Woosuk Park

The present collection of essays honours John Woods on the occasion of his eightieth birthday from contributors who wish to pay homage to this remarkable researcher whom they see not only as a scholar of prodigious energy and insight, but as a friend, colleague, collaborator, or former teacher. All of the essays touch upon topics Woods has taken a direct or indirect interest in, ranging from technical problems of mathematical logic and applications of formal methods through philosophical logic, philosophy of language, epistemology and history of ancient and modern logic. The sections themselves of the book cover relevance, paradoxes, inconsistency, fallacies, abduction, fictions, logic naturalized, law, argumentation and narratives, and many other topics: and represent the main research areas which have profited from Woods' reflections.

The status of abduction is still controversial. When dealing with abductive reasoning misinterpretations and equivocations are common. What did Peirce mean when he considered abduction both a kind of inference and a kind of instinct or when he considered perception a kind of abduction? Does abduction involve only the generation of hypotheses or their evaluation too? Are the criteria for the best explanation in abductive reasoning epistemic, or pragmatic, or both? Does abduction preserve ignorance or extend truth or both? To study some of these conundrums and to better understand the concept of visual abduction, I think that an interdisciplinary effort is needed, at the same time fecundated by a wide philosophical analysis. To this aim I will take advantage of some reflections upon Peirce’s philosophy of abduction that I consider central to highlight the complexity of the concept, too often seen in the partial perspective of limited formal and computational models. I will ponder over some seminal Peircean philosophical considerations concerning the entanglement of abduction, perception, and inference, which I consider are still important to current cognitive research. Peircean analysis helps us to better grasp how model-based, sentential, manipulative, and eco-cognitive aspects of abduction—I have introduced in my book Abductive Cognition —have to be seen as intertwined, and indispensable for building an acceptable integrated model of visual abduction. Even if speculative, Peircean philosophical results on visual abduction certainly anticipate various tenets of recent cognitive research

Under the rubric of understanding the problem of explainability of AI in terms of abductive cognition, I propose to review the lessons from AlphaGo and her more powerful successors. As AI players in Baduk have arrived at superhuman level, there seems to be no hope for understanding the secret of their breathtakingly brilliant moves. Without making AI players explainable in some ways, both human and AI players would be less-than omniscient, if not ignorant, epistemic agents. Are we bound to have less explainable AI Baduk players as they make further progress? I shall show that the resolution of this apparent paradox depends on how we understand the crucial distinction between abduction and inference to the best explanation. Some further philosophical issues arising from explainable AI will also be discussed in connection with this distinction.

How do we discover and justify axioms of mathematics? In view of the long history of the axiomatic method, it is rather embarrassing that we are still lacking a standard answer to this simple question. Since the axiom of choice is arguably one of the most frequently discussed famous axioms throughout the history of mathematics, Thomas Forster’s recent identification of the axiom as an inference to the best explanation provides us with a nice point of departure. I will argue that, by separating sharply between abduction and IBE, we can give a convincing account of both the discovery and the justification of the axioms of mathematics.

Inspired by Bermúdez’s notion of proto-logic, I would like to fathom what the true proto-logic could be like. But this will be approached only in a negative way of figuring out what it could not be. I shall argue that it could not be purely deductive by exploiting the recent researches in logic of maps. This will allow us to reorient the search for proto-logic, starting with animal abduction. I will also suggest that proto-logic won’t get off the ground without proto-geometry. These negative results will shed some lights on some further conceptual and historical issues around the language of thought hypothesis to arrive at the true proto-logic.

Historians of philosophy will spill huge amounts of ink scrutinizing the reason why abduction was highlighted so much in the first two decades of the 21st century. Not to mention the numerous scholarly articles on abduction published in logic, cognitive science, artificial intelligence, semiotics, and philosophy of science, several monographs on abduction appeared during this period: Magnani, Walton, Gabbay and Woods, Aliseda, to name a few. It looks as if they were responding to Hintikka’s influential paper “What Is Abduction? The Fundamental Problem of Contemporary Epistemology” published in this journal at the end of the last century.In order to appreciate...

To date there seems to be no disciplined way of distinguishing between ad hoc hypotheses and legitimate auxiliary hypotheses. This is embarrassing not just for Popperian falsificationist scientific methodology, for the need for such a distinction seems an important part of scientific practice. Do scientists bother about ad hoc hypotheses at all? Did any towering figure in the history of science care about ad hoc hypotheses? Ironically, the answers to these questions seem to be “Yes” and “No” in both cases. Inspired by Paglieri and Woods’ recent proposal for a theory of enthymeme based on the principle of parsimony, I propose to approach the problem of ad hoc hypothesis by interpreting it as a kind of enthymeme resolution. One reason for this interpretative strategy lies in its potential for understanding the pervasiveness and the longevity of the Aristotelian scientific methodology embedded in the scientific practice throughout the ages.

The problem I tackle in this article is: Do we have in Scotus a modal logic or a counterpart theory? We need to take a rather roundabout path to handle this problem. This is because, whether it be in Lewis's original formulation or in others' applications, the crucial concept of 'counterpart' has never been clearly explicated. In section two, I shall therefore examine the recent controversy concerning Leibniz's views on modalities which centers around the counterpart relation. By fully exploiting the lessons learned from such an examination, I shall then launch a trilemma against a Leibnizian in section three. Section four shall make the claim that unlike Leibniz's case, Scotus's position is not endangered by the trilemma. One important premise will be adopted from my thesis presented elsewhere regarding the different between Scotus's haecceitas and Leibniz's individual essence. Another will be secured from a brief report on Scotus's views on similarity, which might be utterly original to modern eyes jaundiced by contemporary set theories.

This book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic. It offers extensive information on Gottlob Frege’s logic, discussing which aspects of his logic can be considered truly innovative in its revolution against the Aristotelian logic. It presents the work of Hilbert and his associates and followers with the aim of understanding the revolutionary change in the axiomatic method. Moreover, it offers useful tools to understand Tarski’s and Gödel’s work, explaining why the problems they discussed are still unsolved. Finally, the book reports on some of the most influential positions in contemporary philosophy of mathematics, i.e., Maddy’s mathematical naturalism and Shapiro’s mathematical structuralism. Last but not least, the book introduces Biancani’s Aristotelian philosophy of mathematics as this is considered important to understand current philosophical issue in the applications of mathematics. One of the main purposes of the book is to stimulate readers to reconsider the Aristotelian position, which disappeared almost completely from the scene in logic and mathematics in the early twentieth century.

This book offers a novel perspective on abduction. It starts by discussing the major theories of abduction, focusing on the hybrid nature of abduction as both inference and intuition. It reports on the Peircean theory of abduction and discusses the more recent Magnani concept of animal abduction, connecting them to the work of medieval philosophers. Building on Magnani's manipulative abduction, the accompanying classification of abduction, and the hybrid concept of abduction as both inference and intuition, the book examines the problem of visual perception together with the related concepts of misrepresentation and semantic information. It presents the author's views on caricature and the caricature model of science, and then extends the scope of discussion by introducing some standard issues in the philosophy of science. By discussing the concept of ad hoc hypothesis generation as enthymeme resolution, it demonstrates how ubiquitous the problem of abduction is in all the different individual scientific disciplines. This comprehensive text provides philosophers, logicians and cognitive scientists with a historical, unified and authoritative perspective on abduction.

Arthur N. Prior, in the Preface of Past, Present and Future, made clear his indebtedness to “the very lively tense-logicians of California for many discussions”. Strangely,with a notable exception of Copeland, there is no extensive discussion of these scholars in the literature on the history of tense logic. In this paper, I propose to study how Nino B. Cocchiarella, as one of the Californian tense-logicians, interacted with Prior in the late 1960s. By gathering clues from their correspondence available at Virtual Lab for Prior Studies, I will highlight some of the differences between their views on tense-logic, which might still have far-reaching philosophical implications. I will conclude with a sketchof how to study in what ways Prior and Cocchiarella influenced some other Californian tense-logicians.

This paper examines the concept of information in situation semantics. For this purpose the most fundamental principles of situation semantics are classified into three groups: principles of the more fundamental kind, principles related to regularity, and principles governing incremental information. Fodor’s well-known criticisms of situation semanticists’ concepts of information target the first group. Interestingly, situation semanticists have been anxious to articulate either the principles of the second group or the principles of the third group in order to meet these criticisms. Based on these observations, I will launch a dilemma for situation semanticists. Either they fail to handle information about individuals or they fail to present any acceptable account of the laws of nature. Millikan’s version of situation semantics, I shall argue, is not the exception to the rule.

In some sense, both ontological and epistemological problems related to individuation have been the focal issues in the philosophy of mathematics ever since Frege. However, such an interest becomes manifest in the rise of structuralism as one of the most promising positions in recent philosophy of mathematics. The most recent controversy between Keränen and Shapiro seems to be the culmination of this phenomenon. Rather than taking sides, in this paper, I propose to critically examine some common assumptions shared by both parties. In particular, I shall focus on their assumptions on haecceity as an individual essence, haecceity as a property, the classification of properties, and thereby the search for the principle of individuation in terms of properties. I shall argue that all these assumptions are mistaken and ungrounded from Scotus’ point of view. Further, I will fathom what consequences would follow, if we reject each of these assumptions.

ACCORDING TO DUNS SCOTUS, what makes a material substance an individual is a positive entity which falls within the category of substance and contracts the specific nature to this or that. That entity, called haecceitas, together with the formal distinction, constitutes the core of Scotus' theory of individuation. But what is haecceitas? Haecceitas is not definable. Nor can we be acquainted with it. Then how could we understand it? Both negatively and positively, Scotus himself tried to give an answer to this question. Before presenting his haecceitas theory, Scotus criticized six different types of rival theories available in his day: the position of the nominalists, the double negation theory, the theory of individuation by actual existence, the theory of individuation by quantity or other accidents, the theory of individuation by matter, and the theory attributed to Godfrey of Fontaines. In other words, he was explaining "what haecceitas is not" when he criticized these theories. More importantly, he tried to give us a positive characterization of haecceitas. Since he used "individual difference" as a synonym for "haecceitas," he resorted to an analogy between the specific difference and the individual difference in order to explain the notion of haecceitas. The problem is that twentieth-century ontologists may not be patient enough to study the triple analogy, which again presupposes Scotus' doctrines of the formal distinction and the ultimate difference. In order to draw their attention to Scotus' theory of individuation, one would need to discuss the following questions: How can we translate the term "haecceitas" into modern terminology? Is there any counterpart of haecceitas in contemporary ontology? For what reasons should we reintroduce haecceitas into the current discussion of individuation, if it has a good counterpart? Is there still anything significant left to add to our understanding of haecceitas?

Both the defenders and the challengers of the indispensability argument seem to ignore the obvious fact that it is meant to be an analogical inference. In this note, I shall draw attention to this fact so as to avoid unnecessary confusions in any future discussion of the indispensability argument. For this purpose, I shall criticize Maddy’s version of the indispensability argument. After having noted that Quinean holism does not have to be one of the necessary premises, I shall suggest alternative formulations of the indispensability argument as an analogical inference. Also, some further reflections on how to evaluate Maddy’s objections to the indispensability argument will be in due order.