@article {dozudic_d2010:2076,
title = {Doubting the Truth of Hume{\textquoteright}s Principle},
journal = {Organon F},
volume = {17},
number = {3},
year = {2010},
pages = {269-287},
type = {State},
abstract = {Hume{\textquoteright}s Principle (HP) states that for any two (sortal) concepts, F and G, the number of Fs is identical to the number of Gs iff the Fs are one-one correlated with the Gs. Backed by second-order logic HP is supposed to be the starting point for the neo-logicist program of the foundations of arithmetic. The principle brings a number of formal and philosophical controversies. In this paper I discuss some arguments against it brought out by Trobok, as well as by Potter and Smiley, designed to undermine a claim that HP and its instances (such as {\textquotedblleft}the number of the forks on the table is identical to the number of the knives on the table iff the forks are one-one correlated with the knives{\textquotedblright}) are true. Their criticism starts from distinguishing the objective truth from a weak or stipulative one, and focusing on fictional identities such as {\textquotedblleft}Hamlet = Hamlet{\textquotedblright} or {\textquotedblleft}Jekyll = Hyde.{\textquotedblright} They argue that numerical identities (as occur in instances of HP) are much the same as fictional identities; that we can attribute them only a weak or stipulative truth; and, consequently, that neo-logicists are not entitled to ontological conclusions concerning numbers they derive from HP and its instances. As opposed to that, I argue that such a criticism is ill-conceived. The analogy between the numerical and fictional identities is far-fetched. So, relative to such a criticism, HP has more prospects than some authors are prepared to admit.},
url = {http://www.klemens.sav.sk/fiusav/doc/organon/2010/3/269-287.pdf},
author = {Do{\v z}udi{\'c}, Du{\v s}an}
}