The Greek word, pistus or one of its cognates is used for "believe" in the NT. There was a different Greek word used for "to know" which was a mere intellectual grasp of a concept. (I forget what it is at the moment.) In any case, pistus implied a heartfelt desire to follow the object of faith (a deity of some sort) and to do as he/she did. Those who don't follow Christ in their behavior (i.e. they are grossly sinful) should be worried that they are not in the faith at all.
I don't think that a person who could tread on the Blood of Jesus in that way, is saved at all and never was. 1 John gives us that criteria because John notes that those who "went out" were not believers in the first place.
John was speaking about gnostics.
They had already invaded the church...he wrote his epistles late...maybe about 80 or 85 AD. The word you might be thinking of, in fact, is gnosis...to know.
You'll find that unbelief has the connotation of disobedience in the word...so we can know that to believe means to obey, as your description above states. To believe, to be a disciple, to do as we are taught.
You can believe that the person was never saved to begin with..
I just don't see how we could go against scripture to come to this conclusion.
Jesus Himself said that some are saved temporarily and then they fall away.
Luke 8:13 HE said they BELIEVED, which is necessary for salvation,,,,TEMPORARILY. And THEN,,they fell away...FROM WHAT?
Hebrews has 10:39 stating that "we are not those that shrink back to destruction",,,
doesn't this mean that some had shrunken back to destruction?
What about 2 Timothy 4:7 ? Paul said that he had KEPT THE FAITH.