 According to an argument that Avicenna attributes to the defenders of  (SM),  on the one hand, mathematical objects are separate in definition (or in mind). They can be defined (or conceived) with no reference to matter or material beings. On the other hand, everything that is separate in definition (or in mind) is separate in existence. Therefore, the argument concludes, mathematical objects are separate in existence. They exist as fully separate beings which have no association with matter or material beings (Avicenna [MPh]: chap. VII.2, sec. 5). However, Avicenna finds this argument wanting. He argues that there is a difference between (a) defining (or conceiving) something without the condition of materiality and (b) defining (or conceiving) something with the condition of immateriality. He says that mathematical objects are separate in definition only in the sense of (a). But the second premise of the argument under discussion is true only if the separation in definition is considered in the sense of (b). The mere fact that something can be defined without the condition of materiality does not entail that that thing can exist in the extramental realm fully separate from matter. But mathematical objects cannot be defined with the condition of immateriality. It is not plausible to suppose immateriality as an essential component of the definitions of mathematical objects, or so Avicenna claims. Thus, this argument is fallacious and cannot establish (SM) (Avicenna [MPh], chap. VII.2, secs. 16–17; Marmura 2006: 360–63; Porro 2011: 292–93; Zarepour 2019: sec. 4.1).