Rather than continuing the discussion about quadrupel in the travel to Belgium thread, I think it would be better to give it its own thread.
The Trappists fled to Belgium during the French Revolution when monasteries were taken over and eventually all religious orders were dissolved. The name Trappist, btw, comes from the French town of La Trappe.
After settling in Belgium, the Trappists did not offer beer for sale until the middle 19th century. Some had built small breweries to make beer for the monks consumption, but this beer was not intended for sale.
The first record of a beer sale was 1 June 1861 at Westmalle. It was for a barrel of beer. This barrel contained 300 liters of beer (a huge amount) and is believed to represent the full output of the brewery. A record from 1868 shows that the brewery produced 35-40 barrels of that size per year.
And that is how commercial brewing began at the Trappist monasteries in Belgium. The beer brewed in 1861 at Westmalle was not the same as the beer drunk by the monks (which they began making in 1836).
The Trappists were Catholics. They believed in the Father, Son and Holy Spirit. The Holy Trinity. Not the Holy Quadrupel.
There is no mystery of how the beers got their 'names' (enkel, dubbel, tripel or single, double, triple). As time past, some of the Trappists introduced a second beer and then, in 1934 Westmalle introduced what at the time was called "Superbier". In 1956, that beer was modified and given the name Tripel.
And so, the Holy Trinity of beer was complete. And has remained complete since then.
There is indeed a beer named Quadrupel sold by a Trappist monastery in the Netherlands called 'Onze Lieve Vrouw van Koningshoeven.' That monastery has a line of beers called La Trappe, named, of course, after the French town where the order began.
Unlike the Belgian Trappists, the Dutch are far more commercial. While no Belgian monastery makes more than three beers, Koningshoeven makes nine, including beers called Quadrupel and a second beer called Quadrupel Oak Aged (yes, in English). They also make a Bock beer. And earlier in the 20th century, they also offered soft drinks and other products.
It is perhaps not well known outside Europe, but Koningshoeven was removed from the Trappist brewing association for several years around the year 2000 for letting commercial brewers make their beers without any influence from the monks. Their beers are still made by the Dutch commercial brewer called Bavaria, but, in keeping with the rules of the Trappist association, it is said a monk now plays a more active roll.
It is, I suspect, the Quadrupel made by Koningshoeven that is now mistaken as being a sort of beer made by the other Trappist breweries in Belgium. That is not the case. The last time a new beer was added to the Belgian monasteries output was 1934 when the Tripel (not with that name) was born.
Since the Dutch monastery introduced the Quadrupel (I believe after the year 2000), not a single monastery in Belgium has changed their line. And no other monastery in Europe has adopted the name since the Catholic church is founded upon the idea of the Holy Trinity. Not the Holy Quadrupel.
As many of you can imagine, monastery life has changed considerably from the middle ages. Religion is no longer mandatory and, as a result, the monasteries in this part of Europe are having considerable trouble attracting new members. I believe at one point not very long ago, the monastery at Koningshoeven had only six monks left (and not all Europeans). I don't know how many there are now.