Martin (1992: 413):
Table 6.19. Congruent and metaphorical realisations of interpersonal meanings [2] modulation inclination obligation congruent Modal verb may must metaphorical Verb complex be allowed to be obliged to causative Process allow (x) to do oblige (x) to do Epithet permissable necessary Thing permission necessity projecting Process (I) recommend (I) insist conjunction in case so
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[1] The congruent realisations of modulation are those of implicit manifestation: the subjective orientation being realised as a finite modal operator (e.g. will, should) and the objective orientation involving a hypotactic verbal group complex (e.g. willing to x, supposed to x); see Halliday & Matthiessen (2004: 513, 517). Halliday (1994: 82) also lists modal Adjuncts of readiness and obligation.
The metaphorical realisations of modulation are those of explicit manifestation. For obligation, the subjective orientation is realised as a projecting desiderative mental clause (e.g. I want…) and the objective orientation as an attributive clause with a factual Carrier (e.g. it's expected…). See Halliday & Matthiessen (2004: 613ff).
[2] These are neither inclination nor metaphorical. Verbal group complexes featuring allowed to x realise implicit objective obligation of low value; see Halliday & Matthiessen (2004: 620-1).
[3] These are congruent, not metaphorical, realisations. Verbal group complexes featuring obliged to x realise implicit objective obligation of high value.
[4] As Epithet, these serve as Attribute in metaphorical realisations of objective orientation (e.g. it's permissible…, it's necessary…). In congruent realisations, they can function as Post-Deictic in a nominal group (Halliday & Matthiessen 2004: 317, 612). However, permissible expresses low value obligation, not inclination (in contrast to the high value obligation of necessary.)
[5] Some nominalised forms can serve as an objective orientation of modulation, such as as a matter of necessity, but they are intermediate between explicit and implicit manifestation, and so intermediate between metaphorical and congruent. See Halliday & Matthiessen (2004: 615-6). However, permission expresses low value obligation, not inclination (in contrast to the high value obligation of necessity.)
[6] Neither of these functions as a metaphorical (explicit subjective) realisation of modulation. On the one hand, there is no inclination counterpart for the probability metaphor I think (Halliday & Matthiessen 2004: 619). On the other hand, the explicit subjective realisation of modulation is realised by a clause featuring a desiderative mental Process, whereas insist serves as a verbal Process (cf. demand).
[7] The conjunction groups in case and so — both of which can express causal-condition expansion relations — are not metaphorical realisations of inclination and obligation.
[2] These are neither inclination nor metaphorical. Verbal group complexes featuring allowed to x realise implicit objective obligation of low value; see Halliday & Matthiessen (2004: 620-1).
[3] These are congruent, not metaphorical, realisations. Verbal group complexes featuring obliged to x realise implicit objective obligation of high value.
[4] As Epithet, these serve as Attribute in metaphorical realisations of objective orientation (e.g. it's permissible…, it's necessary…). In congruent realisations, they can function as Post-Deictic in a nominal group (Halliday & Matthiessen 2004: 317, 612). However, permissible expresses low value obligation, not inclination (in contrast to the high value obligation of necessary.)
[5] Some nominalised forms can serve as an objective orientation of modulation, such as as a matter of necessity, but they are intermediate between explicit and implicit manifestation, and so intermediate between metaphorical and congruent. See Halliday & Matthiessen (2004: 615-6). However, permission expresses low value obligation, not inclination (in contrast to the high value obligation of necessity.)
[6] Neither of these functions as a metaphorical (explicit subjective) realisation of modulation. On the one hand, there is no inclination counterpart for the probability metaphor I think (Halliday & Matthiessen 2004: 619). On the other hand, the explicit subjective realisation of modulation is realised by a clause featuring a desiderative mental Process, whereas insist serves as a verbal Process (cf. demand).
[7] The conjunction groups in case and so — both of which can express causal-condition expansion relations — are not metaphorical realisations of inclination and obligation.