| (1) | a. | If he submitted his paper to a journal,... |
| b. | If he submits his paper to a journal,... | |
| c. | If he will submit his paper to a journal,... | |
| ...we won't include it in our book. |
The protasis of (1a) does and that of (1b) does not retain its interpretation in isolation: cf. (2a,b). (2c) is normally used instead of (2b), but substituting (2c) into the protasis yields (1c), a sentence that is hardly acceptable and in any case not equivalent to (1b).
| (2) | a. | He submitted his paper to a journal. |
| b. | He submits his paper to a journal. | |
| c. | He will submit his paper to a journal. |
These facts have led some authors to conclude that the protasis of (1b) is in fact (2c). I will argue instead that the protases of (1a,b,c) are (2a,b,c), respectively. The contrasts between (1) and (2), in particular the fact that (1c) and (2b) are peculiar while (1b) and (2c) are not, are explained on pragmatic grounds. Central to the proposal is a distinction between truth and assertability.
The protases in (1) identify those worlds at which the sentences in (2) are true. The truth of a sentence is a timeless property of worlds, defined with reference to future facts if required. Assertions, on the other hand, are located in time and must be supported at utterance time to be felicitous. The form of the sentence determines the relevant notion of support: deducibility for non-modalized sentences such as (2a,b), and inductive support for sentences marked with the modal 'will,' such as (2c).
More specifically: Settledness is the familiar notion from Priorian tense logic, defined as necessity with respect to historical alternatives; scheduling is necessity with respect to a modal base. Non-modalized sentences such as (2a,b), whether they are asserted about the facts or about the contents of a schedule, must be deducible in one of these senses in order for the assertion to be felicitous. This is generally possible with reference to the past, but not in general with future reference; hence the restriction to scheduling readings present in (2b) and absent in (2a). The modalized sentence (2c) has weaker assertability conditions: It may be "true enough" to be asserted in contexts in which (2b) is not supported. On the other hand, it does not seem appropriate for the expression of uncertainty as to the truth of (2b). I will suggest that (2c) asserts that (2b) is true with probability 1.