Many important lines of argumentation have been presented during the last decades claiming that machines cannot think like people. Yet, it has been possible to construct devices and information systems, which replace people in tasks which have previously been occupied by people as the tasks require intelligence. The long and versatile discourse over, what machine intelligence is, suggests that there is something unclear in the foundations of the discourse itself. Therefore, we critically studied the foundations of used theory languages. By looking critically some of the main arguments of machine thinking, one can find unifying factors. Most of them are based on the fact that computers cannot perform sense-making selections without human support and supervision. This calls attention to mathematics and computation itself as a representational constructing language and as a theory language in analysing human mentality. It is possible to notice that selections must be based on relevance, i.e., on why some elements of sets belong to one class and others do not. Since there is no mathematical justification to such selection, it is possible to say that relevance and related concepts are beyond the power of expression of mathematics and computation. Consequently, Turing erroneously assumed that mathematics and formal language is equivalent with natural languages. He missed the fact that mathematics cannot express relevance, and for this reason, mathematical representations cannot be complete models of the human mind.