[Preliminary aspects relating to the problem-solving process].

Certain theoretical and methodological aspects related to cognition and problem solving processes are reviewed in order to emphasize the inferencial procedures by which individuals overcome difficulties and limitations present in a problem situation and realize and overcome their own inferential limitations. The rôle that certain primary elements, like axioms, have in the process of making explicit and complete formal structures is also emphasized. Ability to demonstrate correctly and some limitations concerning the methalogic properties of axiomatic systems are also seen in relation to the inferential processes of cognition. Eliminatory inferential processes for adopting decisions are discussed and focused from opposite standpoints as those of associative learning theory and Gestalt theory. The inferential process is evaluated from the internal difficulty of a problem state of nature to the intellective resources available to the subject in order to validate the adopted decisions in problem solving. This comprises methods going from trial-and-error exploration to insight phenomena, through the formulation of all logical possibilities and the process of discarding them by means of experience or inference. According to the symbolic level that represents the problem state of nature formal structures are built up to the point by which they need to be gestallically closed by the inclusion of new primary terms or concepts that could be identified as axioms. This king of closure is postulated as a requirement of the aptitude for mathematics.