Verbs and predication
Verbs can be described as ‘predicators’, and the role of the verb in the clause can be described as ‘predicating’. Could we use these notions to give a foundation to the category of verb? Can we say that verbs are defined by their role as predicators? Unfortunately, the answer to this has to be ‘no’. Let’s see why.
The predicate is the part of the sentence which attributes a property to a referent (see Rothstein 2006). The term ‘property’ is a bit misleading: it covers not just adjectival properties, but verbal ones too. So in (1), the referent in question is Stephen, and the properties attributed to him are all properties which consist of performing a certain action: walking home, shooting Nazis and accepting the glass. Because these actions all involve other entities (home, Nazis and the glass) the sentences include the NPs home, seventeen Nazis and the glass, which specify additional information about the action.

These NP objects aren’t necessary for a predication, since we can remove them and still succeed in attributing properties to Stephen: the properties of walking (2a), shooting (2b) and accepting (2c):

As a result, it’s conventional in linguistics to say that it’s the verb which is the predicator in a sentence: in a well-formed English sentence, there must be a verb, but there need not be anything other than a verb. The verb can bring associated NPs along as objects or complements, as in (1), but these associated NPs don’t themselves predicate, as we can see if we remove the verb from the sentences of (1):

These sentences are ill-formed: in the absence of a verb, the non-subject NPs can’t contribute to specifying the property attributed to Stephen. For this reason the verb is thought of as the necessary part of the predicate, and the verb is known as the predicator.
That, then, explains what predicates and predicators are. Back to the question of whether we could define verbs in terms of predication, thereby providing a semantic basis for the category. Unfortunately, it turns out there are also other parts of speech than the verb which can be considered as predicates. Look at (4):

Here we find additional properties being attributed to the referents of the sentence. In (4a) and (4d), the property of being ecstatic/ten feet tall/ ravenous or delighted is attributed to the sentence’s subject (Stephen), while in (4b) and (4c) properties are attributed to the sentence’s objects: in (4b) the property of being dead is attributed to the Nazis, and in (4c) the property of being empty is attributed to the glass. This creates a serious problem if we want to define verbs as predicators, since what the sentences in (4) show is that not all predicators are verbs. If we’re planning to identify verbs with the class of predicators, the (4) examples show that this will also include ecstatic, ten feet tall, ravenous, dead and empty as verbs – a consequence we must avoid, since these words aren’t verbs on anyone’s criterion!
Can we do anything about this? Perhaps we could introduce a contrast between ‘primary’ and ‘secondary’ predicators, and say that primary predicators like those in (2) are verbs, but that secondary predicators like the highlighted words in (4) are not. But how do we define primary predicator? It seems the only obvious way is to say that the primary predicator is the main verb. But this would be circular: since we want to use ‘primary predicator’ as a definition of verb, we can’t use ‘verb’ to define ‘primary predicator’. To do so would be uninformative: it would leave us with no way of identifying either the verbs or the primary predicator in a clause, since we would have to be able to identify each before we could identify the other. (Someone might suggest here that we define primary predicator as something like ‘the only obligatory predicator in a clause’. The problem with this is that the idea of a clause itself depends on the notion ‘verb’, which means that a circularity will once again be introduced.)
There’s one other compelling reason not to identify the notions of ‘verb’ and primary predicator: in some languages, like Warlpiri, nouns can be the primary predicators:

On morphological criteria, mata ‘tired’(which can also mean ‘lame’) is a noun in Warlpiri (as seen in Table 9.1 above, there is no separate adjective category), yet in this sentence it is the only possible primary predicator.
The upshot of this dispiriting situation is this. We have to conclude that verbs can’t be usefully defined as the class of (primary) predicators in a language: to define them in this way only gives the appearance of a definition, and does not actually get us anywhere.