Why is it possible to replace 都 with 也 in 什么都没有? I know 也 only as "also", but I see it now and then used in ways difficult to understand, especially in some negative statements. Why is this so? Does 也 also have some meaning not mentioned in dictionaries which is used in these cases?
什麼都 can be used in both positive and negative statements while 什麼也 is usually used in negative statements. So, instead of focusing on the usage of 也 here, 什麼都 and 什麼也 can be regarded as phrases which are sometimes used interchangeably.

For example:


  我們以為什麼都知道，而實際上什麼也不知道。/ 我们以为什么都知道，而实际上什么也不知道。


One possible translation:  


  We thought we knew/know everything but, in fact, we knew/know nothing at all.


So, it's ok to say (although the above example would read better):


  我們以為什麼都知道，而實際上*什麼都*不知道。/ 我们以为什么都知道，而实际上*什么都*不知道。


but odd to say:


  我們以為*什麼也*知道，而實際上什麼也不知道。/ 我们以为*什么也*知道，而实际上什么也不知道。