I wonder if this suggestion is Wittgensteinian at heart or whether it just seeks an agreed upon justification methodology. That is, would it be incompatible for someone who held meaning is attached to private states to demand an agreed upon methodology as you have here. And contrawise, would it be non-Wittgensteinian to allow for subjectively based justifications? I would think not so long as the meaning was tied to use such that the community of speakers could follow how the term was used and engage in the practice.
So what this boils down to is how to avoid Gettier cases, which do seem to arise from reasonable evaluations based upon incomplete knowledge. Your idea seems straightforward: force a community based standard for what constitutes a justification to avoid poor reasoning and perhaps require deeper investigation before declaring "knowledge."
If you tell me you're coming to my house, I see a blue jeep coming toward my house, you own a blue jeep, I say I know you're on the way, and you then arrive moments later to my house, we can say that I had knowledge of your arrival of the JTB variety. But then we learn it wasn't your jeep I saw and you took the bus, now we have a broken J, and a Gettier problem.
If you mean to add to the J methodology a stricter confirmation of all facts to avoid sloppier individualized justifications, that could be a solution, but I ask why that invokes Wittgensteinian other than perhaps reference to community involvement, but, as noted, the community could still use the word justification to mean whatever it decided without concern for avoiding Gettier.
That is, Wittgenstein wouldn't care whether a term were more useful. He'd only insist it's meaning were derived from use. — Hanover
I do think the framing is Wittgensteinian, but not because it appeals to “community agreement” as if justification were whatever a group votes into existence. The Wittgensteinian point I'm borrowing is about grammar: what makes a claim of justification intelligible is that it's answerable to standards of correct and incorrect application, and those standards are exhibited in a practice, in how we check, correct, and withdraw claims when error signals appear.
On “private meaning,” I'd put it this way. A person can have private experiences, and can have subjective certainty, but if the meaning of the terms involved were tied only to private states, then the distinction between correct and incorrect use would collapse. You could still demand an “agreed methodology,” but it would be unstable, because there would be no shared criteria to tell whether the methodology was actually being followed or merely seemed to be. That's why, in my framework, justification is not a private experience. It is practice-governed standing, and it is “objective” in the modest sense that the criteria for support, error, defeat, and correction can, in principle, be stated and applied within the practice. This is not consensus, not social permission, and not institutional authority, it is answerability to criteria.
That doesn't make subjectively based justification illegitimate. It means that subjective support has to be connected to use and to criteria that others can follow. If I say “I see blue,” or “I remember,” those are first-person claims, but they still live inside practices with mistake-conditions and correction, misperception, lighting, memory distortion, and so on. I'm not excluding subjective sources. I'm saying that their justificatory standing depends on how they are embedded in standards of assessment.
Now to Gettier. I'm not trying to avoid Gettier by requiring stricter confirmation of all facts. That would be impossible and it would smuggle in an infallibilist demand. The point is different: Gettier cases arise because we treat “seems justified” as if it were the same as having justificatory standing. In your blue-jeep example, what fails is not simply that you lacked a further fact, it is that the apparent support was not connected in the right way to the truth-maker, and the route is lucky. The practice would normally treat that as a fragile inference, and it would tighten the standards when the stakes are higher.
My proposal is not “let the community define justification however it likes.” It's: if we are using the word “justification” at all, we are already committed to certain constraints, no false grounds, practice safety, and defeater sensitivity, because those constraints are built into how justificatory talk functions in our life. Wittgenstein would not tell us to adopt a more useful vocabulary, but he would help us see what our vocabulary already commits us to when we use it.
If you want a one sentence summary: the Wittgensteinian element is not communal voting, it is the insistence that justification has a grammar of correct use and correction, and once we make that explicit, many Gettier intuitions are revealed as cases where the support was only apparent.