What is called ‘back-shifting’, relates to change of tense-aspect marking in a clause, when direct speech is converted to indirect speech. Compare:

(35) ‘John is hungry,’ Fred told us

(35’) Fred told us that John was hungry

(36) ‘Mary is having to leave,’ Jane said

(36’) Jane said that Mary was having to leave

(37) ‘Charlie ate the chocolate biscuits,’ Kate announced

(37’) Kate announced that Charlie had eaten the chocolate biscuits

(38) ‘Charlie has been eating the chocolate biscuits,’ Kate announced

(38’) Kate announced that Charlie had been eating the chocolate biscuits

That is, actual present becomes actual past, but all of actual past, previous present and previous past become previous past; this applies to perfective and to imperfective.

As noted in the discussion, something similar to back-shifting occurs in the correspondence between THAT and TO complement clauses. For example, I believe that Mary eats mangoes corresponds to I believe Mary to eat mangoes, with that. . . -s corresponding to to plus the base form of the verb. Similarly, -ed, has . . . -en and had . . . -en all correspond to to have (base form) . . . . -en.

It is instructive now to examine how back-shifting applies to modals and semi-modals. Semi-modals show present and past tense, and behave like other verbs under back-shifting; for example:

(39) ‘John isn’t able to tie his shoelaces,’ Mary remarked

(39’) Mary remarked that John wasn’t able to tie his shoelaces

However, in modern English modals have no past tense forms. How then are they back-shifted? Here are some examples:

(40) ‘It will rain this afternoon,’ she said

(40’) She said that it would rain that afternoon

(41) ‘I shan’t go,’ I said

(41’) I said that I wouldn’t go

(42) ‘I ought to do it,’ she said

(42’) She said that she should do it

(43) ‘I must go,’ I said

(43’) I said that I had to go

(44) ‘I may get the job,’ Mary speculated

(44’) Mary speculated that she might get the job

At an earlier stage of the language, four of what are now modals did exist in present and past forms:

Nowadays, would, should, could and might function as modals in their own right. But the historical tense connection is echoed in back-shifting. Would is the back-shifted version of will (as it should be, were it the past form of will) and also of would; similarly for the other three. Should now indicates obligation, quite different from the prediction of shall, and the back-shift for shall—as for will and would—is would.

It was remarked that it is hard to discern any semantic difference between should and ought to. In keeping with this, should can be used as the back-shift equivalent of should and also ought to (although it is also possible for ought to to function as its own backshift). Modal must and semi-modal has to were linked as alternative ways of expressing necessity modality. Had to functions as back-shifted version of both, demonstrating the close semantic link between modals and semi-modals, despite their differing grammatical properties. Finally, is to, being the only modal to mark tense, has a regular back-shifted form was to.