I just stumbled upon the following statement:
(1) The number of discovered chemical elements is 118. Take the sentence "The number of chemical elements is necessarily greater than 100". Again, there are two interpretations as per the de dicto / de re distinction. According to the de dicto interpretation, even if the inner workings of the atom could differ, there could not be fewer than 100 elements. The second interpretation, de re, is that things could not have gone differently with the number 118 turning out to be fewer than 100. Intuitively, this claim is true. Of all the ways the world could have turned out, presumably there are no possibilities wherein 118 is fewer than 100. That 118 is greater than 100 is a necessary fact. [Wikipedia]
In one of the answers to a related SE question, somebody said:
(2) There exist true mathematical statements. They are true in all possible worlds where our logic is valid, which means necessarily true.
100 < 118 is obviously a true mathematical statement in our world, given that
< denotes a standard order relation on natural numbers. However, I can easily imagine a possible world where our logic is valid, still, standard
< is defined to mean, e.g.:
... < 99 < 118 < 101 < ... < 117 < 100 < 119 < ...
Is there any problem with that? The condition (2) is satisfied, so can we conclude that the statement
100 < 118 is actually contingent? Is (1) incorrect, or is (2) incorrect, or am I missing something?
EDIT: What is it exactly that makes de re reading true, and de dicto reading false?