Cockburn and Dummett on Understanding Statements About the Past

So I've been reading David Cockburn's (boy, I bet with a name like that he got made fun of as a kid) book Other Times. It's very different from anything else I've read on time since it takes a weird Wittgensteinian behavioristically anti-realist "No, I'm not an anti-realist" stand that threatens to collapse into either a strong anti-realism or a confused realism. A few comments on some stuff I've read:

Cockburn's take on Dummett is that Dummett thinks that it is wrong to think that there is a common core, "A is F", which, when one understands that and also has a general understanding of the past and future tenses, one can then understand "A was F" or "A will be F". Cockburn's Dummet (CD hereafter) thinks that, instead, to understand "A was F" is to know, for instance, what counts as present evidence for that - which will depend on the kind of event in question. On CD's view, it's not enough to have the general understanding of the tenses plus an understanding of the present-tensed version of the sentence. But isn't it? If one knows what being A and being F are, one knows the kinds of causes and effects associated with them to some degree. If one (perhaps expertly) deeply understands "A is F", one needs to understand what being A and being F are. But that, combined with a general understanding of the past tense, will also yield knowledge of what counts as present evidence for the past tense claim that A was F.

On pg. 61, Cockburn says that a 'fundamental aspect of our use of a sentence' is 'the ways in which it may feature in the justification of actions and emotions. This feature...is not one we should expect to be able to derive from other feature of its use... We cannot even characterise those supposed 'other' features of the use of a sentence independently of the actions and emotions with which it is characteristically linked.' I'm not sure there's sufficient evidence for this sort of claim. It's not clear how justification can be fundamental unless we become some sort of behaviorist or something close to it. Even then, I'm not sure what justification would even mean. If the entire meaning of a sentence is captured in its inferential role and we leave no room for reference or reality or correspondence to external facts, this is an extreme anti-realism. Otherwise, either the facts expressed will themselves determine the sentences' inferential role or, more in line with Cockburn's ideas, the inferential role of a sentence will determine the facts. That is, if p justifies q then, given that facts are "chosen" from the world that match the given inferential role, the fact expressed by p will be the sort to ground such a justification or be a reason - not just any old facts, but the ones that actually fit the role. Either way, we still can ask about what in reality is playing that role. Cockburn doesn't seem to allow this - his whole focus is on sentences and our behavior but he fails to deal with what those sentences correspond to.