In the philosophy of mathematics, if-then-ism is the view that mathematical assertions of existence, like the statement that there exist numbers which are their own squares, should, strictly speaking, be prefaced by "If numbers exist, then there exist...". However, I have just noticed a problem with this view. For someone who believes that mathematical objects don't exist, they would also believe something like, "If numbers exist, then 2+2=5", since they believe the antecedent is false. So, how does one deal with this problem? Have any philosophers talked about this problem, and suggested possible solutions? Of course, this is not a problem for someone like me who believes mathematical entities like sets and numbers exist. I am merely asking how someone who does not believe in mathematical entities would deal with this conundrum.

In the philosophy of mathematics, if-then-ism is the view that mathematical assertions of existence, like the statement that there exist numbers which are their own squares, should, strictly speaking, be prefaced by "If numbers exist, then there exist...". However, I have just noticed a problem with this view. For someone who believes that mathematical objects don't exist, they would believe something like, "If numbers exist, then 2+2=5", since they believe the antecedent is false. So, how does one deal with this problem? Have any philosophers talked about this problem, and suggested possible solutions? Of course, this is not a problem for someone like me who believes mathematical entities like sets and numbers exist. I am merely asking how someone who does not believe in mathematical entities would deal with this conundrum.