How should the following phrase be written:
"Billy is quite confused, so rather than sleep, he ponders."
Would the verb sleep, always be in the plural form and never sleeps?
How should the following phrase be written:
"Billy is quite confused, so rather than sleep, he ponders."
Would the verb sleep, always be in the plural form and never sleeps?
As Wayfaring Stranger suggested, the present participle would also work:
[1] Billy is quite confused, so rather than s̲l̲e̲e̲p̲i̲n̲g̲, he ponders.
The various functions of rather than
Rather than is a bit of a grammatical jack-of-all-trades, and it can function as quasi-coordinator [2a], a subordinator [2b], or a preposition [2c].
[2] a. He ponders rather than s̲l̲e̲e̲p̲s̲.
b. He ponders, rather than s̲l̲e̲e̲p̲.
c. He ponders, rather than s̲l̲e̲e̲p̲i̲n̲g̲.
It can be fronted when functioning as a subordinator or a preposition, but not when functioning as a quasi-coordinator. This is why one cannot have sleeps in the example given in the original question:
[3] a. *Rather than s̲l̲e̲e̲p̲s̲, he ponders. (not acceptable)
b. Rather than s̲l̲e̲e̲p̲, he ponders.
c. Rather than s̲l̲e̲e̲p̲i̲n̲g̲, he ponders.
The terminology and discussion above come from ComGEL 10.40; 12.69; 13.103; 14.15, 16, 19n; 15.52. Here are some relevant examples found in that source:
As a quasi-coordinator:
He is [to be pitied] rather than [to be disliked].
As a subordinator:
He paid the fine rather than [appeal to a higher court].
(bare infinitival clause)
Rather than [Robert drive in his present state], I'd prefer to drive him home myself.
(bare infinitival clause with a subject)
As a preposition:
Their actions precipitated the war rather than [averting it].
Bare infinitival vs. finite verb
As sumelic pointed out, in your example, one should not think of sleep as a finite verb in the plural, but rather as bare infinitival, a non-finite verb. Here 'bare' refers to the fact that we don't have a to as a part of the infinitival (i.e. it's just sleep rather than to sleep). To see that sleep is here indeed a bare infinitival rather than a finite verb in the plural, consider this example:
Rather than K̲i̲m̲ ̲g̲i̲v̲e̲ ̲t̲h̲e̲ ̲i̲n̲t̲r̲o̲d̲u̲c̲t̲o̲r̲y̲ ̲l̲e̲c̲t̲u̲r̲e̲, why don't you do it yourself? (CGEL, p. 1187)
If give were a finite verb here, it would have to be in the third person singular, gives. But it is not. What we have instead is a (somewhat rare) case of a bare infinitival clause with a subject. Distressingly (to some speakers), if the subject were a pronoun, it would almost certainly be in the accusative (e.g. me) rather than in the nominative (i.e. I): Rather than m̲e̲ give the introductory lecture, why don't you do it yourself? Many speakers are uncomfortable with this specter of a subject in the accusative, which normally belongs to the informal style, and so would often opt for a subjectless construction: Rather than h̲a̲v̲e̲ Kim give the introductory lecture, why don't you do it yourself?