Lakatos’s Challenge? Auxiliary Hypotheses and Non-Monotonous Inference

Summary  Gerhard Schurz [2001, Journal for General Philosophy of Science, 32, 65–107] has proposed to reconstruct auxiliary hypothesis addition, e.g., postulation of Neptune to immunize Newtonian mechanics, with concepts from non-monotonous inference to avoid the retention of false predictions that are among the consequence-set of the deductive model. However, the non-monotonous reconstruction retains the observational premise that is indeed rejected in the deductive model. Hence, his proposal fails to do justice to Lakatos’ core-belt model, therefore fails to meet what Schurz coined “Lakatos’ challenge”. It is argued that Lakatos’s distinction between core and belt of a research program is not mapable onto premise-set and consequence-set and that Schurz’s understanding of a ceteris paribus clause as a transfinite list of (absent) interfering factors is problematic. I propose a simple reading of Lakatos’s use of the term ceteris paribus clause and motivate why the term hypothesis addition, despite not being interpretable literally, came to be entrenched.

It is not that we propose a theory and Nature may shout NO; rather we propose a maze of theories and Nature may shout INCONSISTENT. Lakatos (1978, p. 45)

     

Beyond the Information Given: Causal Models in Learning and Reasoning

ABSTRACT— The philosopher David Hume's conclusion that causal induction is solely based on observed associations still presents a puzzle to psychology. If we only acquired knowledge about statistical covariations between observed events without accessing deeper information about causality, we would be unable to understand the differences between causal and spurious relations, between prediction and diagnosis, and between observational and interventional inferences. All these distinctions require a deep understanding of causality that goes beyond the information given. We report a number of recent studies that demonstrate that people and rats do not stick to the superficial level of event covariations but reason and learn on the basis of deeper causal representations. Causal-model theory provides a unified account of this remarkable competence.     

SAD as a mathematical assistant—how should we go from here to there?

The System for Automated Deduction (SAD) is developed in the framework of the Evidence Algorithm research project and is intended for automated processing of mathematical texts. The SAD system works on three levels of reasoning: (a) the level of text presentation where proofs are written in a formal natural-like language for subsequent verification; (b) the level of foreground reasoning where a particular theorem proving problem is simplified and decomposed; (c) the level of background deduction where exhaustive combinatorial inference search in classical first-order logic is applied to prove end subgoals.

We present an overview of SAD describing the ideas behind the project, the system's design, and the process of problem formalization in the fashion of SAD. We show that the choice of classical first-order logic as the background logic of SAD is not too restrictive. For example, we can handle binders like Σ or lim without resort to second order or to a full-powered set theory. We illustrate our approach with a series of examples, in particular, with the classical problem .     

Thought experiments and conceptual revision

The idea that claims about the physical world might be arrived through a priori reasoning has a long history in physics. But it is clear that empiricist notions of the nature of science, and in particular the empirical nature of physics, have held sway in this century. Yet, in the idea of thought experiments in science, we might find the survival of earlier a priori reasoning to the truth of claims about the physical world. This paper challenges the notion that science can be understood as a purely empirical endeavor and points out what reforms would be necessary for teaching the image of science to our young.     

The blaze of her splendors: Suggestions about revitalizing fallacy theory

Criticisms of fallacy theory have been lodged from many different directions. In this paper, I consider the classic criticism of incompleteness by DeMorgan, Finocchiaro's claim that fallacies probably exist only in the mind of the interpreter, McPeck's claim that fallacies are at best context-dependent and Paul's complaints about the teaching of fallacies. I seek not merely to defend fallacy theory against unfair criticisms but also to learn from the criticisms what can be done in order to make fallacy theory a viable theory of criticism. I argue that this will involve several changes: rethinking of the nature of fallacy; addressing some theoretical issues; and presenting fallacy theory in a more rigorous fashion. The paper concludes with reflections on how Quine's ontological advice about the resolution of ontological disputes might be applied to the issue of whether or not there are fallacies.     

Stimulus equivalence and transitive associations: A methodological analysis

When a number of two-stimulus relations are established through training within a set of stimuli, other two-stimulus relations often emerge in the same set without direct training. These, termed "transitive stimulus relations," have been demonstrated with a variety of visual and auditory stimuli. The phenomenon has served as a behavioral model for explaining the emergence of rudimentary comprehension and reading skills, and the development of generative syntactic repertoires. This article considers the range of relations that can arise between a given number of stimuli in a class, the number of directly established two-stimulus relations necessary for the emergence of transitive relations, the forms that training sets of stimuli can take, and the number of transitive two-stimulus relations that can be induced without direct training. The procedures needed to establish and assess transitive stimulus control, the possible interactions between the training and testing procedures, and the constrainst these interactions place upon the analysis of transitive stimulus control are also examined. The present analysis indicates that in a transitivity test, choice among such stimuli may be controlled by (1) the relation between the sample and the positive comparison stimulus (transitive stimulus control), (2) the relation between the sample and the negative comparison stimulus (S- rule control), and (3) possible discriminative properties that may inadvertently be established in the positive and negative comparison stimuli (valence control). Methods are described for distinguishing these three forms of stimulus control.     

Freedom,determinism and circular reasoning

This paper uses a short dialogue between a determinist and a free-will advocate as a basis for exploring some of the elements of circular reasoning which have for centuries kept alive one of the classical debates of philosophy, the freedom-versus-determinism debate. The chronic circularity which infests both sides of the debate arises from a procedural asymmetry in the argument, which in turn is produced by the different metaphysical commitments of the debaters.     

The computational value of debate in defeasible reasoning

Defeasible reasoning is concerned with the logics of non-deductive argument. As is described in the literature, the study of this type of reasoning is considerably more involved than the study of deductive argument, even so that, in realistic applications, there is often a lack of resources to perform an exhaustive analysis. It follows that, in a theory of defeasible reasoning, the order and direction in which arguments are developed, i.e. theprocedure, is important. The aim of this article is to show that debate is the most efficient procedure to argue in the presence of limited resources. To do so, there is first some general theory on defeasible argumentation, which is followed by an introduction to the problem of dialectical search. The problem of dialectical search is (or at least, should be) the essential issue in every theory on argumentation, and emerges at every occasion that involves adjudication on competing arguments. Starting with an example, it is explained that dialectical search can be best scheduled according to classical debating techniques, that work along well-tried methods. These methods (which include various forms of curtailment, interruption, and interpretation) have proven their value in keeping debating efforts within reasonable bounds. How they apply in a theory of formal argument, will be shown in this article.This research was made possible by SION, and is financed by NWO under contract number 612-316-019. Part of this research has been conducted at the Vrije Universiteit Amsterdam. This article contains fragments of Chapter 6 and Chapter 7 of the author's dissertation. Studies in Defeasible Argumentation (1993).     

Casuistry as methodology in clinical ethics

This essay focuses on how casuistry can become a useful technique of practical reasoning for the clinical ethicist or ethics consultant. Casuistry is defined, its relationship to rhetorical reasoning and its interpretation of cases, by employing three terms that, while they are not employed by the classical rhetoricians and casuists, conform, in a general way, to the features of their work. Those terms are (1) morphology, (2) taxonomy, (3) kinetics. The morphology of a case reveals the invariant structure of the particular case whatever its contingent features, and also the invariant forms of argument relevant to any case of the same sort: these invariant features can be called topics. Taxonomy situates the instant case in a series of similar cases, allowing the similarities and differences between an instant case and a paradigm case to dictate the moral judgment about the instant case. This judgment is based, not merely on application of an ethical theory or principle, but upon the way in which circumstances and maxims appear in the morphology of the case itself and in comparison with other cases. Kinetics is an understanding of the way in which one case imparts a kind of moral movement to other cases, that is, different and sometimes unprecedented circumstances may move certain marginal or exceptional cases to the level of paradigm cases. In conclusion, casuistry is the exercise of prudential or practical reasoning in recognition of the relationship between maxims, circumstances and topics, as well as the relationship of paradigms to analogous cases.