Leśniewski's Systems of Logic and Foundations of Mathematics by Rafal Urbaniak

Author:Rafal Urbaniak
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

29The quantification in a given language is called referential (or objectual) with respect to a given semantics of this language if the truth in a model of quantified statements is dependent upon there being (or not) some objects in the domain of this model satisfying (or not) the formula resulting from the initial formula by deleting the quantifier. Or, in other words, in the objectual interpretation variables in a model are assigned objects in the domain of this model. The objectual reading is often opposed to the substitutional reading, where variables are rather associated with a substitution class—the class of expressions (which do not belong to the domain of the model), and the satisfaction of a formula in a model is defined via some results of substitution being true (or not). Clearly, Ontology as an axiomatic system can be given both an objectual and a substitutional interpretation. Presumably, the question of whether quantification in Ontology is objectual or substitutional boils down to something like: ‘which interpretation is in accordance with Leśniewski’s views?’.

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