Abduction or retroduction, as introduced by C.S. Peirce in the double sense of searching for explanatory instances and providing an explanation is a kind of complement for usual argumentation. There is, however, an inferential step from the explanandum to the abductive explanans . Whether this inferential step can be captured by logical machinery depends upon a number of assumptions, but in any case it suffers in principle from the triviality objection: any time a singular contradictory explanans occurs, the system collapses (...) and stops working. The traditional remedies for such collapsing are the expensive mechanisms of consistency maintenance, or complicated theories of non-monotonic derivation that keep the system running at a higher cost. I intend to show that the robust logics of formal inconsistency, a particular category of paraconsistent logics which permit the internalization of the concepts of consistency and inconsistency inside the object language, provide simple yet powerful techniques for automatic abduction. Moreover, the whole procedure is capable of automatization by means of the tableau proof-procedures available for such logics. Some motivating examples are discussed in detail. (shrink)

Though pictures are often used to present mathematical arguments, they are not typically thought to be an acceptable means for presenting mathematical arguments rigorously. With respect to the proofs in the Elements in particular, the received view is that Euclid's reliance on geometric diagrams undermines his efforts to develop a gap-free deductive theory. The central difficulty concerns the generality of the theory. How can inferences made from a particular diagrams license general mathematical results? After surveying the history behind the received (...) view, this essay provides a contrary analysis by introducing a formal account of Euclid's proofs, termed Eu. Eu solves the puzzle of generality surrounding Euclid's arguments. It specifies what diagrams Euclid's diagrams are, in a precise formal sense, and defines generality-preserving proof rules in terms of them. After the central principles behind the formalization are laid out, its implications with respect to the question of what does and does not constitute a genuine picture proof are explored. (shrink)

Automated Software Testing (AST) using Model Checking is in this article epistemologically analysed in order to argue in favour of a model-based reasoning paradigm in computer science. Preliminarily, it is shown how both deductive and inductive reasoning are insufficient to determine whether a given piece of software is correct with respect to specified behavioural properties. Models algorithmically checked in Model Checking to select executions to be observed in Software Testing are acknowledged as analogical models which establish isomorphic relations with the (...) target system’s data set. Analogical models developed in AST are presented as abductive models providing hypothetical explanations to observed executions. The model assumption—algorithmic check—software testing process is understood as the abduction—deduction—induction process defining the selective abduction and turned to isolate a set of model-based hypotheses concerning the target system behaviours. A manipulative abduction process is finally recognized in the practice of adapting, abstracting and refining models that do not provide successful predictions. (shrink)

This article presents a formal theory of robot perception as a form of abduction. The theory pins down the process whereby low‐level sensor data is transformed into a symbolic representation of the external world, drawing together aspects such as incompleteness, top‐down information flow, active perception, attention, and sensor fusion in a unifying framework. In addition, a number of themes are identified that are common to both the engineer concerned with developing a rigorous theory of perception, such as the one on (...) offer here, and the philosopher of mind who is exercised by questions relating to mental representation and intentionality. (shrink)

Several of the so-called “fallacies” in Aristotle are not in fact mistaken inference-types, but mistakes or breaches of rules in the questioning games which were practiced in the Academy and in the Lyceum. Hence the entire Aristotelian theory of “fallacies” ought to be studied by reference to the author's interrogative model of inquiry, based on his theory of questions and answers, rather than as a part of the theory of inference. Most of the “fallacies” mentioned by Aristotle can in fact (...) be diagnosed by means of the interrogative model, including petitio principii, multiple questions, “babbling’, etc., and so can Aristotle's alleged anticipation of the fallacy of argumentum ad hominem. The entire Aristotelian conception of inquiry is an interrogative one. Deductive conclusions caught Aristotle's attention in the form of answers that every rational interlocutor must give, assuming only his own earlier answers. Several features of Aristotle's methodology can be understood by means of the interrogative model, including the role of endoxa in it. Theoretically, there is also considerable leeway as to whether “fallacies” are conceived of as mistakes in questioning or as breaches of the rules that govern questioning games. (shrink)

This article generalizes the explanationist account of inference to the best explanation. It draws a clear distinction between IBE and abduction and presents abduction as the first step of IBE. The second step amounts to the evaluation of explanatory power, which consist in the degree of explanatory virtues that a hypothesis exhibits. Moreover, even though coherence is the most often cited explanatory virtue, on pain of circularity, it should not be treated as one of the explanatory virtues. Rather, coherence should (...) be equated with explanatory power and considered to be derivable from the other explanatory virtues: unification, explanatory depth and simplicity. (shrink)

During the first phase of Greek mathematics a proof consisted in showing or making visible the truth of a statement. This was the epagogic method. This first phase was followed by an apagogic or deductive phase. During this phase visual evidence was rejected and Greek mathematics became a deductive system. Now epagoge and apagoge, apart from being distinguished, roughly according to the modern distinction between inductive and deductive procedures, were also identified on account of the conception of generality as continuity. (...) Epistemology of mathematics today only remembers the distinction, forgetting where they agreed, in this manner not only destroying the unity of the perceptual and conceptual but also forgetting what could be gained from Aristotelian demonstrative science. (shrink)

This paper primarily deals with theconceptual prospects for generalizing the aim ofabduction from the standard one of explainingsurprising or anomalous observations to that ofempirical progress or even truth approximation. Itturns out that the main abduction task then becomesthe instrumentalist task of theory revision aiming atan empirically more successful theory, relative to theavailable data, but not necessarily compatible withthem. The rest, that is, genuine empirical progress aswell as observational, referential and theoreticaltruth approximation, is a matter of evaluation andselection, and possibly new (...) generation tasks forfurther improvement. The paper concludes with a surveyof possible points of departure, in AI and logic, forcomputational treatment of the instrumentalist taskguided by the `comparative evaluation matrix''. (shrink)

Diagrams have been rightly acknowledged to license inferences in Euclid’s geometric practice. However, if on one hand purely visual proofs are to be found nowhere in the Elements, on the other, fully fledged proofs of diagrammatically evident statements are offered, as in El. I. 20: “In any triangle the sum of two sides is greater than the third.” In this paper I will explain, taking as a starting point Kenneth Manders’ analysis of Euclidean diagram, how exact and co-exact claims enter (...) proposition I. 20. Then, I will ultimately argue that this proposition serves broader explanatory purposes, enhancing control on diagram appearance. (shrink)

There are many disputes about induction in the logic and philosophy of science. One of the problem is that we often use the term „induction“ in different meanings. This is precisely the point of Aristotle, the first thinker who analyzed induction systematically. The aim of the paper is to show that we are confronted with at least four different meanings of induction in Aristotleś writings, to analyze them and to show the role of induction in acquiring scientific knowing and the (...) consequences for the structure and characteristics of Aristotleś system of scientific knowledge. (shrink)