My main question is this:
Let p be a sentence. Can I have the proposition expressed by p be the same even if the referent of p is different?
So as an example I'm thinking of stuff like:
p = 'My brother is tall'
Suppose I state that p, then 'my brother' might refer to an individual called Adam.
Suppose instead that someone else state that p, then 'my brother' might refer to an individual called Ben.
Am I justified in saying that regardless of the difference referent, we have expressed the same proposition?
More specifically I am looking at sentences of the form 'In my current state, I have knowledge'. I want to say that utterances of this sentence at different times express the same proposition, even if the state referred to is different.
I want to say that the notion of 'current' is de dicto as opposed to de re
Edit: What I'm trying to do:
Essentially, I'm interested in this paper by Wesley Holliday:https://pdfs.semanticscholar.org/dae6/739b8b05bf2845f2de41611c3cd0c9ae03d5.pdf
Here he proposes an epistemic logic that essentially time indexes knowledge claims. Knowledge is obtained when in all related states (modally understood), p is the case. Because different epistemic worlds have different epistemic states, the knowledge proposition is different.
So what happens is he wants to look at the schema of:
phi -> (After some update) K phi
Put phi as some epistemic proposition, e.g. Kp or Moore's sentence (which we write as p and not Kp)
What this is meant to represent is that if phi true, then after some epistemic event, phi is known.
Suppose we use phi as Kp then we get:
Kp -> (After some update) K Kp
Now according to holliday, since updates change the epistemic world (epistemic model changes), the Kp in the antecedant and the Kp in consequent represent different propositions since they refer to different epistemic states. (Essentially the modal relation of accessible world changes after the update). So he understands the first K to do with a state E1 and the second K to do with a state E2.
My hope was to say that knowledge is non indexical. That the proposition expressed by K is literally 'the current epistemic state is such that knowledge', so that the K's represent the same thing, even though they refer to different states (E1, E2). In the truth value sense, I am more just trying to allow for the 'content' in some way of Knowledge to change, despite the expressions (or character?) being identical.