There are many possibilities, with varying degrees of believability.
Experiences of unlove are to them unbelievable and point, fundamentally and finally, to the necessity and believability of love.
Old English belyfan "to believe," earlier geleafa (Mercian), gelefa (Northumbrian), gelyfan (West Saxon) "believe," from Proto-Germanic *ga-laubjan "to believe," perhaps literally "hold dear, love" (cf. Old Saxon gilobian "believe," Dutch geloven, Old High German gilouben, German glauben), ultimately a compound based on PIE *leubh- "to care, desire, love" (see belief).
Spelling beleeve is common till 17c.; then altered, perhaps by influence of relieve, etc. To believe on instead of in was more common in 16c. but now is a peculiarity of theology; believe of also sometimes was used in 17c. Related: Believed (formerly occasionally beleft); believing. Expression believe it or not attested by 1874; Robert Ripley's newspaper cartoon of the same name is from 1918. Emphatic you better believe attested from 1854.