The eco-cognitive model of abduction: Ἀπαγωγή now: Naturalizing the logic of abduction

Abduction (ἀπαγωγή, in ancient Greek, often translated as “leading away” or “reduction”) is a procedure in which something that lacks classical explanatory epistemic virtue can be accepted because it has virtue of another kind: Gabbay and Woods [15] contend (GW-schema) that abduction presents an ignorance-preserving or (ignorance-mitigating) character. From this perspective abductive reasoning is a response to an ignorance-problem; through abduction the basic ignorance – that does not have to be considered a total “ignorance” – is neither solved nor left intact. Abductive reasoning is an ignorance-preserving accommodation of the problem at hand. Is abduction really ignorance-preserving? To better answer this question I will introduce (and take advantage of) an eco-cognitive model (EC-Model) of abduction. It will be illustrated that through abduction, knowledge can be enhanced, even when abduction is not considered an inference to the best explanation in the classical sense of the expression, that is an inference necessarily characterized by an empirical evaluation phase, or an inductive phase, as Peirce called it. To further deepen the eco-cognitive character of abduction a simple genealogy of logic is provided: Aristotle clearly states that in syllogistic theory local/environmental cognitive factors – external to that peculiar inferential process, for example regarding users/reasoners, are given up. Indeed, to define syllogism Aristotle first of all insists that all syllogisms are valid and contends that the necessity of this kind of reasoning is related to the circumstance that “no further term from outside (ἔξωθɛν) is needed”, in sum syllogism is the fruit of a kind of eco-cognitive immunization. At the same time Aristotle presents a seminal perspective on abduction: the second part of the article considers the famous passage in Chapter B25 of Prior Analytics concerning ἀπαγωγή (“leading away”), also studied by Peirce. I contend that some of the current well-known distinctive characters of abductive cognition are already expressed, which are in tune with the EC-Model. By providing an illustration of the role of the method of analysis and of the middle terms in Plato's dialectic argumentation, considered as related to the diorismic/poristic process in ancient geometry – also, later on, emphasized by Proclus – I maintain that it is just this intellectual heritage which informs Aristotle' Chapter B25 on ἀπαγωγή. Even if, in general, Aristotle seems to sterilize, thanks to the invention of syllogistic theory, every “dialectic” background of reasoning, nevertheless in Chapter B25 he is still pointing to the fundamental inferential role in reasoning of those externalities that substantiate the process of “leading away” (ἀπαγωγή). Hence, we can gain a new positive perspective about the “constitutive” eco-cognitive character of abduction, just thanks to Aristotle himself. Finally, the paper presents an excursus on Aristotle's enthymemes from signs, disregarded by Peirce, but extremely important to stress the Aristotelian treatment of what I have called selective abduction. A forthcoming companion paper [35] will further deepen the EC-Model of abduction stressing stricter logical aspects: the first result will be that, contrarily to the classical logical view, relevance and plausibility in abductive reasoning have to be relativized and so the epistemologically embarrassing concepts of irrelevance and implausibility exculpated: they are not always offensive to reason.     

The logic of the medical research article

As do all forms of science, medical theories have a factual as well as a logical basis. New information is presented in medical research articles. These papers have three separate arguments: the argument of the hypothesis, the argument of the experimental protocol, and the argument of the hypothesis's judgment. These arguments may be examples of the hypothetico-deductive or confirmational model of scientific inference. The logical form of these arguments are informal and inductive rather than formal and deductive. Understanding the nature of the logic of the medical research article may help avoid erroneous conclusions.     

Logic and Philosophy of Logic in Wittgenstein

This essay discusses Wittgenstein's conception of logic, early and late, and some of the types of logical system that he constructed. The essay shows that the common view according to which Wittgenstein had stopped engaging in logic as a philosophical discipline by the time of writing Philosophical Investigations is mistaken. It is argued that, on the contrary, logic continued to figure at the very heart of later Wittgenstein's philosophy; and that Wittgenstein's mature philosophy of logic contains many interesting thoughts that have gone widely unnoticed.     

Lakatos's criticism of Carnapian inductive logic was mistaken

In [39], Imre Lakatos influentially argued that Carnapian inductive logic was a degenerate research programme. This paper argues that Lakatos's criticism was mistaken and that, according to Lakatos's own standards, Carnapian inductive logic was progressive rather than degenerate.     

Empiricism,judgment, and argument; Toward an informal logic of science

In an attempt to explore the role of argumentation in scientific inquiry, I explore the conception of argument that appears fruitful in the light of the recent trends in the philosophy of science, away from logical empiricism, and toward a greater emphasis on change, disagreement, and history. I begin by contrasting typical instances philosopers theories of both empiricism and apriorism, with typical instances of scientists uses of these two attitudes, suggesting that such practice shows a judiciousness lacking in epistemological theory. Then I examine at some length three important version of scientific judgement, namely Einstein's opportunism, Boltzmann's pluralism, and Huygens's eclecticism. I go on to discuss some recent work in the philosophy of science, exploring connections between the notion of judgment and Feyerabend's anarchism, Harold Brown's view of rationality, and Dudley Shapere's analysis of scientific change. All of this suggests a notion of argument in the sense of informallogic, and I examine some aspects of Galileo's work in its terms.     

The place of human values in the language of science: Kuhn,Saussure, and structuralism

The current paradigm in medicine generally distinguishes between genetic and environmental causes of disease. Although the word paradigm has become a commonplace, the theories of Thomas Kuhn have not received much attention in the journals of medicine. Kuhn's structuralist method differs radically from the daily activities of the scientific method itself. Using linguistic theory, this essay offers a structuralist reading of Thomas Kuhn's The Structure of Scientific Revolutions. Our purpose is to highlight the similarities between these structuralist models of science and language. In part, we focus on the logic that enables Kuhn to assert the priority of perception over interpretation in the history of science. To illustrate some of these issues, we refer to the distinction between environmental and genetic causes of disease. While the activity of scientific research results in the revision of concepts in science, the production of significant differences that shape our knowledge is in part a social and linguistic process.     

Logic programming,probability, and two-system accounts of reasoning: a rejoinder to Oaksford and Chater (2014)

This reply to Oaksford and Chater’s (O&C)’s critical discussion of our use of logic programming (LP) to model and predict patterns of conditional reasoning will frame the dispute in terms of the semantics of the conditional. We begin by outlining some common features of LP and probabilistic conditionals in knowledge-rich reasoning over long-term memory knowledge bases. For both, context determines causal strength; there are inferences from the absence of certain evidence; and both have analogues of the Ramsey test. Some current work shows how a combination of counting defeaters and statistics from network monitoring can provide the information for graded responses from LP reasoning. With this much introduction, we then respond to O&C’s specific criticisms and misunderstandings.     

Mathematical modal logic: A view of its evolution

This is a survey of the origins of mathematical interpretations of modal logics, and their development over the last century or so. It focuses on the interconnections between algebraic semantics using Boolean algebras with operators and relational semantics using structures often called Kripke models. It reviews the ideas of a number of people who independently contributed to the emergence of relational semantics, and compares them with the work of Kripke. It concludes with an account of several applications of modal model theory to mathematics and theoretical computer science.     

On the inseparability of reasoning and virtue: Madame de Maintenon's Maison royale de Saint-Louis

This paper engages with the curriculum at Madame de Maintenon's school for girls at Saint-Cyr to raise and address a set of questions: What is it to teach someone to reason? The curricular materials of Saint-Cyr suggest that learning to reason is a matter of practice. How is one to distinguish autonomous reason giving from habituation or automatic trained responses? How can practices in reason giving informed by social mores have objective validity? Moreover, if we think of the role of a philosopher as the cultivation of rational faculties and recognize that how this role is played is bound up with social norms, by what standards ought we to evaluate whether a philosophical educator is good or bad? Intertwined with the discussion is also a question about the limits of philosophy for the question.     

科学发展与文化逻辑--从杨振宁论中国无科学的观点说起

每一个文明都有自己存在的理由和发展的逻辑线路,不同文明可以有不同的发展程度,但不能有凌驾于其他文明之上的话语解释权.近代科学作为近代西方文明的产物,也同时是古代多种文明融合的产物.科学发展离不开自身所属的文化逻辑,但反过来具备同等文化逻辑的文明未必就一定产生科学.科学作为文化的一种形态,它没有必要成为所有文明的必经之路.我们在尊重、发展作为现代化工具的科学技术的同时,要反对用科学话语来解释工具之上的东西.     

Logic of primary-conditionals and secondary-conditionals

Firstly, the authors analyzed the properties of primary-onditionals and secondary-conditionals, establish the minimum system C2L _m of primary-conditionals and secondary-conditionals, and then prove some of the formal theorems of the system which have important intuitive meanings. Secondly, the authors constructed the neighborhood semantics, prove the soundness of C2L _m, introduce a general concept of canonical model by the neighborhood semantics, and then prove the completeness of C2L _m by the canonical model. Finally, according to the technical results of the minimum system C2L _m, the authors discuss some of the important problems concerning primary-conditionals and secondary-onditionals. __________ Translated from Luoji Yu Renzhi 逻辑与认知 (Logic and Cognition) (online journal), 2004 (3)     

Dual Intuitionistic Logic and a Variety of Negations: The Logic of Scientific Research

We consider a logic which is semantically dual (in some precise sense of the term) to intuitionistic. This logic can be labeled as “falsification logic”: it embodies the Popperian methodology of scientific discovery. Whereas intuitionistic logic deals with constructive truth and non-constructive falsity, and Nelson's logic takes both truth and falsity as constructive notions, in the falsification logic truth is essentially non-constructive as opposed to falsity that is conceived constructively. We also briefly clarify the relationships of our falsification logic to some other logical systems.     

Vladimir Alexandrovich Smirnov as a Founder of Research Schools in Logic and Methodology of Science in the USSR and Russia

The article gives a short account of V.A. Smirnovs scientific biography, including his work in Tomsk University in Siberia and in the Department of Logic of the Institute of Philosophy in Moscow.     

SLAP: Specification logic of actions with probability

A logic for specifying probabilistic transition systems is presented. Our perspective is that of agents performing actions. A procedure for deciding whether sentences in this logic are valid is provided. One of the main contributions of the paper is the formulation of the decision procedure: a tableau system which appeals to solving systems of linear equations. The tableau rules eliminate propositional connectives, then, for all open branches of the tableau tree, systems of linear equations are generated and checked for feasibility. Proofs of soundness, completeness and termination of the decision procedure are provided.     

An Operational Logic of Proofs with Positive and Negative Information

The logic of proofs was introduced by Artemov in order to analize the formalization of the concept of proof rather than the concept of provability. In this context, some operations on proofs play a very important role. In this paper, we investigate some very natural operations, paying attention not only to positive information, but also to negative information (i.e. information saying that something cannot be a proof). We give a formalization for a fragment of such a logic of proofs, and we prove that our fragment is complete and decidable.     

The Logic and Meaning of Plurals. Part II

In this sequel to “The logic and meaning of plurals. Part I”, I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization of truth for the regimented languages that results from augmenting elementary languages with refinements of basic plural constructions of natural languages, and account for the logic of plural constructions by characterizing the logic of those regimented languages.

Overcoming Instructor‐Originated Math Anxiety in Philosophy Students: A Consideration of Proven Techniques for Students Taking Formal Logic

Every university student has his or her nemesis. Biology and social science students anticipate with great apprehension their required statistics course, while many philosophy students live in fear of formal logic. Math anxiety is the common thread uniting all of them. This article argues that since formal logic is an algebra requiring similar kinds of symbol‐manipulation skills needed to succeed in a basic mathematics course, then if logic students have math anxiety, this can impede their progress. Further, it argues that math anxiety is primarily caused by and exacerbated by poor instruction. Formal logic instructors who employ effective instructional techniques for reducing it can help their students overcome math anxiety to foster learning. Methods of instruction leading to anxiety reduction and evidence supporting their efficacy are discussed, including co‐operative learning, the mastery goal approach, and self‐paced learning. None of these methods holds back more advanced students.     

The expressibility of fragments of Hybrid Graph Logic on finite digraphs

Hybrid Graph Logic is a logic designed for reasoning about graphs and is built from a basic modal logic, augmented with the use of nominals and a facility to verify the existence of paths in graphs. We study the finite model theory of Hybrid Graph Logic. In particular, we develop pebble games for Hybrid Graph Logic and use these games to exhibit strict infinite hierarchies involving fragments of Hybrid Graph Logic when the logic is used to define problems involving finite digraphs. These fragments are parameterized by the quantifier-rank of formulae along with the numbers of propositional symbols and nominals that are available. We ascertain exactly the relative definability of these parameterized fragments of the logic.