Guest Lecture Professor David Makinson- 'Hamilton’s particles: an exercise in third-order logic'

Sir William Hamilton is remembered for his proposal to extend the four traditional categoricals to eight by applying quantifying particles to the predicate term as well as to the subject term, a step that he called 'quantifying the predicate'. Close reading reveals that he intended the quantified terms to be understood in what is sometimes called a ‘collective’ rather than a ‘distributive’ manner. De Morgan understood this, expressing the distinction with the words ‘cumular’ and ‘exemplar’ but, unwilling to tackle the former, worked on a distributive conception only. Since then, other commentators have followed in his footsteps, comforted by the fact that such a perspective translates readily into the the language of first-order logic. But formal representation of the collective approach needs more sophisticated resources. The talk shows how it may be carried out using the language of third-order logic.