David Peter Burits
University of Vienna
Formal sentences such as ∃x(P(x)) have commonly been interpreted and translated into natural language by one of the following expressions: 1) „There is something that is P“, 2) „Some things are P“, or 3) „Something that is P exists“, and vice versa (here, I have replaced “x” with “something” or “thing” which is, I think, the closest possible translation of variables – which are, after all, not usually employed in natural language). It is easy to show why interpretation 2) is at least pragmatically questionable; however, interpretations 1) and 3) are not much less problematic. Some attempts have been made to remedy these problems – for example, by introducing an existence-predicate besides the existential quantifier (thus treating existence in some thick sense as a property), or by introducing new notation in order to express the phrase “there is” formally.
Without passing any judgement on the success of these attempts, I shall argue that they are deeply misguided in their motivation – aligning and harmonising formal and natural language. Instead, I shall propose a ‘minimal’ theory of existential quantification that posits that the meaning of any well-formed formal expression containing the existential quantifier is not expressible in any natural language and, instead, simply means what it means in its formal representation. My argument will not merely rest on problems of translatability (although they will be considered) – because, as I will try to show, even if translation is unproblematic, translatability should not and cannot be a desideratum of formal languages. Furthermore, I will take into consideration some consequences and possible subsequent developments of this line of argument concerning a few well-known issues tied up with existential quantification, especially whether it has existential import and what it means for ontology – not only language – in general.
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SOPhiA 2026 