Woosuk Park | Korea Advanced Institute of Science and Technology (original) (raw)

Papers by Woosuk Park

Korean Journal of Logic, 2014

Philosophies, May 24, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

PAN-KOREAN PHILOSOPHY, 2009

The Review of Metaphysics, 1990

376 WOOSUK PARK haecceitas^. Haecceitas is not definable. Nor can we be acquainted with it. Then ... more 376 WOOSUK PARK 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 ...

J. Shook and S. Paavola (eds.), Abduction in Cognition and Action: Logical Reasoning, Scientific Inquiry, and Social Practice, Sapere, Springer, Heidelberg/Berlin, 2021

How do we discover and justify axioms of mathematics? In view of the long history of the axiomati... more 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 (IBE) 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.

Springer Handbook of Model-Based Science

Studies in Applied Philosophy, Epistemology and Rational Ethics, 2016

Frege frequently complains that others are ignorant of the distinction between “falling under” an... more 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...

Philosophies, 2022

Under the rubric of understanding the problem of explainability of AI in terms of abductive cogni... more 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 under- standing 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.
Keywords: abduction; AlphaGo; Baduk (Weiqi; Go); explainable AI; inference to the best explanation (IBE)

IfColog journal of logics and their applications (FLAP), 2018

In this paper, I propose to view each move in a game of Baduk (Go, Weiqi) as presenting an enthym... more In this paper, I propose to view each move in a game of Baduk (Go, Weiqi) as presenting an enthymematic argument. It is largely inspired by Paglieri and Woods, who suggested parsimony rather than charity as the driving force of enthymematic argumentation. Since their theory is not the final word in the history of enthymeme, my interpretation of Baduk as enthymematic interaction in terms of their fine distinctions may shed light not only on strategic reasoning in Baduk but also on the study of enthymeme itself.

IfColog journal of logics and their applications (FLAP), 2018

Strategic reasoning is everywhere, as it has been a focal issue in many scientific disciplines. B... more Strategic reasoning is everywhere, as it has been a focal issue in many scientific disciplines. But what is strategy? What is logic of strategy? In recent years, the dominance of game theory can be witnessed in all this. However, there are many serious problems with the concept of strategy in game theory. Not to mention the classical game theory, which aimed at the highest mathematical abstraction, it is rare to find serious attempts to capture the essence of strategic reasoning even in more recent trends in game theory, such as evolutionary or epistemic game theory. It is good news that logicians and game theorists are becoming more enthusiastic about their collaborations. Starting with the active interaction between epistemic logic and game theory, new research fields such as game logic or strategy logic have appeared. I shall argue, however, there is an unbridgeable gap between the concept of strategy in game theory and that in real games. As an antidote, I propose to analyze the concept of strategy in Baduk (Weichi, Go). For, in this ancient Asian board game, which has become famous by the recent success of AlphaGo, we can get lessons for both theoretical and practical reasoning. Admittedly, the previous discussions of strategy in Baduk literature are not thorough enough to secure a rigorous definition of strategy. However, there is one important clue: What is salient in usual approaches to strategic reasoning in Baduk is that strategy is always discussed together with tactics.

Axiomathes, 2021

Inspired by Bermudez’s notion of proto-logic, I would like to fathom what the true proto-logic co... more Inspired by Bermudez’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.

We can witness the recent surge of interest in the controversy over the scientific status of math... more 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 demonstra...

I attempt to get further insights from Cocchiarella’s history and philosophy of logic in understa... more 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, Cocchiare...

Mathematical Reviews, 1989

How do we discover and justify axioms of mathematics? In view of the long history of the axiomati... more 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 (IBE) 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.

Korean Journal of Logic, 2014

Philosophies, May 24, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

PAN-KOREAN PHILOSOPHY, 2009

The Review of Metaphysics, 1990

376 WOOSUK PARK haecceitas^. Haecceitas is not definable. Nor can we be acquainted with it. Then ... more 376 WOOSUK PARK 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 ...

J. Shook and S. Paavola (eds.), Abduction in Cognition and Action: Logical Reasoning, Scientific Inquiry, and Social Practice, Sapere, Springer, Heidelberg/Berlin, 2021

How do we discover and justify axioms of mathematics? In view of the long history of the axiomati... more 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 (IBE) 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.

Springer Handbook of Model-Based Science

Studies in Applied Philosophy, Epistemology and Rational Ethics, 2016

Frege frequently complains that others are ignorant of the distinction between “falling under” an... more 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...

Philosophies, 2022

Under the rubric of understanding the problem of explainability of AI in terms of abductive cogni... more 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 under- standing 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.
Keywords: abduction; AlphaGo; Baduk (Weiqi; Go); explainable AI; inference to the best explanation (IBE)

IfColog journal of logics and their applications (FLAP), 2018

In this paper, I propose to view each move in a game of Baduk (Go, Weiqi) as presenting an enthym... more In this paper, I propose to view each move in a game of Baduk (Go, Weiqi) as presenting an enthymematic argument. It is largely inspired by Paglieri and Woods, who suggested parsimony rather than charity as the driving force of enthymematic argumentation. Since their theory is not the final word in the history of enthymeme, my interpretation of Baduk as enthymematic interaction in terms of their fine distinctions may shed light not only on strategic reasoning in Baduk but also on the study of enthymeme itself.

IfColog journal of logics and their applications (FLAP), 2018

Strategic reasoning is everywhere, as it has been a focal issue in many scientific disciplines. B... more Strategic reasoning is everywhere, as it has been a focal issue in many scientific disciplines. But what is strategy? What is logic of strategy? In recent years, the dominance of game theory can be witnessed in all this. However, there are many serious problems with the concept of strategy in game theory. Not to mention the classical game theory, which aimed at the highest mathematical abstraction, it is rare to find serious attempts to capture the essence of strategic reasoning even in more recent trends in game theory, such as evolutionary or epistemic game theory. It is good news that logicians and game theorists are becoming more enthusiastic about their collaborations. Starting with the active interaction between epistemic logic and game theory, new research fields such as game logic or strategy logic have appeared. I shall argue, however, there is an unbridgeable gap between the concept of strategy in game theory and that in real games. As an antidote, I propose to analyze the concept of strategy in Baduk (Weichi, Go). For, in this ancient Asian board game, which has become famous by the recent success of AlphaGo, we can get lessons for both theoretical and practical reasoning. Admittedly, the previous discussions of strategy in Baduk literature are not thorough enough to secure a rigorous definition of strategy. However, there is one important clue: What is salient in usual approaches to strategic reasoning in Baduk is that strategy is always discussed together with tactics.

Axiomathes, 2021

Inspired by Bermudez’s notion of proto-logic, I would like to fathom what the true proto-logic co... more Inspired by Bermudez’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.

We can witness the recent surge of interest in the controversy over the scientific status of math... more 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 demonstra...

I attempt to get further insights from Cocchiarella’s history and philosophy of logic in understa... more 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, Cocchiare...

Mathematical Reviews, 1989

How do we discover and justify axioms of mathematics? In view of the long history of the axiomati... more 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 (IBE) 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.

Transactions of the Charles S. Peirce Society, 2021

CORCORAN-PARK ON QUINE’S PEANO A review of Quine’s “Peano as logician”. Hist. Philos. Logic 8 (19... more CORCORAN-PARK ON QUINE’S PEANO
A review of Quine’s “Peano as logician”. Hist. Philos. Logic 8 (1987), no. 1, 15–24.

Giuseppe Peano (1858–1932) is remembered mainly for having axiomatized number theory. It is only somewhat less widely known that Peano conjectured and proved that his axiom set is independent in the sense that no one of the axioms is implied by the others. Beyond these two achievements, which alone are sufficient to ensure him a permanent place in history, Peano’s work in logic is not well known. Indeed, the construction of nonstandard models for axiom sets, which is a central feature of Peano’s independence proof, and which was far from being original with Peano, is occasionally attributed to even later logicians such as Hilbert or even Löwenheim.
The author, well known to philosophers and mathematicians for his own contributions to logic, does not limit himself merely to identifying Peano’s innovations and tracing their development within the vast corpus of Peano’s logical writings. He also submits Peano’s work to critical appraisal in the light of modern logic and he traces the trajectories of Peano’s influence on subsequent developments. This rich article manifests on every page not only the importance of
Peano’s analysis of mathematical language but also the author’s mastery both of the Peano corpus and of the intricacies of modern logic. It is a rare event when a modern master undertakes an appraisal of a historic master. This article will be of interest not only to historians of logic but also to logicians who seek some understanding of their debt to the past.