The Four Basic Ontologies of Semantic Interpretation

This paper compares the semantic interpretation of logical, programming, and natural languages. It shows that they are based on different ontologies, and investigates the relation between the ontology assumed and the analysis of empirical phenomena such as truth, the Epimenides paradox, propositional attitudes, and vagueness. Furthermore, it shows that there is a basic difference between a metalanguage-based and a procedural semantics, and that the choice between them depends on the ontology presumed. 1 Metalanguage-based semantics In logic, a semantic relation between the formal language and the world is established by defining the (object-)language, the world (model), and the relation between them in terms of a metalanguage definition. The theory behind this method was presented by ALFRED TARSKI (1902–1983) in a form still valid today. In logical semantics, the task of the interpretation is to specify under which circumstances the expressions of the object language are true. The object language is the language to be semantically interpreted (e.g. quoted expressions like ‘φ & ψ’), while the definitions of the semantic interpretation are formulated in a metalanguage. Tarski’s schema for characterizing truth is the so-called T-condition. 1.1 Schema of Tarski’s T-condition T: x is a true sentence if and only if p. The T-condition as a whole is a sentence of the metalanguage, which quotes the sentence x of the object language and translates it as p. Tarski illustrates this method with the following example: 1.2 Instantiation of Tarski’s T-condition ‘Es schneit’ is a true sentence if and only if it snows. This example is deceptively simple, and has resulted in misunderstandings by many non-insiders.1 What the provocative simplicity of 1.1 and 1.2 does not express when 1Tarski 1944 complains about these misunderstandings and devotes the second half of his paper to a detailed critique of his critics.