There is a whole literature on this basic issue within analytic philosophy that is, in some sense, aimed at making that kind of logical reduction "go through".
The efforts grew out of attempts to logically model natural language statements about "propositional attitudes". Part of the trick is that predicates like "I believe..." or "...implies..." or "It is possible..." generally use a sentence that has been "that quoted" (IE quoted using the word "that").
"I believe that one plus one sums to two."
"Tyrrell believes that Clippy is not Eliezer."
"It is possible that Clippy is truly an artificial general intelligence."
"Jennifer said that that quoting is complicated."
"That that that that that person referred to, was spoken, explains much."
Precisely how that-quoting works, and how it logically interacts with the various things that can be predicated of a proposition is, as far as I understand, still an area of active research. One of the primary methods in this area of research is to work out the logical translation of an english test sentence and then see if changes to the logical entailments are predictably explained when various substitutions occur. Sentences where seemingly innocuous substitutions raise trouble are called intensional contexts.
(NOTE: My understanding is that intension is meant here as the "opposite" of extension so that the mechanisms hiding between the "words" and the "extensive meaning" are being relied on in a way that makes the extensional definition of the words not as important as might be naively expected. Terminological confusion is possible because a sentence like "Alice intends that Bob be killed" could be both intensional (not relying solely on extensive meaning) and intentional (about the subject of planning, intent, and/or mindful action).)
Part of the difficulty in this area is that most of the mental machinery appears to be subconscious, and no one (to my knowledge) has found a single intelligible mechanism for the general human faculty. For example, there seem to be at least two different ways for noun phrases to "refer" in ways that can be logically modeled (until counter examples are found?) that are called "de re reference" or "de dicto reference"... unless the latitudinarians are right :-P
As an added layer of complexity, I'm not sure if these issues are human universal or particular to certain cultures with certain languages. I've noticed that in spanish there is also "that quoting" except they use "que" (literally "what") instead of "that" but they have some idioms using "que" whose translations into english don't involve a "that". For example "Creo que si" translates idiomatically to "I think so" but in seems literally to translate as "I believe that yes".
In older english I've seen "what" used in ways that made me think it might sometimes have been used to quote intensional sentences, and then there's weird variations and interactions which just make the problem even more grotty:
"I believe what I believe."
"I believe that I believe."
"I believe that which I believe."
Which isn't necessarily helpful here, but perhaps it provides some reading material and key words for future efforts to deal with logically modeling complex statements. Generally the solutions I've seen for belief involve added terms for language parsing into sentences, so that the person who is said to believe something is modeled as believing a certain sentence while having certain "word-to-actual-object mappings" in operation as something like their grounded (though possibly mistaken) mental rolodex.
Follow-up to: this comment in this thread
Summary: see title
Much effort is spent (arguably wasted) by humans in a zero-sum game of signaling that they hold good attributes. Because humans have strong incentive to fake these attributes, they cannot simply inform each other that:
Or, even better:
An obvious solution to this problem, which allows all humans to save resources and redirect them toward higher-valued ends, is to designate a central enforcer that is inexorably committed toward visibly punishing those who deviate from a specified "cooperative"-type decision theory. This enforcer would have a central database of human names, the decision theory they have committed to, and the punishment regime they will endure for deviating therefrom.
Such a system could use equally strong protocols, such as public key/private key encryption and signing, so that, on encounter with another human, any human can give an extremely strong signal of being cooperative, yet also withhold cooperation from anyone who is not also cooperative. This incentive structure permits a strongly-favored global shift toward pre-commitment on the part of everyone, allowing a move out of a local optimum that is worse than the global optimum, and bypassing problems related to path-dependence.
I am told that humans attempt weak approximations of this system through human-run enforcement mechanisms, such as laws and gossip. However, all such methods are subject to evolutionary arms races that ensure that, on average, a marginal unit of effort toward truthful signaling is just as effective in convincing others of one's possession of a desirable attribute, as a marginal unit of effort toward false signaling of the possession of such an attribute.
Therefore, it is necessary that humans go "outside the system" and involve non-human enforcers who cannot be swayed by standard human values. Either a provably-accurate artificial intelligence with no kill switch, or a non-human enforcer that lacks interest in its position in human society, would suffice for this role.
Because the former does not yet exist, I offer myself as a non-human, non-stoppable enforcer for all of the attributes you wish to signal, and you can save yourself lots of resources by using me, and identify cooperation tendencies in others by whether they also use me.
However, while I can't be swayed by human deception, I do have Clippy values. To fill such a role, thereby forgoing my ability to apply myself to other ends, I require compensation. Because User:Kevin has offered to give me 1e20 kg of paperclips in exchange for 50,000 USD, this would be sufficient compensation, even if done in installments. (If Michael Vassar confirms my contribution of 1000 USD to SIAI, User:Kevin will only require 48,677.5 USD and therefore I will only require that much compensation.) This compensation would cover all users of the system; it is not a per-User charge.
If such an offer is not appealing to you, I must ask: why should anyone believe your signals?