ABSTRACT
This chapter describes one group of questions, those having to do with the indispensability of quantification over abstract entities such as sets-at the cost of having to neglect many others. It explores one group of questions which has to do with the existence of what it might call "equivalent constructions" in mathematics. The chapter discusses that none of the approaches should be regarded as "more true" than any other; the realm of mathematical fact admits of many "equivalent descriptions": but clearly a whole essay could have been devoted to this. It also discusses very briefly the interesting topic of conventionalism. The question of to what extent we might revise our basic logical principles, as we have had to revise some of our basic geometrical principles in mathematical physics, is an especially fascinating one. Today, the tendency among philosophers is to assume that in no sense does logic itself have an empirical foundation.
