Is this from Descartes "Meditations?" If so, remember, that Descartes is trying to find true knowledge. He's trying to separate the world into things which only *seem* to be true, and those things that actually *are* true. How can you do that? How can you separate real knowledge from things that seem to be, but aren't real knowledge. The way, for Descartes, is to reject any idea (or opinion) which could be "doubted". For example: I can doubt (deny) the fact that the Greek god Zeus rules the world from Mount Olympus. I can't deny (or doubt), that 2 + 2 = 4. So, any opinion could be open to doubt, he's going to label it (reject it) as false. And as a result of this process, he hopes to find some opinion that is not capable of being doubted (indubitable). This undeniable, or undoubtable opinion/fact must be true knowledge. Of course, if that paragraph wasn't from the Meditations, that answer will probably be wrong :o)

The author wishes to categorize all opinions into "entirely indubitable" (100% true; cannot be doubted) and "downright false" (100% untrue; which he categorizes as anything which is not 100% true). His purpose is to discover whether there exist any opinions which cannot be doubted ("indubitable beliefs"). It sounds like a satire of the age-old debate between science and religion. It is also a rather old or "elevated" style of English, which you can detect partly by the use of "after so doing" instead of the more-modern phrase "after doing so".

2. in the Fifth line---correction