Abstract
An elementary exercise in symbolizing an existential to universal relation reveals expressive limitations in standard first-order predicate-quantificational logic. Alternative translations of a sample some-every sentence are considered and rejected after criticism, leaving as the best choice a particular structure that demonstrably does not serve for all predicates available to the ordinary language to which the sample sentence belongs. We explain the difficulties encountered in trying to arrive at an adequate translation of the sentence in classical logic, as background to examining five alternative nonclassical logics to resolve the problem. We settle finally if only provisionally in the process on a version of intensional logic that permits reference and true predication of constitutive properties to nonexistent as well as existent objects.
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