(C）shall is used for the future tense, or suggestion or obligation, normally related to the first person ; should as the past tense form of shall does not usually indicate the past tense but obligation or suggestion.
Hall (ibid）claims that the functions and usages of each MV are clearly cut, i.e.the present tense forms of MVs are related to reality (constituted by the addresser, real world and probable action）while the past forms of MVs non-reality (constituted by the reduction of the role of the addresser, as well as the addition of the imaginary world and the possible action).Put in another way, some MVs are more realistic while others are not in the sense of truth conditions.
Nevertheless, it can be found that Hall’s definition seems to be different from what he claims.His definition seems to imply that modal devices are pluralistic in functions.Take will for example.This MV can indicate present and future volition.It should be noted that present volition is different from future volition, for in the latter case uncertainty is more obvious than in the former case.Take should for another example.This MV can indicate either obligation or suggestion.Again, obligation differs from suggestion in that the former stresses the responsibilities of the addressees whereas the latter offers options to the addressees.Seen in this light, it is impractical to explore the functions of MVs according to the monosemantic method.
2.1.2.2 The logic and truth method
The logic and truth method uses logic and truth as a means of inferring modality (cf.Perkins, 1983; von Wright, 1984).According to this method, the modality of MVs can be best illustrated by the following formula (Perkins, 1983: 34):
K (C does not preclude that e occur)
Where: i.K = natural laws
ii.C = an empirical circumstance
iii.e = an event
iv.K (x）= x is the case relative to K
Perkins (ibid）infers the modality of MVs by the above formula of inference.Take the MV can for example.If inferred by Perkins’ formula, the MV can expresses dynamic modality, i.e.it is concerned with the disposition of certain empirical circumstances with regards to the occurrence of some events:
(i）There is a natural law (K）for people to encode and decode the modality of the MV can;
(ii）The MV can is normally related to the empirical circumstance (C）of personal ability;
(iii）The agent disposes the act involved (e).
(iv）Thus, the inferred modality (x）of the MV can is relative to K.
According to this formula, the dynamic modality of the MV can is inferable.
This method is best embodied in the theory of scalar quantity.When scalarized, modal devices are explored through the angle of truth conditions.The scalar quantity of MVs is an expansion and formalization of Grice’s first maxim of quantity (Grice, 1975: 45）in the context of linguistic elements that are related to each other as weaker and stronger instances of a particular semantic domain.According to Grice (ibid), speakers are expected to make their contributions as informative as required in a given context, and the use of a weaker expression implies that the stronger expression does not apply to the situation, and therefore implies the negative of the stronger expression.
The studies on scalar quantity of MVs are based on the entailment existing in the quantification of such indefinite numerals as all and some.Consider the following:
(15）All of the cyclists arrived on time.
(16）Some of the cyclists arrived on time.
Examples (15）and (16）can be expressed by the following formula of scalarity: -some +> not all (+> is a symbol of “entail”).According to this formula, some in Example (15）entails all in Example (16）in terms of semantics.
As illustrated by Horn (1972, 1989), Gazdar (1979), Levinson (1983, 2000）and Van der Auwera (1996), the same basic mechanism can be applied to the domain of epistemic modality, which usually comes in varying strengths, ranging from possibility to probability and necessity, depending on the degree of commitment to the proposition the speaker wishes to express.Take the following two statements for example:
(17）John may be the murderer.
(18）John cannot be the murderer.
By means of alternative statements, Examples (17）and (18）can be restated respectively as:
(19）It is not certain that John is the murderer.
(20）It is not possible that John is the murderer.
Also, a formula can be used to express the relationship between the MVs may and cannot in Examples (17）and (18):
not certain +> not (not possible）+> possible (+> is a symbol of “entail”)
As the formula shows, the MV may is weaker than the MV cannot in modal strength, and may entails cannot.Verstraete (2005: 1401-1418）holds that scalar quantity applies to deontic modality as well as epistemic modality.
Deontic modality denotes permission, necessity and obligation.As with epistemic modality, the deontic domain has traditionally been described in terms of varying degrees of strength which can be said to form a scale.Permission is generally taken to be the weaker type of deontic expressions, in parallel with possibility in the epistemic domain, and obligation is taken to be the stronger type, in parallel with necessity in the epistemic domain.Between these two extremes, there are various intermediate degrees such as suggestions or advice.Sweetser (1990）and Traugott & Dasher (2002）give an account of the historical reasons for grouping together permission with possibility as well as obligation with necessity.Verstraete (2005）assumes that the parallelism makes it possible to analyze deontic modality in terms of scalar organization as well, though to some extent differently.