Woosuk Park

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.

This is a collection of my papers on the history and philosophy of logic and mathematics published for the last thirty years. Virtually all the chapters tackle some particular logical, methodological, epistemological, and ontological issues that are not entirely clear in official history of modern logic. In retrospect, there were some very good reasons for me to be fascinated by the particular issues and the philosophers at the earlier stages of my research. Topically speaking, these chapters can be grouped under four parts. Part 1, which deals with Gottlob Frege, was motivated to understand what aspects of his logic were truly innovative in its revolution against the Aristotelian logic. Part 2 treats Hilbert and his associates and followers in the hope to understand the revolutionary change in the axiomatic method.

Michael Friedman’s project both historically and systematically testifies to the importance of the relativized a priori. The importance of implicit definitions clearly emerges from Schlick’s General Theory of Knowledge (Schlick 1918). The main aim of this paper is to show the relationship between both and the relativized a priori through a detailed discussion of Friedman’s work. Succeeding with this will amount to a contribution to recent scholarship showing the importance of Hilbert for Logical Empiricism.

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.

We still do not know against what historical/philosophical background and motivation Tarski’s definition of logical consequence was introduced, even if it has had such a strong influence. In view of the centrality of the notion of logical consequence in logic and philosophy of logic, it is rather shocking. There must be various intertwined reasons to blame for this uncomfortable situation. There has been remarkable progress achieved recently on the history of analytic philosophy and modern logic. In view of the recent developments of the controversies involved, however, we will have to wait years to resolve all these uneasiness. In this gloomy situation, Douglas Patterson’s recent study of Tarski’s philosophy of language and logic seems to have the potential to turn out to be a ground breaking achievement (Patterson 2012). This chapter aims at uncovering the state-of-the-art and fathoming the future directions of the research in this problem area by examining critically some unclear components of Patterson’s study.

If N. Cocchiarella’s recent discussion of Frege’s function-correlate is correct, we have reason to assimilate Frege’s ontology to the Avicennian-Scotistic tripartite ontology of individuals, universals, and common natures in themselves. Further, to the extent that Scotus’ ontology is similar to Frege’s ontology, we may have indirect evidence concerning how Bergmann would think about such an interpretation of Scotus’ haecceitas ontology. I want to show that current treatments of individuation can be seriously challenged by the possible return of the common nature. My strategy will be as follows. In Sect. 1, I shall discuss Cocchiarella’s thesis regarding Frege’s function-correlates. In Sect. 2, by using Cocchiarella’s thesis, I shall try to compare Frege’s ontology with the Avicennian-Scotistic tripartite ontology. Some of the similarities and differences between these two ontologies will become clearer in the process. In Sect. 3, I shall examine Bergmann’s interpretation of Frege’s ontology. After having drawn attention to how Bergmann criticizes Frege’s introduction of concept-correlates and value-ranges, we may understand, in Sect. 4, how Bergmann would view Frege’s and Scotus’ tripartite ontologies. Hopefully the peculiarity of Bergmann’s theory of universals and his bare particular theory of individuation will stand out clearly against the background of Frege’s and Scotus’ ontologies.

This chapter intends to examine the widespread assumption, which has been uncritically accepted, that Zermelo simply adopted Hilbert’s axiomatic method in his axiomatization of set theory. What is essential in that shared axiomatic method? And, exactly when was it established? By philosophical reflection on these questions, we are to uncover how Zermelo’s thought and Hilbert’s thought on the axiomatic method were developed interacting each other. As a consequence, we will note the possibility that Zermelo, in his early as well as late thought, had views about the axiomatic method entirely different from that of Hilbert. Such a result must have far-reaching implications to the history of set theory and the axiomatic method, thereby to the philosophy of mathematics in general.

We can witness the recent surge of interest in the controversy over the scientific status of mathematics among Jesuit Aristotelians around 1600. Following the lead of Wallace, Dear, and Mancosu, I propose to look into this controversy in more detail. For this purpose, I shall focus on Biancani’s discussion of scientiae mediae in his dissertation on the nature of mathematics. From Dear’s and Wallace’s discussions, we can gather a relatively nice overview of the debate between those who championed the scientific status of mathematics and those who denied it. But it is one thing to fathom the general motivation of the disputation, quite another to appreciate the subtleties of dialectical strategies and tactics involved in it. It is exactly at this stage when we have to face some difficulties in understanding the point of Biancani’s views on scientiae mediae. Though silent on the problem of scientiae mediae, Mancosu’s discussions of the Jesuit Aristotelians’ views on potissima demonstrations, mathematical explanations, and the problem of cause are of utmost importance in this regard, both historically and philosophically. I will carefully examine and criticize some of Mancosu’s interpretations of Piccolomini’s and Biancani’s views in order to approach more closely what was really at stake in the controversy.

In recent years there has been a surge of interest in Gödel’s ontological proof of the existence of God. In spite of all this extensive concern, it is not certain whether there is any improvement in understanding the motivations of Gödel’s ontological proof. Why was Gödel so preoccupied with completing his own ontological proof? To the best of my knowledge, no one has dealt with this basic question seriously enough to answer it. In this chapter, I propose to examine Gödel’s ideas against a somewhat larger background in order to understand his motivation for establishing the ontological proof. I shall point out that the value of Gödel’s proof is to be found in the possible role of his proof of the existence of God in his philosophy as a whole as well as in its relative merit as an ontological proof. Hopefully, my guiding question as to Gödel’s motivation will turn out to be extremely fruitful by enabling us to fathom his mind regarding God and mathematics.

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.

We can witness the recent surge of interest in the interaction between cognitive science, philosophy of science, and aesthetics on the problem of representation. This naturally leads us to rethinking the achievements of Goodman’s monumental book Languages of Art. For, there is no doubt that no one else contributed more than Goodman to throw a light on the cognitive function of art. Ironically, it could be also Goodman who has been the stumbling block for a unified theory of representation. In this paper, I shall contrast the ways how differently misrepresentation has been treated in cognitive science, aesthetics, and philosophy of science. And I shall show that it is Goodman’s unnecessary separation of resemblance and representation in art that made such a difference. As a conclusion, I will indicate some of the most promising projects toward the unified theory of representation the revolt against Goodman’s rejection of resemblance theories might promise to us.