 A second version of the third strategy, developed by Katz (1981, 1998) and Lewis (1986, section 2.4), is to argue that we can know that our mathematical theories are true, without any sort of information-transferring contact with mathematical objects, because these theories are necessarily true. The reason we need information-transferring contact with ordinary physical objects in order to know what they're like is that these objects could have been different. For instance, we have to look at fire engines in order to know that they're red, because they could have been blue. But we don't need any contact with the number 4 in order to know that it is the sum of 3 and 1, because it is necessarily the sum of 3 and 1. (For criticisms of this view, see Field (1989, pp. 233–38) and Balaguer (1998a, chapter 2, section 6.4).)