In studying the philosophy of Objectivism, I learned that existence exists and that it is governed by the laws of identity and causality. The law of identity, A is A, things are what they are, means that all things have a specific nature and will behave according to that nature and that this nature represents the context in which it exists. What I understand from this then is that reality itself is contextual.
Since reality is contextual, this in turn means that our knowledge of reality, to be true, that is, to correspond to reality, must also be contextual.
"Concepts are not and cannot be formed in a vacuum; they are formed in a context; the process of conceptualization consists of observing the differences and similarities of the existents within the field of one’s awareness (and organizing them into concepts accordingly). From a child’s grasp of the simplest concept integrating a group of perceptually given concretes, to a scientist’s grasp of the most complex abstractions integrating long conceptual chains—all conceptualization is a contextual process; the context is the entire field of a mind’s awareness or knowledge at any level of its cognitive development." (Introduction to Objectivist Epistemology p.55)This understanding has helped me to see that out of context statements cannot be trusted as knowledge. For example, 'All swans are white' is an out of context proposition and is refuted with the discovery of a colored swan. But the statement 'All swans known to me (within my field of awareness) are white' is contextual and is not refuted with the discovery of a colored swan. In this case the context of my knowledge has expanded to include colored swans. This new expanded knowledge does not contradict or refute my former knowledge that 'All swans known to me are white.' Expansion of previous knowledge is not a contradiction of it.
In terms of certainty then, it was proper for me to be certain of both of my propositions since they both met the requirement of contextuality. Context however, is not the only requirement for certainty. Just as in the categories of 'possible' and 'probable' knowledge, there must be some evidence in support of the proposition, so it is with certainty. but with certainty, all the available evidence must be in support of the proposition. There can be no contrary evidence. If there is some contrary evidence then certainty cannot be claimed.
There is the argument that as long as it's possible to be wrong one cannot claim certainty. But Objectivism has helped me to understand that this is the argument from infallibility and is false. The possibility of error is not evidence of it. Such an argument is just another example of the arbitrary which, per post #4, is always meaningless and is to be dismissed out of hand.
So, this then is something I can add to my always allow list, at least for consideration, 'propositions that are contextual' and the fifth way that Objectivism has benefited me.