speculate v.

late 14c., "intelligent contemplation, consideration; act of looking," from Old French speculacion "close observation, rapt attention," and directly from Late Latin speculationem (nominative speculatio) "contemplation, observation," noun of action from speculatus, past participle of Latin speculari "observe," from specere "to look at, view" (from PIE root *spek- "to observe").

The meaning "pursuit of the truth by means of thinking" is from mid-15c. The disparaging sense of "mere conjecture" is recorded from 1570s. The meaning "buying and selling in search of profit from rise and fall of market value" is recorded from 1774; its short form spec is attested from 1794.

Protestant clergy were at least as bigoted as Catholic ecclesiastics, nevertheless there soon came to be much more liberty of speculation in Protestant than in Catholic countries, because in Protestant countries the clergy had less power. The important aspect of Protestantism was schism, not heresy, for schism led to national Churches were not strong enough to control the lay government. This was wholly a gain, for the Churches, everywhere, opposed as long as they could practically every invention that made for an increase of happiness or knowledge here on earth.  [Bertrand Russell, "A History of Western Philosophy," 1945]

Proto-Indo-European root meaning "to observe."

It forms all or part of: aspect; auspex; auspices; auspicious; bishop; circumspect; conspicuous; despicable; despise; episcopal; especial; espionage; espy; expect; frontispiece; gyroscope; haruspex; horoscope; inspect; inspection; inspector; introspect; introspection; perspective; perspicacious; perspicacity; prospect; prospective; respect; respite; retrospect; scope; -scope; scopophilia; -scopy; skeptic; species; specimen; specious; spectacle; spectacular; spectrum; speculate; speculation; speculum; spice; spy; suspect; suspicion; suspicious; telescope.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit spasati "sees;" Avestan spasyeiti "spies;" Greek skopein "behold, look, consider," skeptesthai "to look at," skopos "watcher, one who watches;" Latin specere "to look at;" Old High German spehhon "to spy," German spähen "to spy."