Halliday & Matthiessen (2004: 619ff):
The basic distinction that determines how each type of modality will be realised is the orientation: that is, the distinction between subjective and objective modality, and between the explicit and implicit variants… . The third variable in modality is the value that is attached to the modal judgement: high, median or low. … The median value is clearly set apart from the two ‘outer’ values by the system of polarity: the median is that in which the negative is freely transferable between the proposition and the modality… . With the outer values, on the other hand, if the negative is transferred the value switches (either from high to low, or from low to high)… . This generates a set of 4x4x3x3 = 144 categories of modality. … The actual number of systematic distinctions that are made in this corner of the language runs well into the tens of thousands;