•  22
    This paper presents three explanations of why Frege took the universal, rather than the existential, quantifier as primitive in his formalization of logic. The first two explanations provide technical reasons related to how Frege formalizes the logic of truth-functions and the logic of quantification. The third, philosophical explanation locates the reason in Frege's logicist goal of analyzing arithmetical concepts---especially the concepts of 0 and 1---in purely logical terms.
  •  1134
    [Author's note: although this paper is written in Korean, it is archived here in the hope of bringing it to the attention of a wider audience including scholars of pragmatics and of Korean linguistics.] Recently, Korean linguists and philosophers of language have engaged in discussions on the meaning and usage of the Korean determiner ‘uri’ as in such phrases as ‘uri manura [our wife]’ which might seem strange given the monogamous marital institution of Korea. The aim of this paper is to provide…Read more
  •  77
    The Problem of Fregean Equivalents
    Dialectica 73 (3): 367-394. 2019.
    It would seem that some statements like ‘There are exactly four moons of Jupiter’ and ‘The number of moons of Jupiter is four’ have the same truth-conditions and yet differ in ontological commitment. One strategy to resolve this paradoxical phenomenon is to insist that the statements have not only the same truth-conditions but also the same ontological commitments; the other strategy is to reject the presumption that they have the same truth-conditions. This paper critically examines some popula…Read more
  •  518
    Baxter and Cotnoir on Composition as Identity
    철학사상 [CHUL HAK SA SANG: Journal of Philosophical Ideas] 73 105-125. 2019.
    This paper provides a critical examination of three related attempts to defend Composition as Identity (CI), namely the thesis that if some things compose something, then they are it. First, it will be argued against Donald Baxter’s view of composition as ‘loose identity’ that by construing composition as strictly a many-many relation, the view trivializes CI, and cannot be an option for the advocate of CI who takes composition as a genuine many-one relation. Second, it is argued against Baxter’…Read more
  •  130
    Plural Identity
    Philosophy and Phenomenological Research 102 (1): 87-105. 2019.
    Plural identity—the relation of identity between some things xx and some things yy—has been standardly defined in terms of the plural relation one of (or among). This paper challenges that standard view. To that end, it will be argued, first, that the identity relation, singular or plural, can only be defined in a higher-order language, second, that the standard definition of plural identity in terms of the one of (or among) relation should be regarded instead as providing a criterion of identit…Read more
  •  100
    The adverbial theory of numbers: some clarifications
    Synthese 197 (9): 3981-4000. 2020.
    In a forthcoming paper in this journal, entitled “Bad company objection to Joongol Kim’s adverbial theory of numbers”, Namjoong Kim presents an ingenious Russell-style paradox based on an analogue of Kim’s definition of the number 1, and argues that Kim’s theory needs to provide a criterion of demarcation between acceptable and unacceptable definitions of adverbial entities. This paper addresses this ‘bad company’ objection and some other related issues concerning Kim’s adverbial theory by clari…Read more
  •  23
    A Philosophical Inquiry Into the Concept of Number
    Dissertation, University of Notre Dame. 2004.
    The dissertation is an inquiry into the ontology and epistemology of numbers. As regards the former, the Fregean conception of numbers as objects and the Russellian conception of numbers as higher-level entities are both critically examined. A conception of numbers as modes of existence , that is, ways or manners in which things exist, is introduced and defended instead. As regards the latter, the basic concepts of arithmetic are explicated in terms of pure logic alone, and all the truths of ari…Read more
  •  108
    What are numbers?
    Synthese 190 (6): 1099-1112. 2013.
    This paper argues that (cardinal) numbers are originally given to us in the context ‘Fs exist n-wise’, and accordingly, numbers are certain manners or modes of existence, by addressing two objections both of which are due to Frege. First, the so-called Caesar objection will be answered by explaining exactly what kind of manner or mode numbers are. And then what we shall call the Functionality of Cardinality objection will be answered by establishing the fact that for any numbers m and n, if ther…Read more
  •  91
    A Logical Foundation of Arithmetic
    Studia Logica 103 (1): 113-144. 2015.
    The aim of this paper is to shed new light on the logical roots of arithmetic by presenting a logical framework that takes seriously ordinary locutions like ‘at least n Fs’, ‘n more Fs than Gs’ and ‘n times as many Fs as Gs’, instead of paraphrasing them away in terms of expressions of the form ‘the number of Fs’. It will be shown that the basic concepts of arithmetic can be intuitively defined in the language of ALA, and the Dedekind–Peano axioms can be derived from those definitions by logical…Read more
  •  100
    A Strengthening of the Caesar Problem
    Erkenntnis 75 (1): 123-136. 2011.
    The neo-Fregeans have argued that definition by abstraction allows us to introduce abstract concepts such as direction and number in terms of equivalence relations such as parallelism between lines and one-one correspondence between concepts. This paper argues that definition by abstraction suffers from the fact that an equivalence relation may not be sufficient to determine a unique concept. Frege’s original verdict against definition by abstraction is thus reinstated
  •  123
    What Are Quantities?
    Australasian Journal of Philosophy 94 (4): 792-807. 2016.
    ABSTRACTThis paper presents a view of quantities as ‘adverbial’ entities of a certain kind—more specifically, determinate ways, or modes, of having length, mass, speed, and the like. In doing so, it will be argued that quantities as such should be distinguished from quantitative properties or relations, and are not universals but are particulars, although they are not objects, either. A main advantage of the adverbial view over its rivals will be found in its superior explanatory power with resp…Read more
  •  81
    Euclid Strikes Back at Frege
    Philosophical Quarterly 64 (254): 20-38. 2014.
    Frege’s argument against the ancient Greek conception of numbers as 'multitudes of units’ has been hailed as one of the most successful in his "Grundlagen". The aim of this paper is to show that despite Frege’s best efforts, the Euclidean conception remains a viable alternative to the Fregean conception of numbers by arguing that neither a dilemma argument Frege brings against the Euclidean conception nor a possible argument against it based on the truth of what is known as "Hume’s Principle" su…Read more
  •  139
    Concepts and intuitions in Kant's philosophy of geometry
    Kant Studien 97 (2): 138-162. 2006.
    This paper is an exposition and defense of Kant’s philosophy of geometry. The main thesis is that Euclidean geometry investigates the properties of geometrical objects in an inner space that is given to us a priori (pure space) and hence is a priori and synthetic. This thesis is supported by arguing that Euclidean geometry requires certain intuitive objects (Sect. 1), that these objects are a priori constructions in pure space (Sect. 2), and finally that the role of geometrical construction is t…Read more
  •  77
    Yi on 2
    Philosophia Mathematica 18 (3): 329-336. 2010.
    Byeong-Uk Yi has argued that number words like ‘two’ primarily function as numerical predicates as in ‘Socrates and Hippias are two ’, and other grammatical uses of number words can be paraphrased in terms of the predicative use. This paper critically examines Yi’s paraphrase scheme and also some other alternative schemes, and argues that the adjectival use of number words as in ‘The Scots and the Irish are two peoples’ cannot be paraphrased in terms of the predicative use.
  •  79
    The sortal resemblance problem
    Canadian Journal of Philosophy 44 (3-4): 407-424. 2014.
    Is it possible to characterize the sortal essence of Fs for a sortal concept F solely in terms of a criterion of identity C for F? That is, can the question ‘What sort of thing are Fs?’ be answered by saying that Fs are essentially those things whose identity can be assessed in terms of C? This paper presents a case study supporting a negative answer to these questions by critically examining the neo-Fregean suggestion that cardinal numbers can be fully characterized as those things whose identi…Read more
  •  131
    Frege's context principle: An interpretation
    Pacific Philosophical Quarterly 92 (2): 193-213. 2011.
    This paper presents a new interpretation of Frege's context principle on which it applies primarily to singular terms for abstract objects but not necessarily to singular terms for ordinary objects