Grice and Meinong on the 'intentionality' behind "Pegasus"

From M. R's, online 'nonexistent objects', in Stanford Encyclopedia:

"Austrian philosopher Alexius Meinong (1853–1920). Therefore, it is appropriate to give an outline of the basic principles of and motives behind this theory. Meinong was concerned about the problem of intentional states which are not directed at anything existent. The starting point of this problem is the so-called “principle of intentionality”, which says that mental phenomena are characterized by an “intentional directedness” towards an object. For instance, to love is always to love something, to imagine is always to imagine something, and so forth. In other words, every intentional act is “about” something. The problem is that sometimes people imagine, desire or fear something that does not exist. Some people fear the devil, although the devil doesn't exist. Many people hope for peace in the Middle East. But there is no peace in the Middle East. Ponce the Leon searched for the fountain of youth, even though it doesn't exist. It is easy to imagine a golden mountain, even if no such thing exists. Cases like these seem to be clear counterexamples to the principle of intentionality. However, many philosophers found this principle too appealing to be given up completely. While some came to the conclusion that intentionality is not a real relation and therefore does not require the existence of an object (see, for instance, Brentano 1874, Searle 1983), Meinong offered another solution: there is indeed an object for every mental state whatsoever—if not an existent then at least a nonexistent one.[3] The problem of intentionality may still count as one of the most important motivations for thinking there are nonexistent objects. But there are other motivations as well."