Measurement-Theoretic Resemblance Nominalism
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 is one of the most essential problems in the philosophy oflanguage. This problem consists in a crossroads of ontology and semantics. When we translate a natural language into a first-order (modal) language, (though it is a problem which formal language weshould adopt in translation), the semantic problem as to which entity we should choose as the semantic
value of a symbol in the model of first-order modal logic depends crucially on the ontological problem
as to which ontology we should adopt. According to Rodriguez-Pereyra [5], there are at least two kindsof Nominalism, one that maintains that there are no universals and one that maintains that there are noabstract objects. On the other hand, Realism about universals is the doctrine that there are universals,and Platonism is the doctrine that there are abstract objects. The doctrines about universals and thedoctrines about abstract objects are independent. According to Rodriguez-Pereyra [5], Nominalisms
about universals can be classified into at least eight types: (1) Trope Theory, (2) Predicate Nominalism,(3) Concept Nominalism, (4) Ostrich Nominalism, (5) Mereological Nominalism, (6) Class Nominalism, (7) Resemblance Nominalism, and (8) Causal Nominalism. Resemblance Nominalism in generalis confronted with at least six problems: (1) Imperfect Community Problem, (2) Companionship Problem, (3) Mere Intersections Problem, (4) Contingent Coextension Problem, (5) Necessary Coextension
Problem, and (6) Infinite Regress Problem. According to Rodriguez-Pereyra (2015), the Resemblance
Nominalism does not reify resemblance. In this abstract, because of limitations of space, we focus onCompanionship Problem in the above six problems. Goodman [2] poses the following problem that isanticipated by Carnap [1]:Problem 1（Companionship） When the class of particulars instantiating F1 is a proper subclass ofthe class of particulars instantiating F2 , F2 is said to be a companion to F1 . Even if every particularinstantiating F2 resembles all particulars instantiating F1 , not all of them instantiate F1 . So merely
resembling all particulars instantiating F1 does not guarantee that a particular instantiates F1 . If so,
how can particulars instantiating F1 be F1 in terms of resemblance?
Rodriguez-Pereyra [4]’s Resemblance Nominalism is based on the motivation that particulars
a1 , a2 , . . . , an resemble each other (in the property-realist terms, share a property) only if sets containing them as urelements resemble each other. All of the imperfect community, companionship,1

mere intersections, contingent coextension, necessary coextension, and infinite regress problems
can be solved by Rodriguez-Pereyra’s Resemblance Nominalism. Paseau [3] provides Resemblance
Nominalism based on a comparative resemblance relation that relies on the following two ideas:
The first is to allow the resemblance to hold between sets of arbitrary size, not only n-th rank pairsets as in Rodriguez-Pereyra’s theory. The second is to take resemblance as a comparative relation:
R + (x1 , x2 , x3 , x4 ) which means that x1 resembles x2 more than x3 resembles x4 . In property-realist
terms, it means that the number of properties shared by x1 and x2 is greater than the number ofproperties shared by x3 and x4 . In both Rodriguez-Pereyra’s theory and Paseau’s theory, the degree ofresemblance n is defined:
Definition 1（Degree of Resemblance） The particulars resemble to the degree n iff they shares nproperties.
Paseau himself points out the problem about the degree of resemblance:
Problem 2（Degree of Resemblance） Suppose, for example, that a and b share their Fdeterminate, but that their G, H, and J determinates are toward the opposite ends of the scale,and that c and d have determinates of these four determinables that are extremely close on the scale,but do not exactly share any. Clearly, c resembles d more than a resembles b, yet R + (a, b, c, d) holds.
In both Rodriguez-Pereyra’s theory and Paseau’s theory, the resemblance between particulars is related
to the resemblance between the sets of them in order to solve the above-mentioned problems. But
Paseau himself points out the problem about this relation:
Problem 3（Set/Members Resemblance） Sets have different abundant properties from their members, so the number of properties shared by sets is not a guide to how many properties their members
share. For example, {a, b} and {c, d} resemble simply in virtue of being sets, whether or not a and b
and c and d share any properties.
The aim of this talk is to propose, in terms of measurement theory, an absolute-difference-structured
new model of first-order modal resemblance logic (MRL) that can furnish solutions to all of the imperfect community, companionship, mere intersections, contingent coextension, necessary coextension,
infinite regress, degree of resemblance, and set/members problems. （使用言語：日本語）

参考文献[1] R. Carnap. Der logische Aufbau der Welt, The Second Edition. Felix Meiner, Hamburg, 1961.
[2] N. Goodman. The Structure of Appearance, The Third Edition. Reidel, Dordrecht, 1977.
[3] A. Paseau. Resemblance theories of properties. Philosophical Studies, 157:361–382, 2012.
[4] G. Rodriguez-Pereyra. Resemblance Nominalism. Clarendon Press, Oxford, 2002.
[5] G. Rodriguez-Pereyra. Nominalism in metaphysics, 2015. Stanford Encyclopedia of Philosophy.

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