Logic is seen today as a mathematical science fundamentally linked to the faculty of understanding, unrelated to our capacity of imagining or conceiving. Under the label psychologism, one usually considers any association between logic and conceivability (or imagination) as spurious and misled. This doctoral thesis has as its goal showing that, contrarily to what is ordinarily thought, there is in logic, understood as a science, an undeniable methodological employment of the faculty of conceivability or imagination. In order to show this, we firstly examine the conceivability principle (the proposition p is conceivable if and only if p is possible) on autonomous basis. We examine the main contemporary positions against and in favor of this principle and come to a qualified version of the principle, which we purport to be free of counterexamples; it will have been shown, therefore, that, under certain circumstances, there is an essential relation between modal concepts (possibility, necessity, contingency, impossibility) and our faculty of conceiving or imagining: whatever is conceivable is possible - even though it is not always true that whatever is inconceivable is impossible. Secondly, we show how the conceivability principle was an irreplaceable tool in the hands of the great pioneers of logic, in a very well delimited task: codifying new logical languages. Therefore, we hold that Aristotle, as he firstly codified the logic of categorical propositions, and Frege, as he elaborated quantified functional logic, were bound to employ conceivability as a basic parameter so as to examine the expressive correctness of the language they were codifying and determine the validity of various propositions and arguments. In order to make clear the place of conceivability in logic, we examine Aristotle´s Frege´s logic and epistemology and find concrete elements indicating the employment of this notion in the primitive context of logical codification we have mentioned. We emphasize that, in the context in which these authors were working, there were no epistemological options other than the resource to the conceivability principle.