Primary (interceptive) saccades toward a moving target have been proposed to be the outcome of the summation of signals “computed” by two parallel and distinct pathways in the brain. One computation would estimate the location where the target first appeared whereas the other would calculate the subsequent target displacement amplitude from velocity signals. These computations would involve activity propagating through a pathway involving the superior colliculus (snapshot of position) and another involving the cerebellum (motion integration). Rather skeptical that kinematic parameters could be embedded within the brain activity and that massively distributed and recurrent neuronal networks would subtend human-like arithmetic computations, we re-examined this theory. We recorded the activity of saccade-related neurons in the superior colliculus with the aim to verify whether the population bursting activity would include cells coding for saccade vectors corresponding to the current and perhaps the future location of the target. Thus, we found that during the saccade-related burst, the active assembly consists of a continuum of commands, ranging from those related to antecedent target locations to commands related to its current location. Regarding the other pathway, we tested its contribution by inactivating one of its output nuclei, the caudal fastigial nucleus. Like saccades toward a static target, the horizontal component of interceptive saccades became hypometric when directed toward the contralesional side and hypermetric when they were ipsilesional. The horizontal dysmetria depended on target velocity, but the use of accelerating or decelerating targets revealed that velocity was not the crucial parameter. Altogether, our investigations lead to a viewpoint from which basic intrinsic properties of the brain suffice to explain the generation of accurate visually-guided (saccadic and pursuit) eye movements without considering that kinematic notions would be embedded within the brain activity and that the brain networks would perform arithmetic computations upon them.