, en este dominio, una de las ideas más originales de Thom.The main thesis of this essay is that causal determinism is a property of nature and the main principle of natural intelligibility. It can be expressed in Lucretius’ words: “Nothing comes out of nothing or passes into nothing”. Everything is the effect of a web of causes and is, in its turn, cause of something else. It follows that the essence of an intelligibility-oriented scientific theory —which is different from science in a positivist or pragmatist sense— is the search for causal determinism. The development of this thesis is guided by René Thom’s thought. This means that causal determinism is analysed, first, in its relation to stability and instability; second, in its relation to the prima facie indeterminism of quantum mechanics; third, in its relation to the aporetic roots of science such as the duality determinism —indeterminism, and, finally, in its relation to the method which allows science to follow the causal determinist ideal: the reduction of the possible— a strategy which is, in this field, one of Thom’s most original ideas.