Be careful with unstated assumptions about belief aggregation. “the discourse” doesn’t have beliefs. People have beliefs, and discourse is one of the mechanisms for sharing and aligning those beliefs. It helps a lot to give names to people you’re worried about, to make it super-clear whether you’re talking about your beliefs, your current conversational partner’s beliefs, or beliefs of other people who hear a summary from one of you.
If Alice discourages Bob from saying X, then Charlie might go on believing not-X. This is a very different concern from Bob being worried about believing a false not-X if not allowed to discuss the possibility. Both concerns are valid, IMO, but they have different thresholds of importance and different trade-offs to make in resolution..
In a math conversation, people are going to say and possibly write down a bunch of beliefs, and make arguments that some beliefs follow from each other. The conversation itself could be represented as a transcript of beliefs and arguments. The beliefs in this transcript are what I mean by “the discourse’s beliefs”.
Be careful with unstated assumptions about belief aggregation. “the discourse” doesn’t have beliefs. People have beliefs, and discourse is one of the mechanisms for sharing and aligning those beliefs. It helps a lot to give names to people you’re worried about, to make it super-clear whether you’re talking about your beliefs, your current conversational partner’s beliefs, or beliefs of other people who hear a summary from one of you.
If Alice discourages Bob from saying X, then Charlie might go on believing not-X. This is a very different concern from Bob being worried about believing a false not-X if not allowed to discuss the possibility. Both concerns are valid, IMO, but they have different thresholds of importance and different trade-offs to make in resolution..
In a math conversation, people are going to say and possibly write down a bunch of beliefs, and make arguments that some beliefs follow from each other. The conversation itself could be represented as a transcript of beliefs and arguments. The beliefs in this transcript are what I mean by “the discourse’s beliefs”.