Socrates was a classical Greek philosopher, and teacher of Plato, who lived during the 5th century BC. During that time, the immortal Flint had known Socrates personally. (TOS: "Plato's Stepchildren", "Requiem for Methuselah")
A holographic simulation of Socrates was among the historical personality profiles studied by The Doctor, in 2373, during his attempt to expand his personality sub-routines. In the simulation Socrates played kal-toh against T'Pau, as The Doctor conducted his interviews with the other historical figures.
When The Doctor's alter-ego, created from the combined 'dark threads' of the sub-routines of these historical figures, began to destabilize his program, he took to altering their sub-routines, to solve his own issues. His "work" was later discovered by Kes, when she found the upper body of the Socrates hologram laying on the holodeck floor. (VOY: "Darkling")