Philosophical Investigations, reading it together. Some relevant passages from Stanley Cavell Claim of Reason, which I've been quoting incessantly, which might be useful here:
On necessity:
"It is not necessary that human beings should have come to engage in anything we would call calculation (inferring, etc.). But if their natural history has brought them to this crossroads, then only certain procedures will count as calculating (inferring, etc.) and only certain forms will allow those activities to proceed. It is not necessary that the members of a group should ever have found pleasure and edification in gathering together to hear the stories of their early history related; but if they do, then only certain kinds of stories, in certain structures, will provide (what we can comprehend as) that pleasure and edification. "There must be agreement not only in definitions but also . . . in judgements. This seems to abolish logic, but does not do so."
In particular, I take it: It is not necessary that we should recognize anything as "logical inference"; but if we do, then only certain procedures will count as drawing such inferences, ones (say) which achieve the universality of agreement, the teachability, and the individual conviction, of the forms of inference we accept as logic. There is no logical explanation of the fact that we (in general, on the whole) will agree that a conclusion has been drawn, a rule applied, an instance to be a member of a class, one line to be a repetition of another (even though it is written lower down, or in another hand or color); but the fact is, those who understand (i.e., can talk logic together) do agree. And the fact is that they agree the way they agree; I mean, the ways they have of agreeing at each point, each step.
... Wittgenstein's view of necessity is, as one would expect, internal to his view of what philosophy is. His philosophy provides, one might say, an anthropological, or even anthropomorphic, view of necessity; and that can be disappointing; as if it is not really necessity which he has given an anthropological view of. As though if the a priori has a history it cannot really be the a priori in question. - "But something can be necessary whatever we happen to take as, or believe to be, necessary." - But that only says that we have a (the) concept of necessity - for it is part of the meaning of that concept that the thing called necessary is beyond our control.
If the wish were not mere father but creator of the deed, we would have no such concept. If upon doing a calculation I could wish, and my wish bring it about, that the figures from which I "started" become altered, if necessary, in order that the result of my calculation prove correct; and if I could wish, and my wish bring it about, that the world alter where necessary so that the altered figures are still of what they are supposed to be; then the sense of necessity (standing over myself, at any rate) is not likely to be very strong in me. What we take to be necessary in a given period may alter. It is not logically impossible that painters should now paint in ways which outwardly resemble paintings of the Renaissance, nor logically necessary that they now paint in the ways they do. What is necessary is that, in order for us to have the form of experience we count as an experience of a painting, we accept something as a painting. And we do not know a priori what we will accept as such a thing. But only someone outside such an enterprise could think of it as a manipulation or exploration of mere conventions"
On Convention:
"The conventions we appeal to may be said to be "fixed", "adopted", "accepted", etc. by us; but this does not now mean that what we have fixed or adopted are (merely) the (conventional) names of things. The conventions which control the application of grammatical criteria are fixed not by customs or some particular concord or agreement which might, without disrupting the texture of our lives, be changed where convenience suggests a change. (Convenience is one aspect of convention, or an aspect of one kind or level of convention.)
They are, rather, fixed by the nature of human life itself, the human fix itself, by those "very general facts of nature" which are "unnoticed only because so obvious", and, I take it, in particular, very general facts of human nature - such, for example, as the fact that the realization of intention requires action, that action requires movement, that movement involves consequences we had not intended, that our knowledge (and ignorance) of ourselves and of others depends upon the way our minds are expressed (and distorted) in word and deed and passion; that actions and passions have histories.
... That human beings on the whole do not respond in these ways is, therefore, seriously referred to as conventional; but now we are thinking of convention not as the arrangements a particular culture has found convenient, in terms of its history and geography, for effecting the necessities of human existence, but as those forms of life which are normal to any group of creatures we call human, any group about which we will say, for example, that they have a past to which they respond, or a geographical environment which they manipulate or exploit in certain ways for certain humanly comprehensible motives.
Here the array of "conventions" are not patterns of life which differentiate human beings from one another, but those exigencies of conduct and feeling which all humans share. Wittgenstein's discovery, or rediscovery, is of the depth of convention in human life; a discovery which insists not only on the conventionality of human society but, we could say, on the conventionality of human nature itself, on what Pascal meant when he said "Custom is our nature" (Pensees, §89)".