narrow and vague are not mutually exclusive contradictory concepts..i am not therefore saying "direct" as a concept is "A" and also not "A" at the same time.

ur definitions of vague and narrow arent in keeping with mine.

1) narrow - Barely sufficient.

narrow - definition of narrow by the Free Online Dictionary, Thesaurus and Encyclopedia.

2) vague - Not clear in meaning or application. Indistinctly felt, perceived, understood, or recalled.

vague - definition of vague by the Free Online Dictionary, Thesaurus and Encyclopedia.

1 causes 2. the law of the excluded middle is in no way breached. if ur about to say im being selective in my definitions i could just as easily same the same to u, however i refer u to the above websites as references.

the real point remains that ur definition is lacking..ur equation simply does not fully define this none scientific term. im sure u agree.