Niko Tinbergen proposed that function or adaptive value is one of four 'why' questions concerning behaviour to be pursued, along with mechanism, development, and evolution. Cognition is more often addressed mechanistically than functionally. Here I examine some functional explanations of insect cognition. Given that all animals live on an Earth with many enduring properties, they might universally show certain adaptations accommodating these properties of the world. Probabilistic properties have been proposed as the basis for a universal law of generalization. This law was verified earlier in vertebrates. Work on honeybees testing this law upholds it. Another possible universal is the decay of the weight assigned to evidence as a function of time elapsed since the evidence was encountered, a temporal weighting rule. Thus, shortly after the encounter of evidence, the most recent evidence should have the most weight. But after sufficient time has elapsed, all evidence should be weighted about equally, and the 'proposition' with the most evidence supporting it should be favored. While this rule has been confirmed in various vertebrates, work on honeybees fails to support it. Other functional properties may not be universal, but be tuned to the requirements of the tasks for which a cognitive system has evolved. Navigational memories in insects are a case in point. An unusual suite of memory properties is expected in the case of path integration, a system in which an animal keeps track of the distance and direction from the starting point of the current journey (usually home). Path integration needs to be good from the start, good enough to get the animal home even on the first trip. Repeated training should not improve performance significantly. Being used for the current journey, it does not need to last long, and should show decay within a day. Finally, past journeys should not influence the current memory because the job is to keep track of the current journey. No integration of past experience beyond the current trip should take place. All three predictions, uncharacteristic of 'typical' memory systems, have been confirmed in the memory for distance traveled in two species of desert ants.