Propositional content and reference

Question

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.

Answer 1

Let’s distinguish between expressions and their utterances. The latter are the bursts of sound and marks on paper we encounter every day. The former are entities of a more abstract sort: they are the types of which the utterances are tokens. To illustrate, suppose Jack says to Jill ‘I love you’, and Jill replies ‘I love you’. Then this little exchange involves only one sentence, but two utterances.

When we talk about ‘meaning’, we can often neglect this difference between expressions and their utterances. Yet when indexicals are involved (expressions, like I, now, here - and my) the difference is crucial. Indexicals in the sense of expressions don’t have referents, and indexical-containing sentences don’t express propositions. Only utterances of indexicals have referents and utterances of indexical-containing sentences express propositions.

When you utter ‘I am tall’ (or ‘My brother is tall’), your utterance of I refers to you and your utterance of the sentence expresses the proposition that you are tall. (If you believe in singular propositions, then you yourself are a constituent of that proposition.) When I utter ‘I am tall’, my utterance of 'I' refers to me and my utterance of the sentence expresses the proposition that I am tall. Thus, we don’t express the same proposition, exactly because our utterances of I have different referents.

So far so good – except that we uttered the same sentence and so we feel that there must be some level of ‘meaning’ at which we’ve ‘said the same’, as it were. This is where the notion of character come into play. Roughly, a character is a general rule for assigning contents to indexicals and indexical-containing sentences. So, the rule for I would be that it always denotes the speaking. Who ‘the speaker’ is, varies from utterance to utterance, of course.
When you utter 'In my current state, I have knowledge' at different times, this will express different propositions - propositions that contain the respective times of utterance. At the level of character, you 'say the same' every time, of course.

This is a very rough outline of what’s going on. Indexicals are a major topic in philosophy of language, and a host of complex theories have been developed to deal with them; see e.g. here for more details. I can also supply more information in the comments.