As I pointed out yesterday, tense and aspect are not addressed (apart from a brief introduction in chapter 2) until chapter 16. As a result, much of the relevant material is spread throughout the preceding chapters. In chapter 2 (which, according to Cowan, "can be viewed as optional"), we get a quick introduction to the verb. The section on "Verb Forms" begins on p. 20. Here we learn that
"Verbs can take several different forms. For instance the verb work may have the infinitive form shown in (31a), in which work is preceded by to, or it may have the bare inifinitive form shown in (31b)." (emphasis added)
Even though I would argue that to is not really part of the verb, this is the traditional analysis common in most ESL materials. Moreover, the grammar is pedagogical, not theoretical, in its orientation, so there is good reason to take this position.
It then continues, "Verbs can also take a variety of inflected forms. Some of these inflected forms are shown in (32)." (emphasis added; note that inflect/inflection/inflected do not appear in the index or the glossary though they are defined on the next page.)
"(32) a. She works every day. inflected for present tense
b. He is working right now. present participle
c. I've worked there for a long time. past participle"
You'll notice that with all of the hedging, TGE fails to provide a definitive list of verb forms. This is not simply a local problem. No such list is provided anywhere in the book. Although it does eventually bring up most of them, nowhere does it mention the plain present tense, at least not as far as I can tell. Since it doesn't mention it, obviously it never explains that the plain present tense looks the same as the bare infinitive. This is potentially a confusing point and deserves attention.
Its treatment of the past participle is similarly sketchy. TGE explains that some past participles take -en while others take -ed, but it doesn't explain which; nor does it provide a list of common irregular verbs. At least chapter 2 does a better job on this point than the glossary in which the entry for past participle is simply: "Verb + -ed (He has finished his novel.)" You will certainly notice how this could be confused with the past tense.
Unfortunately, adding to the confusion, the only mention of past tense in the entire chapter is in the following excerpt,
"For example, some verbs do not take the regular -ed past inflection. Instead they either undergo an internal vowel change (e.g., run becomes ran) or they change their form entirely."
A reader who has little or no grammatical meta knowledge could easily assume that "-ed past" refers only to the past participle, which was explicitly mentioned, or that the past tense is formed using the past participle. There is nothing clearly explaining the difference. The above description also ignores verbs like put or fit which are inflectionally identical in the plain form, plain present tense, past tense, and past participle.
No special attention is given to be's inflectional paradigm.
The next stab at verb forms appears in Chapter 14, "Modal Verbs". On page 294, it asks us to "note that a verb following a modal is always in its basic (bare infinitive) form." We haven't run across the term basic form before, nor is it in the glossary, but I suppose this is a minor terminological issue. On the next page, we learn that "some modals, however, have what can be seen as a corresponding irregular past tense form, for example, could in the case of can." Again, we have a curious vagueness that is not, as far as I can tell, remedied later. It would be a simple thing to include a table like the following:
Present Tense | Past tense
can | could
may | might
will | would
shall | should
TGE recognises three types of modals: pure, marginal, and semi-. Finally, here we get a definitive list with the marginal modals listed as: dare, need, and ought to, and the semimodals listed as: be going to, be supposed to, had better, had best, have got to, and have to. But once again we get very unclear advice on their forms: "With most of the semimodals, the words have, had, and be contract with not, are involved in subject-aux inversion, and occur in tags." We are left to figure out which ones don't.
In Chapter 16, "Tense and Aspect", TGE takes the modern view that English has but two tenses. Once again, though, things aren't laid out specifically and completely. On p. 350 it explains that "of the three times shown in (1), only two are expressed in English by inflections on the verb -- present and past." It appear then that a tense must be inflected and may not be phrasal, though this is by no means made explicit. Why is inflection important? TGE doesn't tell us. The inflectional criteria is not mentioned in the glossary.
Despite this nod to modern grammar, TGE still confounds the ideas of tense and time. In the glossary, tense is described thus: "A feature of verbs -- the time that an action occurs in relation to the moment of speaking. English marks two tenses -- present and past (future time is expressed with will or be going to.)"
No mention is made of modal uses of past tense lexical verbs (e.g., I'd rather you came at 6:00. Or I wish he was here.) No mention is made of the fact that past tense pure modals usually refer to future or present time, not past time. TGE does explain the distinct meanings of each of the nine pure modals though; it just doesn't do so with reference to tense. Where there is discussion of mismatch between time and tense, such as with the historical present on p. 358 or unreal conditions on p. 359, no explanation is provided for this seeming contradiction between these uses and the definition which has tense = time.
It appears that TGE completely fails to recognize the huge advantages in a grammar that accrue from dispensing with a future tense. Certainly it doesn't explain why you might prefer this analysis, and indeed, having briefly acknowledged the lack of an English future tense, it then returns to "the 12 so-called tenses of English... because English language instruction on verb forms is in terms of these twelve tenses, the rest of this explanation is devoted to presenting each tense and its meaning, basic and otherwise. We will use the tense designations in (7)." This leaves me wondering why Cowan even bothered to bring up the future tense issue at all. As with so many things in this grammar, no clear answer is forthcoming.