Balzacian Hours

"There is a lot more expressive power that we still need to cater for in order to express, for instance, truths of existence and identity. Here we may follow existing practice, however, and use the symbols ‘E!’ and '=’ respectively for these purposes. But we also need quantifiers – at least a particular and a universal quantifier – although for this purpose too we may as well again follow existing practice and use the symbols ‘9’ and ‘8’. However, we shall not adopt the usual assumption that existence can be ‘analysed’ in terms of ‘9’ and ‘¼’. And another appropriate diversion from standard practice would be to favour so-called restricted quantifiers for most purposes. For instance, in order to represent the sentence ‘Some (individual) horses are white’, we shall use a formula such as ‘(9x: αx)(Fx)’, where ‘α’ = ‘horse’ and ‘F' = ‘white’. Similarly, in order to represent the sentence ‘Some (species of) mammals are viviparous’, we shall use a formula such as ‘(9φ: βφ)(Gφ)’, where ‘β’ ¼ ‘mammal’ and ‘G’ ¼ ‘viviparous’. (It will be noticed, incidentally, that I am here adopting the convention of using x, y, z, … as variables ranging over primary substances and φ, χ, ψ, … as variables ranging over secondary substances.)" is a Malebranchean moment.