There seem to be several philosophers who believe science (plus human norms for Sellars) can in principle leave no unanswered questions about reality. I would call this finite or exhaustible.
"In the dimension of describing and explaining the world, science is the measure of all things, of what is that it is, and of what is not that it is not"*
Is describing and explaining the world through science everything to Sellars though? No
"he does not believe that describing and explaining are the only significant dimensions of human activity"
"Sellars would never hold that all our questions are to be settled by scientific investigations."
But the normative nature of the mind, meaning, and language can be reconciled and united with science, elimating all dualism.
"His philosophy of mind abandons many of the assumptions taken for granted by the Cartesian tradition (e.g., the transparent or self-intimating nature of the mental), moving towards a naturalism that respects the normative dimension of mind."
"his own call for a “synoptic vision” that unites a science-generated picture of empirical reality with “the language of community and individual intentions”
"Sellars calls for a stereoscopic vision in which the descriptive resources of the sciences are united with the language of individual and community intentions and the dualism of the manifest and scientific images is transcended."
So in summary: I take Sellars to mean science+norms of language and meaning will transcend all dualisms, giving an exhaustible account of reality. In as much as we understand anything, "it rained" -> "the road is wet"; "the ball is red" -> "the ball is colored", we can understand everything.
"Since science in principle can say all that can be said, there is no unanswerable question left. But though there is no theoretical question left, there is still the common human emotional experience, which is sometimes disturbing for special psychological reasons."
I take Carnap to mean, science can answer all questions (unlike Sellars), but the nature of the human psyche may make certain realizations hard to accept (e.g. emotionally, spiritually).
So to me Sellars and Carnap seem to say an exhaustible understanding of all of reality is possible. What I would like to know (1) is this a fair depiction of their stances (2) how do mathematical objects that suggest inexhaustibility such as, no highest real number, non-computable numbers existing but never "known", Godel incompleteness, halting problem, fit in with the above? The only way I can make them fit is a nominal or fictionalist account, where there really aren't inexhaustible objects. They are limited to and by human activity, e.g. there is the highest real number, the highest one a human ever writes down or uses in a proof.