 Another argument for the superiority of the platonist semantics of mathematical discourse over the psychologist semantics is based on the fact that in ordinary usage, one way to say that something doesn't exist is to say that “it exists only in your  head”.[5]  To say that mathematical objects exist only in our heads, it seems, is just to say that they don't exist. For to say that they (as opposed to our ideas of them) exist is to say that they exist independently of us and our thinking. Quine put this point in a very compelling way in connection with a conceptualistic view of mythical objects like Pegasus. He writes (1948, p. 2):