Woosuk Park

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.

According to Lorenzo Magnani, optimization of situatedness supersedes “other criteria like minimality, consistency, relevance, plausibility, etc.”, which are merely “special subcases of optimization”. Inspired by this thesis, I reflect upon not only his thesis itself but also his EC-model and his plan for naturalizing logic.After briefly reporting how Magnani assessed AKM-schema and GW-schema, special attention will be paid to understanding how Magnani appropriated Estrada-González’s ideas about inferential problems and abductive problems. As this prompts the crucial question as to how and why Magnani presents his EC-model without EC-schema, I shall probe it by examining the value of his thesis, his possible route to arrive at his thesis, and his eventual plan for naturalizing logic. In the hope of promoting more active interaction and collaboration among the researchers of abduction, I shall raise some small questions about his thesis and his plan.

I attempt to get further insights from Cocchiarella’s history and philosophy of logic in understanding the contrast of Aristotelian and Fregean logic. Recently Cocchiarella proposed a conceptual theory of the referential and predicable concepts used in basic speech and mental acts (Cocchiarella in Synthese 114:169–202, 1998). This theory is interesting in itself in that singular and general, complex and simple, and pronominal and nonpronominal, referential concepts are claimed to be given a uniform account. Further, as a fundamental goal of this theory is to generate logical forms that represent the cognitive structure of our speech and mental acts, as well as logical forms that represent only the truth conditions of those acts, it is an indispensable part of Cocchiarella’s conceptual realism as a formal ontology for general framework of knowledge representation. In view of the recent surge of interest in his formal ontology by cognitive scientists and AI people, at least, Cocchiarella’s theory of reference deserves careful examination. Above all, however, the utmost value of Cocchiarella’s theory of reference must be found in its challenge against what he calls “the paradigm of reducing general reference to singular reference of logically proper names” that pervades the 20th century (Cocchiarella in Synthese 114:169–202, 1998, 170). The aim of the present chapter is to provide an impressionistic sketch of Cocchiarella’s challenge.

Frege frequently complains that others are ignorant of the distinction between “falling under” and “subordination”. This criticism is not only directed against the philosophers who are under the influence of Aristotelian logic but also against the mathematicians of his time. I shall show that this distinction must be the vantage point for understanding Frege in both historical and philosophical contexts. Strangely, this distinction is not studied extensively nowadays. There are some good reasons for this. First, ironically, it is so well established as to become a triviality. Secondly, some people think that Frege’s criticism of the aggregate view of sets is outdated. Consequently, we cannot understand why this distinction was so important to Frege. In what problem situation did Frege formulate this distinction? Were there any rival theories of predication? Was this distinction an ad hoc device for Frege in order to establish other important theses? What would happen if we lack this distinction? This chapter aims at a partial answer to these questions.

Bernays has not drawn scholarly attention that he deserves. Only quite recently, the reevaluation of his philosophy, including the projects of editing, translating, and reissuing his writings, has just started. As a part of this renaissance of Bernays studies, this chapter tries to distinguish carefully between Hilbert’s and Bernays’ views regarding the axiomatic method. We shall highlight the fact that Hilbert was so proud of his own axiomatic method on textual evidence. Bernays’ estimation of the place of Hilbert’s achievements in the history of the axiomatic method will be scrutinized. Encouraged by the fact that there are big differences between the early middle Bernays and the later Bernays in this matter, we shall contrast them vividly. The most salient difference between Hilbert and Bernays will shown to be found in the problem of the uniformity of the axiomatic method. In the same vein, we will discuss the later Bernays’ criticism of Carnap, for Carnap’s project of philosophy of science in the late 1950s seems to be a continuation and an extension of Hilbert’s faith in the uniformity of the axiomatic method.

This chapter is an attempt to probe the question as to why Maddy gave up mathematical realism and moved to her own version of mathematical naturalism. According to one widespread hypothesis, Maddy’s change of mind was brought up by her criticism of Quine-Putnam indispensability argument. Though quite convincing, it is not good enough to explain why one has to give up mathematical realism. The analogy of science and mathematics will instead be shown to be the better perspective to fathom Maddy’s changing beliefs. For this purpose, we have to understand to what extent Maddy’s thought in her realist years, which was strongly influenced by Quine and Gödel, was governed by the analogy between science and mathematics. Also, we have to understand why Maddy gave up the analogy, and thereby gave up mathematical realism. Finally, some criticisms against Maddy’s abandonment of the analogy will be examined so as to hint at the reasons why I believe Maddy’s intellectual journey in mathematical ontology is rather regress than progress.

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. (See MacBride 2006b) Rather than taking sides, in this chapter, I propose to critically examine some common assumptions shared by both parties. In particular, I shall focus on their assumptions on (1) haecceity as an individual essence, (2) haecceity as a property, (3) the classification of properties, and thereby (4) 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.

In the last three decades, abduction has been extensively studied in logic, semiotics, philosophy of science, computer science, artificial intelligence, and cognitive science. The surge of interest in abduction derives largely from serious reflection on the neglect of the logic of discovery at the hands of logical positivists and Popper, culminating in their distinction between the context of discovery and the context of justification. At the same time, the desire to recover the rationality of science that has been seriously challenged by the publication of Kuhn’s The Structure of Scientific Revolutions might be another important factor. It is remarkable to notice the ubiquity of abduction well beyond the boundary of logic or philosophy.

Elsewhere I discussed analogies and disanalogies between Avicenna’s ideas on estimative faculty of animals and Peirce’s and Magnani’s views on animal abduction Park (2011). There are analogies between them (1) at the level of the problems, (2) at the level of the diagnosis, and (3) at the level of prognosis. Both Avicenna and Peirce-Magnani address their views on the problem of intuition and intelligence of animals. Also, they detect the main cause of the problem in the false dilemma usually posed by the participants of the controversy. Finally, they seek the solution in estimation and abduction in animals respectively that have both intuitive and intelligent elements. On the other hand, some of the disanalogies are also manifest.

In order to fathom Peirce’s mind, and thereby in order to do science and philosophy in Peircean way, vision seems to be a perfect point of departure. For vision allows us to rethink what true interdisciplinarity would be like in our research. In this article, I shall show the central importance of visual abduction and abductive vision in our future study of abduction as well as Peirce’s thought. As exemplified well in Magnani’s study of abduction, we have good reasons to go with and beyond Peirce. After briefly scheming Peirce’s view on perception as abduction, I shall report what has been done in recent years in the fields of visual abduction and abductive vision. The centrality of visual abduction in Magnani’s theory of manipulative abduction will be one focal point. Another will be an examination of Raftopoulos’ discussion of abduction in late vision.

This dissertation consists of a philosophico-historical study of Duns Scotus' theory of individuation. In order to do justice to the history of philosophy, it grants a fair hearing to the problem of individuation as he conceived it, his criticisms of various theories available at his time, and his own intriguing theory of haecceitas. His doctrines of the formal distinction, the real unity of the common nature, and ultimate differences are studied in some detail because his explanation of haecceitas by a triple analogy between the individual difference and the specific difference presupposed them. From a philosophical point of view, however, it is useful to study a contemporary counterpart of haecceitas in order to understand Scotus' conception better. Thus, this study attempts to show that the widespread interpretation of haecceitas as an individual essence or a coordinate quality is not supported by Scotus' major writings. Haecceitas, in fact, is somewhat similar to Bergmann's bare particular. So, a comparison of haecceitas and the bare particular is drawn in order to understand the similarities and differences between them and understand Scotus' theory better

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 (Go, Weiqi) 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 (IBE). 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.