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.
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”).
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:
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.