Following G. T. Fechner (1966), thresholds have been conceptualized as the amount of intensity needed to transition between mental states, such as between a states of unconsciousness and consciousness. With the advent of the theory of signal detection, however, discrete-state theory and the corresponding notion of threshold have been discounted. Consequently, phenomena such as subliminal priming and perception have a reduced theoretical basis. The authors propose a process-neutral definition of threshold that allows for graded perception and activation throughout the system. Thresholds correspond to maximum stimulus intensities such that the distribution of mental states does not differ from that when an appropriate baseline stimulus is presented. In practice, thresholds are maximum intensities such that the probability distribution on behavioral events does not differ from that from baseline. These thresholds, which the authors call "task thresholds", may be estimated with modified item response psychometric measurement models. (Contains 5 figures.)