Quantification and its Discontents
The chapter focuses on quantification as it figures in standard versions of the predicate calculus. These versions are straightforwardly reductive in that non-singular sentences must be re-cast into singular form if they are to receive representation. However, various non-singular sentences, including certain kinds of plural sentences, are refractory to representation in this form. Essentially singular forms of quantifier-expression must be distinguished from non-singular forms to lay the basis for sui generis non-singular forms of quantification, appropriate to both plural nouns and non-count nouns. The maxim ‘to be is to be the value of a variable’ must be rejected.
Keywords: predicate calculus, non-singular quantification, reduction, non-singular variable, instance, sample
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