I disagree with your definition here because you are using some kind of evidence (your experience that he is trustworthy, or that people don't usually lie about their names) to evaluate whether one is telling the truth. Properly basic beliefs are those which are accepted without any evidence provided. See my examples above.
But did you see post #26? Would you car to share how you would alter p1 in order to make the argument sound?
I am disagreeing with your examples, as they are not basic beliefs. The propositions I provided are meant to show that statements like "His name is Steve" are derived beliefs, not basic. They are derived from something, namely, an accepted belief that said person is trustworthy and currently not lying to you. Basic beliefs are usually ones that are incorrigible, though, honestly, there is probably a fallibilist foundationalism that works without incorrigible basic beliefs. However, there is another point I think you are missing. An accepted basic belief must also be epistemically justified; it cannot be just any proposition that is not derived from something, but one we are justified in holding. Merely assuming something to be the case, without a good justification, leads to problems, as you cannot actually make knowledge claims. And since the purpose of this thread relates to knowledge claims, it does serve as a good point to lack actual basic beliefs. Given the nature of things like "logical arguments" in the premise, I assume you do not want to include unjustified assumptions some like to call "basic beliefs"
There is a difference between accepting a proposition and believing a proposition. Beliefs, at least to the extent in which we come to have them, are involuntary. I could not really switch my belief via willpower. What we do have voluntary control over is our decision making in terms of how we can interact with possible evidence, like choosing to do research. We, therefore, have indirect control over our beliefs. The fact remains, however, that we can only be moved by evidence to form belief.
However, there is voluntary accepting a proposition. By this, I mean we hold the proposition as true when we perform actions and when we are considering premises for discussions. This is different than merely believing a proposition, though this fact is often overlooked because the two are often connected to one another. To use the name example, consider a Person X who we are going to meet. We ask our friend who is taking us to go see Person X to tell us X's name. Our friend informs us that his actual first name is embarrassing- so embarrassing, in fact, that Person X does not even acknowledge that as his name in most social settings. Therefore, our friend tells us we should call Person X "Steve". Therefore, we have the proposition "Person X's name is Steve." I do not actually believe this proposition; in fact, I know it is false. However, I accept the proposition. When I act, I hold the proposition as true. I will call Person X Steve. I will refer to Person X as Steve to other people who do not know him. I will not ask about Person X's real name, because I accept the proposition that says Steve is his real name.
Currently as listed, p1 would appear passable on the surface. However, I find it lacking. First, it does not account for the psychology of the person coloring the outcome of their beliefs. Someone with a massive amount of investment in a particular belief, for example, is more likely to ignore evidence that would lead to the rejection of that belief. Pretty much, we can read a psychology book and see all the biases we carry into a discussion.
Second, when I refer to "evidence", I refer to the totality of a person's experience with a subject matter. It is not just what we would call legal evidence, or basic belief, but rather what they have experienced personally in there day to day lives, anecdotal evidence, incomplete or erroneous arguments, the type of people who make the arguments, the amount of experts who reach a particular conclusion, etc. Note that this list does not require all of these things as a necessity. For example, though we count formal arguments as evidence, a person's unique evidence may not include any.
Therefore, I would reform p1 into "A person forms a belief from the evidence they have experienced, after the evidence first filters through the person's psychological bias and quirks."
This leads me to my main complaint: p1 is worded in a way to make most Christians' belief epistemically justified, even though a person's evidence need not include the things you have brought up. I would say a good portion of people do not actually examine logical arguments, especially anything beyond "word of mouth" arguments. Not everyone's evidence follows a rigorous standard when they gather facts. This is the problem with your argument as it stands. A person's belief in a god does not require logical arguments, nor physical evidence, nor even basic beliefs. It can just as easily be based upon a scenario like this:
Steve hears the proposition "the god of Christianity exists". Steve intuition pulls him to believe this proposition. Furthermore, whenever Steve experiences something related to the proposition, he gets a large amount of positive feelings and emotions. For example, whenever he hears the word "Bible", he becomes much more relaxed and gains a more positive outlook. Based upon his psychology, this is enough for Steve to come to believe the proposition "the god of Christianity exists". His total evidence (intuition, emotion) has moved him to believe the proposition.