Atocha Aliseda

Logics in Scientific Discovery

In this paper I argue for a place for logic inscientific methodology, at the same level asthat of computational and historicalapproaches. While it is well known that a awhole generation of philosophers dismissedLogical Positivism (not just for the logicthough), there are at least two reasons toreconsider logical approaches in the philosophyof science. On the one hand, the presentsituation in logical research has gone farbeyond the formal developments that deductivelogic reached last century, and new researchincludes the formalization of several othertypes of reasoning, like induction andabduction. On the other hand, we call for abalanced Philosophy of Science, one inwhich both methods, the formal and thehistorical may be complementary, togetherproviding a pluralistic view of science, inwhich no method is the predominant one.

Mathematical Reasoning Vs. Abductive Reasoning: A Structural Approach

From a logical perspective, mathematical reasoning may be identified with classical, deductive inference. Two aspects are characteristic of this type of reasoning, namely its certainty and its monotonicity. The first of these is exemplified by the fact that the relationship between premises and conclusion is that of necessity; a conclusion drawn from a set of premises, necessarily follows from them. The second aspect states that conclusions reached via deductive reasoning are non-defeasible. That is, once a theorem has been proved, there is no doubt of its validity regardless of further addition of axioms and theorems to the system. There are however, several other types of formal non-classical reasoning, which albeit their lack of complete certainty and monotonicty, are nevertheless rigorous forms of reasoning with logical properties of their own. Such is the case of inductive and abductive reasoning. As a first approximation, Charles S. Peirce distinction seems useful. According to him (Peirce (1931–1935), there are three basic types of logical reasoning: deduction, induction and abduction. While deductive reasoning is for making predictions, inductive reasoning is for verifying those predictions; and abductive reasoning is for constructing hypotheses for puzzling phenomena. Concerning their certainty level, while deductive reasoning is completely certain, inductive and abductive reasoning are not. Induction must be validated empirically with tests and experiments, therefore it is defeasible; and abductive reasoning can only offer hypotheses which may be refuted with additional information. For example, a generalization reached by induction (e.g., all birds fly), remains no longer valid after the addition of a premise which refutes the conclusion (e.g., penguins are birds). As for abduction, a hypothesis (e.g., it rained last night) which explains an observation (e.g., the lawn is wet), may be refuted when additional information is incorporated into our knowledge base (e.g., it is a drought period).

A conditional logic for abduction

We propose a logic of abduction that (i) provides an appropriate formalization of the explanatory conditional, and that (ii) captures the defeasible nature of abductive inference. For (i), we argue that explanatory conditionals are non-classical, and rely on Brian Chellas’s work on conditional logics for providing an alternative formalization of the explanatory conditional. For (ii), we make use of the adaptive logics framework for modeling defeasible reasoning. We show how our proposal allows for a more natural reading of explanatory relations, and how it overcomes problems faced by other systems in the literature.

The Logic of Abduction in the Light of Peirce's Pragmatism

The notion of abduction in the work of Charles Peirce is entangled in many aspects of his philosophy and is therefore not limited to the conception of abduction as a logical inference of its own. The notions of logical inference and of validity that Peirce puts forward go beyond our present understanding of what logic is about. On the one hand, they are linked to his epistemology, a dynamic view of thought as logical inquiry, and correspond to a deep philosophical concern, that of studying the nature of synthetic reasoning. On the other hand, abduction is proposed as the underlying logic of pragmatism: ‘If you carefully consider the question of pragmatism you will see that it is nothing else than the question of the logic of abduction’ (CP 4.196). Abduction is then proposed as an epistemic notion as well as a pragmatic one. How can this be possible? For Peirce, three aspects determine whether a hypothesis is promising: it must be explanatory, testable, and economic. A hypothesis is an explanation if it accounts for the facts. Its status is that of a suggestion until it is verified, which explains the need for the testability criterion. Finally, the motivation for the economic criterion is twofold: a response to the practical problem of having innumerable explanatory hypotheses to test, as well as the need for a criterion to select the best explanation amongst the testable ones. It is the first of these aspects what accounts for the abductive logical formulation and what is related to his epistemology. In particular, our interest is on the role played by the element of surprise in this formulation; and in its connection to the epistemic transition between the states of doubt and belief. The second of these aspects is what is relevant to the connection to pragmatism, for this doctrine provides a maxim which precisely characterizes what is to count as an explanatory hypothesis based on its being subject to experimental verification. As we shall see, abduction may be viewed as an epistemic process for the acquisition of knowledge which combines

LACUNAE, EMPIRICAL PROGRESS AND SEMANTIC TABLEAUX

In this paper I address the question of the dynamics of empirical progress, both in theory evaluation and in theory improvement. I meet the challenge laid down by Theo Kuipers in Kuipers (1999), namely to operationalize the task of “instrumentalist abduction,” that is, theory revision aiming at empirical progress. I offer a reformulation of Kuipers’ account of empirical progress in the framework of (extended) semantic tableaux and show that this is indeed an appealing method by which to account for some specific kind of empirical progress, that of lacunae.

Hypotheses testing in adaptive logics: an application to medical diagnosis

In this article we introduce an adaptive logic: latar , which together with a contraction procedure retro and a way to distinguish kinds of premises (knowledge, hypotheses, observations), serves as a formal setting for hypotheses generation and testing in the empirical sciences, in our case medicine, more in particular, medical diagnosis en neurology. As any other adaptive logic, latar has a dynamic proof theory and allows for a line of a proof to be marked when it is found that it no longer observes the conditions under which it was obtained in the first place. In addition, our latar combines deductive and abductive steps in its dynamic proofs. Adaptive logics serve as a model for the contruction of diagnoses in neurology. As opposed to other abductive models, this one takes into account the fact that diagnostic hypotheses are both produced by an abductive rule and just by assertion, specially when a medical doctor aims at refuting a hypothesis.

Belief as Habit

In this paper we analyze the thesis according to which belief is a habit of conduct, one purely of thought or leading to action, basing our analysis on the notion of abduction interpreted as an epistemic process for belief revision, all of this within the frame of Charles Peirce’s Pragmatism. The notion of abduction in his work is entangled with many aspects of his philosophy. On the one hand, it is linked to his epistemology, a dynamic view of thought as logical inquiry, and corresponds to a deep philosophical concern, that of studying the nature of synthetic reasoning. On the other hand, abduction is proposed as the underlying logic of pragmatism: “If you carefully consider the question of pragmatism you will see that it is nothing else than the question of the logic of abduction.” (1903) [CP 5.196]. Two natural consequences of this analysis are the following: the interpretation of Peirce’s abductive formulation goes beyond that of a logical argument, especially when viewed as an epistemic process for belief revision and habit acquisition. Moreover, the requirement of experimental verification goes beyond hypotheses verification, for it also requires the calculation of their effects; those that produce new habits of conduct, being these theoretical or practical.

Logical, Historical and Computational Approaches

Publisher Summary This chapter focuses on the logical, historical and computational approaches to the philosophy of science. It discusses how the logical approach to philosophy of science was introduced by the Vienna Circle, and developed by them and their followers and associates. The logical approach to philosophy of science remained the dominant subject throughout the 1950s; but, from the early 1960s, it was challenged by a striking development of the historical approach. The historical approach was not introduced for the first time in the 1960s. On the contrary, it had been developed by Mach and Duhem much earlier. Although, Mach and Duhem are cited by the Vienna Circle as important influences on their philosophy, the Vienna Circle did not adopt the historical features of these two thinkers. In the excitement generated by the new logic of Frege and Russell, history of science seems to have been temporarily forgotten. The general idea of the historical approach is not new in the 1960s, however, that decade saw striking developments in this approach. After Kuhn, the analysis of scientific revolutions became a major problem for philosophy of science, while Lakatos applied the historical approach to mathematics for the first time.

The Logic of Abduction: An Introduction

In this chapter, the focus will be on formal models of hypothetical reasoning , in particular on those concerned with abductive reasoning.

Cognitive Structures in Scientific Inquiry

This book is the second of two volumes devoted to the work of Theo Kuipers, a leading Dutch philosopher of science. Philosophers and scientists from all over the world, thirty seven in all, comment on Kuipers’ philosophy, and each of their commentaries is followed by a reply from Kuipers. The present volume is devoted to Kuipers’ neo-classical philosophy of science, as laid down in his Structures in Science (Kluwer, 2001). Kuipers defends a dialectical interaction between science and philosophy in that he views philosophy of science as a meta-science which formulates cognitive structures that provide heuristic patterns for actual scientific research, including design research. In addition, Kuipers pays considerable attention to the computational approaches to philosophy of science as well as to the ethics of doing research. Thomas Nickles, David Atkinson, Jean-Paul van Bendegem, Maarten Franssen, Anne Ruth Mackor, Arno Wouters, Erik Weber & Helena de Preester, Eric Scerri, Adam Grobler & Andrzej Wisniewski, Alexander van den Bosch, Gerard Vreeswijk, Jaap Kamps, Paul Thagard, Emma Ruttkamp, Robert Causey, Henk Zandvoort comment on these ideas of Kuipers, and many present their own account. The present book also contains a synopsis of Structures in Science. It can be read independently of the first volume of Essays in Debate with Theo Kuipers, which is devoted to Kuipers’ From Instrumentalism to Constructive Realism (2000).