He traveled extensively, and became a proficient linguist, acquiring a knowledge of French, German, Italian, Spanish, Greek, Latin, and Arabic.

For studying the Catholic Church, unusual opportunities were thrown open to him, chiefly through the Princess Carolyne zu Sayn-Wittgenstein and Cardinal Hohenlohe, who offered him an apartment in his episcopal palace at Albano, and also in the Villa d'Este at Tivoli.

Here he produced the work that first brought Rosmini to the notice of English-speaking students: The Philosophical System of Antonio Rosmini-Serbati, translated, with a Sketch of the Author's Life, Bibliography, Introduction, and Notes (London, 1882).

Davidson was a frequent contributor to periodicals, and delivered courses of lectures, before the Lowell Institute in Boston and elsewhere, on modern Greece, on Greek sculpture, etc.

[1] Davidson's most successful work was in connection with the Educational Alliance in New York, where he attained wide popularity by a series of lectures on sociology.

A special class was formed for Jewish young men and women, whom he introduced to the great writers on sociology and their problems.

[3] Though initially a panentheist, Davidson's studies in Domodossola—including the work of the Italian Renaissance philosopher Giordano Bruno, Leibniz, Kant, and Rosmini—led him to a panpsychistic monadology, a theory that reality consists of an infinite number of mental or spiritual substances, each with an Aristotelian telos.

This allowed Davidson to reject pantheism, which, he reasoned, led to a God "scattered through the universe...so that the total Absolute exists only in the sum of things taken together."