Where do these crisp ontologies come from, if (under the signalling theory of meaning) symbols only have probabilistic meanings?

There are two things here which are at least potentially distinct: The meaning of symbols in thinking, and their meaning in communication. I'd expect these mechanisms to have a fair bit on common, but specifically the problem of alignment of the speakers which is adressed here would not seem to apply to the former. So I dont think we need to wonder here where those crisp ontologies came from.

This is the type of thinking that can't tell the difference between "a implies b" and "a, and also b" -- because people almost always endorse both "a" and "b" when they say "a implies b". 

One way to eliminate this particular problem is to focus on whether the speaker agrees with a sentence if asked, rather than spontaneaus assertions. This fails when the speaker is systematically wrong about something, or when Cartesian boundaries are broken, but other than that it seems to take out a lot of the "association" problems.

None of this is literally said, but a cloud of conversational implicature surrounds the literal text. The signalling analysis can't distinguish this cloud from the literal meaning.

Even what we would consider literal speech can depend on implicature. Consider: "Why don't we have bacon?" "The cat stole it". Which cat "the cat" is requires Gricean reasoning, and the phrase isn't compositional, either.

To hint at my opinion, I think it relates to learning normativity [LW · GW].

I think one criterion of adequacy for explanations of level 1 is to explain why it is sometimes rational to interpret people literally. Why would you throw away all that associated information? Your proposal in that post is quite abstract, could you outline how it would adress this?

Interrestingly I did think of norms when you drew up the problem, but in a different way, related to enforcement. We hold each other responsible for our assertions, and this means we need an idea of when a sentence is properly said. Now such norms can't require speakers to be faithful to all the propabilistic associations of a sentence. That would leave us with too few sentences to describe all situations, and if the norms are to be reponsive to changing expectations, it could never reach equilibrium. So we have to pick some subset of the associations to enforce, and that would then be the "literal meaning". We can see why it would be useful for this to incorporate some compositionality: assertions are much more useful when you can combine multiple, possibly from different sources, into one chain of reasoning.

If Alice says something to Bob, Alice (in general) has a plan, where Alice's own speech act is part of the plan, and Bob interpreting the speech in a certain way is also part of the plan. If the plan concludes "...and then Bob concludes that I am in his in-group", then that's level 3. If the plan concludes "...and then Bob knows not to swim in the shark-infested river", then that's level 1. Etc.

Without the speaker modeling the listener and incorporating the listener's expected interpretation into a plan, you can't have different levels, I don't think.

I believe the last section of this post is pointing to something central and important which is really difficult to articulate. Which is ironic, since "how does articulating concepts work?" is kinda part of it.

To me, it feels like Bayesianism is missing an API. Getting embeddedness and reflection and communication right all require the model talking about its own API, and that in turn requires figuring out what the API is supposed to be - like how the literal meanings of things passed in and out actually get tied to the world.

Are you saying that a probabilistic analysis of communication that treats communication as evidence for hidden variables/information cannot deal with the meaning of words? If so, why can't the meaning itself be such a hidden information revealed by the message?

Communication of meaning, signaling of truth. I'm not sure what essential difficulty remains if we merely make sure to distinguish between communicating ideas (which in this role are to be made clear, not yet compared against the world), and providing evidence for their relevance to the discussion or for their correspondence-to-the-world truth. Fireflies won't be able to communicate ideas, only signal truths, so this analysis doesn't naturally apply to them. But language can communicate ideas without implication of their truth, and at this point signaling helps if truth is to be extracted somewhat directly from other actors and not evaluated in other ways.

we assume the remark is relevant to the conversation

For example, in this case the assumption is part of how meaning is guessed, but is in general unrelated to how its truth (or truth of its relevance) is to be evaluated. The intermingling of the two aspects of communication is mostly shorthand, it can be teased apart.

I bet this is a side effect of having a large pool of bounded rational agents that all need to communicate with each other, but not necessarily frequently. When two agents only interact briefly, neither agent has enough data to work out what the "meaning" of the other's words. Each word could mean too many different things. So you can probably show that under the right circumstances, it's beneficial for agents in a pool to have a protocol that maps speech-acts to inferences the other party should make about reality (amongst other things, such as other actions). For instance, if all agents have shared interests, but only interact briefly with limited bandwidth, both agents would have an incentive to implement either side of the protocol. Furthermore, it makes sense for this protocol to be standardized, because the more standard the protocol, the less bandwidth and resources the agents will need to spend working out the quirks of each others protocol.

This is my model of what languages are.

Now that you have a well defined map from speech-acts to inferences, the notion of lying becomes meaningful. Lying is just when you use speech acts and the current protocol to shift another agents map of reality in a direction that does not correspond to your own map of reality.

I'm with you on the deficiency of the signalling frame when talking about human communication and communication more generally. Skyrms and others who developed the signalling frame explicitly tried to avoid having a notion of of intentionality in order to explore questions like "how could the simplest things that still make sense to call 'communication' develop in systems that don't have human level intelligence?", which means the model has a gaping hole when trying to talk about what people do.

I wrote a post [LW · GW] about the interplay between the intentional aspects of meaning and what you're calling the probabilistic information. It's doesn't get too into the weeds, but might provoke more ideas in you.

I think part of the story is that language is compositional. If someone utters the words "maroon hexagon", you can make a large update in favor of a specific hypothesis even if you haven't previously seen a maroon hexagon, or heard those words together, or judged there to be anything special about that hypothesis. "Maroon" has been sufficiently linked to a specific narrow range of colors, and "hexagon" to a specific shape, so you get to put those inferences together without needing additional coordination with the speaker.

This seems related to the denotation/connotation distinction, where compositional inferences are (typically?) denotations. Although the distinction seems kind of fuzzy, as it seems that connotations can (gradually?) become denotations over time, e.g. "goodbye" to mean that a departure is imminent, or an image of a red octagon to mean "stop" (although I'd say that the words "red octagon" still only have the connotation of "stop"). And "We should get together more often" is interesting because the inferences you can draw from it aren't that related to the inferences you typically draw from the phrases "get together" and "more often".

This is the type of thinking that can't tell the difference between "a implies b" and "a, and also b" -- because people almost always endorse both "a" and "b" when they say "a implies b".

This is the type of thinking where disagreement tends to be regarded as a social attack, because disagreement is associated with social attack.

This is the type of thinking where we can't ever have a phrase meaning "honestly" or "literally" or "no really, I'm not bulshitting you on this one" because if such a phrase existed then it would immediately be co-opted by everyone else as a mere intensifier.

This "type of thinking" sure seems very accurate to me.

In particular, the third paragraph quoted above seems spectacularly accurate, e.g. the euphemism treadmill.

Alice: "I just don't understand why I don't see Cedrick any more."

Bob: "He's married now."

We infer from this that the marriage creates some kind of obstacle. Perhaps Cedrick is too busy to come over. Or Bob is implying that it would be inappropriate for Cedrick to frequently visit Alice, a single woman. None of this is literally said, but a cloud of conversational implicature surrounds the literal text. The signalling analysis can't distinguish this cloud from the literal meaning.

I'm not sure this is quite true. Just because every utterance produces a 'cloud of implicature' doesn't mean 'literal meaning' isn't also a component of the signal.

And, in practice, it doesn't seem like there is any general way to distinguish the cloud from the literal meaning. One problem being which literal meaning should be considered the literal meaning?

Like logical uncertainty, I see this as a challenge in the integration of logic and probability. In some sense, the signalling theory only allows for reasoning by association rather than structured logical reasoning, because the meaning of any particular thing is just its probabilistic associations.

I'm confused why this is a 'challenge' – or a surprising one anyways. It certainly seems (again!) astonishingly accurate to describe most people as "reasoning by association".

Where do these crisp ontologies come from, if (under the signalling theory of meaning) symbols only have probabilistic meanings?

Wouldn't they come from mostly (or 'almost perfectly') certain meanings? Practically, words seem to almost never correspond to a particularly crisp ontology (compare to, e.g. the elements or subject of a mathematical theory). I don't think there's any word that would – under all circumstances or in all situations – have a (unique) 'literal meaning'.

The explanation of how communication can (reliably) convey 'literal meanings' seems to boil down to 'with great effort, arbitrary depths of circumlocution, and (still) only ever approximately'.

In some sense, the signalling theory only allows for reasoning by association rather than structured logical reasoning, because the meaning of any particular thing is just its probabilistic associations.

ES: Uncertain.

To properly assess the probabilistic associations that a certain set of symbols has, we humans need to first unpack the set to its literal/usual meaning. So when I say "A -> B; Not B.", this first gets parsed and its logical meaning extracted, then this meaning plus the symbols themselves get used to find the probabilistic meaning.

Of course, this process doesn't happen neatly, and some people might use more heuristical methods and skip parsing the symbols partially (i.e., they pattern-match on the current uttering and previous utterances, and directly use the nearest cached Bayesian meaning available). This seems to be pretty common among normal people, and a constant source of friction with intellectuals.