I'm recycling this old question in hopes this mustard-yellow flair will make it get a great answer! (I have been researching Caffarelli's presence at this event since I posted that but I still don't know much about how he escaped, only discovered he and another big castrato who was in Lisbon then have had their stories mushed together in secondary sources a couple of times!)
Wikipedia has this to say on the 1755 Lisbon Earthquake:
The event was widely discussed and dwelt upon by European Enlightenment philosophers, and inspired major developments in theodicy and in the philosophy of the sublime.
However the explanatory paragraphs are rather vague. There some talk of Candide and such but nothing really meriting the term "major developments." Anyone have the deeper picture on this earthquake's effects on European beliefs?
I'm not well versed in the matter, but I can tell you more than that puny paragraph: there was a theological debate over how such great calamities could be reconciled with the good nature of God, and many philosophers took the chance to introduce satirical remarks about those who still held that belief. I'm sorry I can't tell you much more, since that's pretty much all I know about it. I have an edition of Candide lying around somewhere that has a good introduction to the topic, but I'm afraid I can't find it.
EDIT: Found it. According to this little study, it was a debate about the existence of evil in general, since most thinkers, as believers and philosophers, had trouble reconciling these premises:
1.- God is good. 2.- God is omnipotent and omniscient. 3.- There is evil.
One of the presmises had to be false, so different interpretations came about, and apparently, the mainstream proposition at the time was to deny or at least significantly alter the third premise, and ended up concluding that we "live in the best possible world, the most optimal". On the other hand, some others, like Pierre Bayle ended up rejecting the terms of the contradiction itself, and claiming that it was just a mystery of religion. The other, more drastic solution, was to deny either of the first premises, but that didn't take off until the revolutionary radicalism of the late 18th century and first half of the 19th.
Leibniz was one of the most fervent promoters of the optimism that considered this the best possible world, and openly debated Bayle on it, and the poet Pope also seemed to be of that opinion, with his verse "Whatever is, is right". Voltaire, for his part, seems to have also been an optimist, albeit a moderate one (based on Le Mondain), until 1755, when the earthquake hit Lisbon, although the 1746 earthquake in Lima, Peru, already ignited the debate. Voltaire´s other work Poéme sur le désastre de Lisbonne is an even more visceral decrial of outrage, and, according to this edition I'm reading, Voltaire, along with popular opinion, quickly drifted from the previous mild optimism to an admission of incompetence to judge the matter.
Source: Voltaire, Cándido y otros cuentos. Madrid, Alianza Editorial, 2013. Notes and epilogue by Guillermo Graíño Ferrer.
To add just a bit, the Lisbon earthquake contributed to a chain of events leading to the suppression of the Jesuit order and a diaspora of educated Jesuits. The prominent Jesuit Gabriel Malagrida used his pulpit to criticize the government response to the earthquake, managed by the Marquis de Pombal, the Portuguese Prime Minister. Pombal answered by trying to implicate Malagrida in an assassination attempt against the king, which was probably just a botched highway robbery. For three years Pombal failed to secure a favorable judgment, until he maneuvered the case into his brother's court. Malagrida's alleged guilt gave Pombal enough leverage to force the king to expel the Jesuits and repossess their properties in 1759, and in the end, Malagrida was executed in an Auto de Fe of the Inquisition in 1761.
The following year, a French court followed suit using a legal pretext to distrain all Jesuit properties throughout the empire, and parties including Voltaire eventually forced a royal edict suppressing the order in 1764. The Bourbon monarchs of Spain joined ranks, expelling the order in 1767, and they eventually pressured an accommodating pope into suppressing the order as a whole in 1773.
The order did not disappear, however, but rather repositioned. Jesuits in exile found that Catholic countries would not receive them (including the Papal States), so they sought refuge elsewhere. German princes, the Russian czars, and soon the young American republic provided safe haven. Although the order itself dwindled during these years (until its re-establishment following the Napoleonic Wars and the Congress of Vienna), these Jesuits in exile provided areas on the peripheries of the Enlightenment with Enlightenment-trained educators. Perhaps the most prominent such exile was John Carroll, a British-American who had been studying in Europe. After being expelled back to Maryland in 1773, he founded Georgetown University and became the first Catholic Bishop of the United States.
Sadly I don't have any sources on hand to refer you to, but some relevant research can be found here.