Relation-Theory: takes belief to be a relation to internal objects (entities). Virtually all authors are against the assumption of thoughts as internal objects. See also intensional objects, intensions, propositional attitudes.
Relational Theory/Bigelow/Pargetter (Science and Necessity Cambridge University Press 1990 p55) assumes universals (e.g. sets, numbers, properties) and relations between them in order to explain the problem of quantities. See also change, motion, quantities, universals, Platonism, nominalism.
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Relation Theory/Belief/Burge: (Burge 1980): Propositions about propositional attitudes have the form of a relational propositional-attitude predicate with singular arguments for at least one person and something believed. This is a semantic value of the grammatical object of the verb of the propositional attitude.
SchifferVsRelation Theory/SchifferVsFrege/(s): makes mentalistic assumptions, "inner entities".
Origins of Objectivity Oxford 2010