What is certainty? Does it come in amounts or degrees, or is it a matter of being certain or uncertain? How does it differ from feeling confident? What is the purpose or value of certainty (or of more certainty)? How is it to be used in decision making?
Can there be contradicting certainty? Like one is pretty certain of an idea, but also pretty certain of a contradicting idea? Would he then weigh which one he's more certain of? I bring that kind of approach up because it's a common view and maybe saying how Objectivism differs from it, or not, would help clarify things.
Is certainty an Objectivist word for knowledge? How does contextual certainty differ from knowledge?
Edit OPAR speaks of a continuum:
In these cases, the validation of an idea is gradual; one accumulates evidence step by step, moving from ignorance to knowledge through a continuum of transitional states. The main divisions of this continuum (including its terminus) are identified by three concepts: “possible,” “probable,” and “certain.”
But explains certainty:
A conclusion is “certain” when the evidence in its favor is conclusive; i.e., when it has been logically validated. At this stage, one has gone beyond “substantial” evidence. Rather, the total of the available evidence points in a single direction, and this evidence fulfills the standard of proof. In such a context, there is nothing to suggest even the possibility of another interpretation.
This indicates certainty doesn't come in degrees because it's when ALL the evidence goes one way.
To reconcile these, is the idea that "certain" is the endpoint on the continuum, and does not come in degrees? (Whereas probable and possible have different degrees. And the other endpoint, arbitrary, doesn't come in degrees?)
This exact question is answered directly in The Ayn Rand Lexicon under the topic of "Certainty." The opening excerpt describes the "strength" of a conclusion as being possible, probable, or certain. The excerpt also poins out:
All the main attacks on certainty depend on evading its contextual character.... Knowledge is contextual—it is knowledge, it is valid, contextually.
Further discussion can be found in OPAR, Chap. 5 ("Reason"), subsection titled "Certainty as Contextual" (pp. 171-181).
The next Lexicon excerpt mentions (and rejects) infallibility.
The final excerpt explores additional implications of rejecting certainty.
There is also a separate Lexicon topic on "Possible."
Update: Degrees of Certainty
In response to a comment by the questioner, my understanding is that "certainty" and "certain" aren't the same in the Objectivist view. "Certainty" is a continuum; "certain" is the final, fully validated degree of "certainty."
Regarding the relation between "certainty" and knowledge, my understanding is that it depends on exactly what is being claimed as knowledge. If a claim that is only possible or probable is being claimed to be certain, then it can't be considered as knowledge; one can't claim to "know," with certainty, something that one does not know with certainty. One can validly claim, however, to know that there is some evidence supporting a claim or hypothesis and none refuting it, or that there is a great but not-yet-conclusive weight of evidence for it (and none against it). Evidence is evidence and does not cease to exist simply because it isn't yet conclusive. One can certainly know (with certainty) that evidence exists, if one acquires that knowledge (of evidence) by valid rational means.