One hears and sees these two adjectives confused with increasing regularity. E.g., in a Dallas, TX news story an attorney is quoted as saying, “It’s incredulous that this lease is being used….”
The word incredible is derived from the Latin incrēdibilis, which means something that is unbelievable or, in some uses, one who is unbelieving. It occurs in the Great Bible (1539) in Acts 26:8, “Why shulde it be thought a thynge incredyble vnto you, that God shuld rayse agayne the deed?” (Oxford English Dictionary). Today we use it routinely in its figurative sense, “That’s an incredible home run!” In that context it is meant to signal hyperbole. Literally, of course, a 500 foot home run is not incredible since we saw a fellow hit one during the most recent MLB home-run contest. It is amazing. It is remarkable. It is impressive but it is not literally incredible. Something that one has not seen or heard, however, might be incredible. The central claim of the Christian faith, namely the bodily resurrection of Jesus the Messiah is incredible to those who have not been born again by the Spirit of God (see John 3) is literally incredible. It is not possible for one to believe unless he has been born again or born from above.
Looking for an alternative, it has become popular to substitute the related adjective incredulous for incredible. The two words overlap but they are distinct in modern usage. Credulitas also derives from Latin. It signals in Latin about the same thing credulity signals in English, an easiness of belief. Incredulity, then, is a resistance to belief. What the Dallas area lawyer wanted to say was, “I am incredulous” or “it is incredible” but not “it is incredulous…”.
A person who is incredulous is a person who is in a state of disbelief. “I am incredulous of the hourly rate charged by lawyers.” Again, this is an example of hyperbole. The rate is a matter of fact. In this usage it is synonymous with amazed, stunned (as in “stunned disbelief”) or in the UK, “gobsmacked.” One might also use shocked or amazed in the same context to a similar effect.
One caveat to the distinction I am urging: The OED does give seventeenth- and eighteenth-century instances where incredulous was used in the same way we use incredible today. I am incredulous, however, toward the claim that this sense is making a comeback by intentional usage. Such a claim seems incredible to me. Rather, it seems as if they are being confused.