“Web(s) of belief” ≡ “web”
“Object(s) of belief” ≡ “oob”
The justification of the web of belief
A web is more or less justified. The justification of a web is a function of its members in many ways. Here are some ways that I speculate may increase the justification of a web. I do not pretend to offer much argumentation for my thoughts or much certainty in the conclusions. It seems to me that it is extremely hard to have any strong evidence the beliefs about these matters. That shall not keep me from examining the matter and giving my intuitions.
The number of beliefs in a web
Imagine a web with only two beliefs whose oob logically implied each other. Think of any two logically equivalent propositions. The interconnectedness of that web is extremely high since logical implication is one of the strongest relations two oob can stand in (see below) and all the members are connected to each other by logical implication. But still it seems to me that such a web is not very justified. I suggest that we explain that by the number of beliefs in the web. If a person with the aforementioned web gave an argument to another person, the other person would (and should) respond that it is circular. It seems to me that we cannot avoid circularity in our justification (because of the infinite regress argument and that epistemic foundationalism and epistemic infinitism is false). However circularity is not much of a problem when the web contains many thousand belief as it does of any grown-up human.
The number of relations of certain kinds between the oob
The oob are truth carriers. (Just substitute your favorite truth carrier be it propositions, sentences, beliefs etc.)
We may distinguish between three kinds of relations between the oob: (1) positive relations, these are the relations that increase the justification of a web as a function of their number, and the justification of a web is partial function of the positive relations between oob, (2) negative relations, which is the opposite of positive relations; they decrease the justification of a web, (3) neutral relations, relations that have no effect on the justification of a web. We may note that this distinction is true regardless of the distribution of relations in the three categories.
Then we ask ourselves: Which relations are positive relations? Deductive relations such as (for all x, and for all y) “x logically implies y”, “x materially implies y” come to mind. Inductive relations such as “x is explained by y”, and “x gives good reason to believe y”, “x is best explained by y” seem to me to increase the justification of a web.
Similarly, which are negative relations? Basically the same of the above just with the added change that it is the negation of y. If you believe two things, and the one logically implies the negation of the other, you have an inconsistent web. It is impossible for all the oob to be true at the same time in a such web.
That a web has at least two beliefs whose oob are inconsistent does not imply that the justification of the web is zero. To see this we should simply recall that all grown-ups have inconsistent oob and that not all web of grown-ups have an equal level of justification. Hence, it is not the case that if a web contains beliefs whose oob are inconsistent, then the justification of that web is zero. Since if it was the case, then web of all grown-ups would be equally justified, all having zero justification. However, it is still the case that such inconsistent oob reduce the justification of a web, which I why we ought to change our mind when we discover that we hold beliefs whose oob are inconsistent.
I can’t think of any neutral relation, but they are not very relevant anyway, so lets disregard an example of a such. There may be no such relation for all I know.
I mentioned this in passing above but it deserves elaboration. The justification of a web is also a partial function of the interconnectedness of a web. If a web consisted of a thousand beliefs but that these were divided into 10 groups of beliefs each of whose oob did not have any positive relations with the oob of the other groups of belief, then it seems to me that the justification of that web would be very low. This seems best explainable by justification being a partial function of interconnectedness too.