In this paper we deal with a classical question of western philosophy: Is it possible to know that there are things which do not exist? We begin with a brief analysis of some fragments of Parmenides, and later we study whether these arguments are valid using three kinds of epistemic logic: a classical style epistemic logic, where axiom holds (see PDF), a free epistemic logic, where this axiom does not hold, and finally, we study Lenzen's proposal of using two kinds of quantifiers: possibilistic and realistic quantifiers. We conclude that the last last one is the closest to our intuition and a good way to deal with this kind of problem.En este artículo discutimos una pegunta clásica de la filosofía occidental: ¿es posible saber que hay cosas que no existen? Empezamos con un breve análisis de algunos fragmentos de Parménides y a continuación estudiamos si estos argumentos son válidos usando tres tipos de lógica epistémica.