Truth is not a type of belief. — Banno
Amusing.
To continue, the difference between a Peircean and Wittgensteinian epistemology - or at least Banno's understanding of one - looks to hinge on two key issues.
First, Banno is concerned to make truth a property of propositions. So this is the philosophy of language view that reality is some totality of statements. For all practical purposes - ie: the pragmatism that eschews mysticism and unwarranted skepticism - existence or experience reduces to a collection of all that is stateable or sayable.
This stance in itself conflates all forms of language, confusing the difference between the strict and explicit grammars that constitute "logical speech" with the much looser and socially-oriented language that we use in ordinary, not explicitly metaphysical, everyday speech.
Peirce then makes truth a property of semiosis. This is a general method of reasoning that goes even beyond language. Animal brains and animal bodies reason semiotically - they are in a pragmatic sign relation with their world. Human language - both social and logical - are then merely the same semiotic game being played out at higher levels of development.
So Banno wants to deal with a reality imagined as some totality of true statements. And this seems to be what hinge propositions is about. For the door to swing, it must be anchored to something background that doesn't. To keep the linguistic turn going, that background also needs to be understood as some collection of propositions. It becomes propositions all the way down - even if we understand the practical impossibility of cashing out all that background supposition as confirmed true fact.
Peirce, on the other hand, takes the evolutionary approach as revealed by biological and psychological science. He sees the continuity of semiosis that underlies the development of the mind. If there is a hinge that gets swung on, it is the way that logical claims get hung on the bedrock certainty of our general perceptual living in a world. It is the animal level of cognition, the modelling of a biological self in pragmatic interaction with an environment, that is the anchor of our epistemology. We start from that as our primal facts.
So Banno's Wittgenstein has a problem that there is no proper cut-off. If it is propositions all the way down, then any kind of primal certainty has no starting point. But the Peircean view distinguishes grades of semiosis. So a lower grade can be the bedrock for a higher grade. There is an underlying continuity of course, but also a natural cut-off point. And waving his mitts about, that was what Moore would have been hoping to demonstrate.
Then a second key point of difference is that Peirce introduces a further category of epistemology - the vague.
Banno's Wittgenstein is committed to an epistemology of the statable or sayable. And especially when formulated in the language of logic, this is a presumption that only the crisp or definite - the counterfactual - gains admittance to the party.
Now the demand that statements be crisp is an excellent pragmatic maxim. It is the right goal. It is really useful - if you want to analyse reality into some set of answerable facts - for the laws of thought to apply.
However, it is the ideal. And vagueness is then the more primal or foundational condition. Peircean semiotics recognises and builds on that fact. Banno's Wittgenstein can't admit to it as otherwise the whole pretence of a philosophy of language derived theory of truth falls flat like a house of cards.
So again, with hinge propositions, the actual backdrop of belief to which particular propositions are hinged, is usually unanalysed. It is just a congealed mass of ecologically-valid belief or habit so far as our language use is concerned. It is our biological self - the animal self that knows and believes the ecological truth of its world.
Now we can get stuck into that congealed mass and analyse it propositionally. We can break it down linguistically. But it isn't already a collection of facts just waiting to be found. And being knowledge of a constitutionally vaguer kind, much of what it might have to say is going to elude any saying in being ... essentially vaguer. It will just resist full analysis. Although, again, there is no harm in doing our best.
So we can have truth as a property of logical propositions - certain formulas of words.
We can have truth as the report of commonsense experience - the beliefs that seem rooted in our ecologically-validated perceptions.
Or we can have truth in the Peircean sense as the common limit on a process of rational inquiry. We can have truth as the pragmatic fruit of semiosis - an understanding of epistemic mechanism that spans all the natural levels of "knowing", and also distinguishes these levels in terms of their being rooted in a foundational vagueness, and aspiring to an ideal of generality and counterfactual definiteness.