Parece mentira que haya tanta vida en este lugar. ¡Qué felicidad!
It's unbelievable that there's so much life in this place. So much happiness!
Captions 11-12, Café Tacuba - MediodíaPlay Caption
One of the first Spanish words we learn is hay, that odd but ever so useful incarnation of the verb haber that means both "there is" and "there are." Hay dos gatos ("there are two cats"), hay una casa ("there is a house"). Wow, what a simple language!
And then somewhere along the line they told us about the subjunctive, where, even though the there's usually no difference in English, the verb in Spanish is completely different if there exists any sense of uncertainty or doubt. Wow, this might be an impossible language!
Well, haya is where our friend hay meets our nemesis, the subjunctive. Like hay, haya also means "there is / there are", but it is used when the subjunctive is called for. Café Tacuba introduces doubt when it begins the lyric above with "It seems impossible" (Parece mentira- literally "It seems like a lie") so that the phrase that follows utilizes haya instead of hay.
"It seems impossible that there is so much life in this place. What happiness!"
In De consumidor a persona we find a discussion of "Fair Trade" commerce in which haya is used to express possibilities (not certainties):
Que no haya explotación infantil, que haya igualdad entre hombres y mujeres...
That there is no child exploitation, that there is equality between men and women...
Captions 36-37, De consumidor a persona - Short Film - Part 5Play Caption