In this paper I will discuss Hudson's and Milisauskas's contribution to the philosophical debate on the concept of extended mind. With great theoretical depth, the two authors analytically show how the material engagement of Wave Medaillons in Cucuteni culture has a cognitive function; their work demonstrates why such objects can be considered a mental institution and an extension of the users' cognitive processes. I totally agree with the idea that material tools can be part of our cognitive processes; but in this paper I will criticize Clark's and Chalmers's idea that the concept of mind should encompass objects used for cognitive purposes, such as the ones used within the Cucuteni culture. In other words, I will pose that the fact that objects can be part of our cognitive processes does not imply that they are part of our mind. To support my idea, I will start from the observation that, in considering physical tools as part of our mind, we have to extend to material objects something that has no extension (our mind). I will discuss the consequences of this logical paradox by revisiting the famous mental experiment of Otto and Inga. I will focus on the difference between Otto's possibility to refuse to use his notebook and Inga's impossibilities to refuse to use her mind.