Measurement-Theoretic Remarks on Degree ofResemblance
鈴木 聡 (Satoru SUZUKI)
駒澤大学総合教育研究部非常勤講師

The problem of particulars and universals consists in a crossroads of ontology and semantics.
When we translate a natural language into a first-order (modal) language, (though it is aproblem which formal language we should adopt in this translation), the semantic problem
as to which entity we should choose as the semantic value of a symbol in the model of firstorder modal logic depends crucially on the ontological problem as to which ontology we should
adopt. According to Rodriguez-Pereyra [2], there are at least two kinds of Nominalism, onethat maintains that there are no universals and one that maintains that there are no abstract
objects like classes, functions, numbers and possible worlds. On the other hand, Realism about
universals is the doctrine that the are universals, and Platonism is the doctrine that thereare abstract objects. The doctrines about universals and the doctrines about abstract objects
are independent. According to Rodriguez-Pereyra [2], Nominalisms about universals can beclassified into at least eight types: (i) Trope Theory, (ii) Predicate Nominalism, (iii) Concept
Nominalism, (iv) Ostrich Nominalism, (v) Mereological Nominalism, (vi) Class Nominalism,(vii) Resemblance Nominalism, and (viii) Causal Nominalism. Resemblance Nominalism ingeneral is confronted with at least seven problems: (i) Imperfect Community Problem, (ii)Companionship Problem, (iii) Mere Intersections Problem, (iv) Contingent Coextension Problem, (v) Necessary Coextension Problem, (vi) Infinite Regress Problem, and (vii) Degree ofResemblance Problem. As Rodriguez-Pereyra [2] argues, according to Resemblance Nominalism, it is not because things are scarlet that they resemble one another, but what makes themscarlet is that they resemble one another. Resemblance is primitive and the properties of athing are defined by resemblance. Resemblance Nominalism reifies neither resemblance noraccessibility relation in themselves. We [5] proposed, in terms of measurement theory, a new
absolute-diﬀerence-structured model of first-order modal resemblance logic (MRL) that can furnish solutions to all of the problems (i)–(vii). Yi [6] raised a version of degree of resemblanceproblem. Yi [6, pp.622-625] argues as follows:(1) Carmine resembles vermillion more than it resembles triangularity.

1(2) is a resemblance-nominalistic formulation that expresses what makes (1) true:(2) Some carmine particular resembles some vermillion particular more closely than any
carmine particular resembles any triangular particular.
In Rodriguez-Pereyra[1]’s theory , the degree of resemblance n is defined as follows:
Definition 1（Degree of Resemblance） The particulars resemble to the degree n iﬀ they sharesn properties.
Under Definition 1, (2) compares the maximum degrees of resemblance. But (2) is false
because a possible carmine particular completely resembles a possible triangular particular(the same particular might be both carmine and triangular). Rodriguez-Pereyra [3] responses
to Yi by replacing (2) by (3):(3) Some carmine particular resembles some triangular particular less closely than any
carmine particular resembles any vermillion particular.
Under Definition 1, (3) compares the minimum degrees of resemblance. Rodriguez-Pereyra[3, p.225] argues that (3) is true because the minimum degree to which a carmine particular
can resemble a triangular particular (degree 0) is smaller than the minimum degree to which acarmine particular can resemble a vermillion particular (a degree greater than 0). Yi [7, p.796]
criticized this Rodriguez-Pereyra’s response by arguing that it rests on a false assumption: theminimum degree to which a carmine particular can resemble a vermillion particular is greaterthan 0. When we considered this Yi-Rodriguez-Pereyra debate, we realized that the model of
MRL was too weak to solve this type of problem. The aim of this talk is to revise the model ofMRL so that it can solve it in terms of measurement-theoretic multidimensional representation(cf.[4]) of degree of resemblance. （使用言語：日本語）

参考文献[1] Rodriguez-Pereyra, G.: Resemblance Nominalism. Clarendon Press, Oxford (2002)[2] Rodriguez-Pereyra, G.: Nominalism in metaphysics (2015), Stanford Encyclopedia of Philosophy[3] Rodriguez-Pereyra, G.: Resemblance nominalism and abstract nouns. Analysis 75, 223–231 (2015)[4] Suppes, P., et al.: Foundations of Measurement, vol. 2. Academic Press, San Diego (1989)[5] Suzuki, S.: Measurement-theoretic foundations of resemblance nominalism. In: Mineshima, K.
(ed.) Proceedings of the Seventeenth Workshop on Logic and Engineering of Natural Language
Semantics (LENLS 17). JSAI, Tokyo (2019)[6] Yi, B.U.: Abstract nouns and resemblance nominalism. Analysis 74, 622–629 (2014)[7] Yi, B.U.: Nominalism and comparative similarity. Erkenntnis 83, 793–803 (2018)2