It is traditionally believed that cerebral activation (the presence of low voltage fast electrical activity in the neocortex and rhythmical slow activity in the hippocampus) is correlated with arousal, while deactivation (the presence of large amplitude irregular slow waves or spindles in both the neocortex and the hippocampus) is correlated with sleep or coma. However, since there are many exceptions, these generalizations have only limited validity. Activated patterns occur in normal sleep (active or paradoxical sleep) and during states of anesthesia (...) and coma. Deactivated patterns occur, at times, during normal waking, or during behavior in awake animals treated with atropinic drugs. Also, the fact that patterns characteristic of sleep, arousal, and waking behavior continue in decorticate animals indicates that reticulo-cortical mechanisms are not essential for these aspects of behavior. (shrink)

Both Carnap and Quine made significant contributions to the philosophy of mathematics despite their diversedviews. Carnap endorsed the dichotomy between analytic and synthetic knowledge and classified certainmathematical questions as internal questions appealing to logic and convention. On the contrary, Quine wasopposed to the analytic-synthetic distinction and promoted a holistic view of scientific inquiry. The purpose of thispaper is to argue that in light of the recent advancement of experimental mathematics such as Monte Carlosimulations, limiting mathematical inquiry to the domain of (...) logic is unjustified. Robustness studies implemented inMonte Carlo Studies demonstrate that mathematics is on par with other experimental-based sciences. (shrink)