In a library with an actually infinite number of books containing an infinite number of red and an infinite number of black books, the library would contain as many red books as the total books in its collection and as many red books as red and black books combined. But in reality the subset cannot be equivalent to the entire set.
equivalent(Snowdon's proposed reading of 'equivalent' in the context of Hinton's argument about Neutral Experience Reports and Perception-Illusion disjunctions.)
'P' is equivalent to 'Q' if and only if it is a priori that necessarily (P if and only if Q).
Since conclusion 8 follows validly, if premises 6 and 7 are true the argument is sound. In defense of premise 6, he defines an actual infinite as a determinate totality that occurs when a part of a system can be put into a one-to-one correspondence with the entire system (Craig and Sinclair 2009: 104). Craig argues that if actual infinites that neither increase nor decrease in the number of members they contain were to really exist, rather absurd consequences would result. For example, imagine a library with an actually infinite number of books. Suppose that the library also contains an infini...