Modality: Propositions Vs Proposals

Halliday & Matthiessen (2014: 176-7):

What the modality system does is to construe the region of uncertainty that lies between ‘yes’ and ‘no’. But there is more than one route between the two, (1) one for propositions, and (2) one for proposals. (1) In between the certainties of ‘it is’ and ‘it isn’t’ lie the relative probabilities of ‘it must be’, ‘it will be’, ‘it may be’. (2) Likewise, in between the definitive ‘do!’ and ‘don’t!’ lie the discretionary options ‘you must do’, ‘you should do’, ‘you may do’. The space between ‘yes’ and ‘no’ thus has a different significance for propositions and for proposals.