Later writers, such as Diogenes Laërtius who cite Aristotle as the earliest source, say that Socrates had a second wife called Myrto .  Plutarch tells of a similar story, reporting that it comes from a work entitled On Good Birth , but he expresses doubt as to whether it was written by Aristotle.  In Plutarch's version of the story, Socrates, who was already married, attended to Myrto's financial concerns when she became a widow; this does not entail marriage. We have no more reliable evidence on this issue. 
The first query seems to be the more historically apt query, . that the word 'philosopher' was invented [came before] the word 'philosophy', that, according to both Plato and Diogenes Laertius (about Pythagoras), the original point was to distinguish between a "wise man" and "the man who, although himself not wise, ardently desired ["love"] to become wise". And the assignment of a subject matter and naming that subject 'Philosophy' came later, because that required that it be asked "wisdom about what is being sought?", because the Greeks called all knowledge wisdom (including the craftsman's knowledge of his craft), and philosophy is not knowledge about just anything (as Plato points out in Republic 475c-d). If a philosopher was one who loved wisdom, then what he sought was wisdom (Philosophy itself is not wisdom, but only the search for, "love", of wisdom).
[Mill] claimed that mathematical truths were merely very highly confirmed generalizations from experience; mathematical inference, generally conceived as deductive [and a priori ] in nature, Mill set down as founded on induction. Thus, in Mill's philosophy there was no real place for knowledge based on relations of ideas. In his view logical and mathematical necessity is psychological; we are merely unable to conceive any other possibilities than those which logical and mathematical propositions assert. This is perhaps the most extreme version of empiricism known, but it has not found many defenders. ( Macmillan Encyclopedia of Philosophy Vol. 2 (1969), 503).