Please consider reading this answer in the voice of a highly motivated and potentially slightly crazy University Professor which talks about the Topics he loves with great passion: https://images.app.goo.gl/bbcQeEtYZxBRrdew7 (That's not me, but it makes my point.)
I will not link to external third party evidence that the contained thoughts are true. Instead i will write this answer in a way which proves it self to be true, just by logical reasoning. This will help me to prove my point and you to understand the concept. I challenge you to think about the concepts provided, research for more external evidence and think about them on your own to come to a conclusion if they might be true or not.
Your goal in life should always be, to question what's provided to you as knowledge, to research and think about it, gather evidence and then build knowledge on your own.
I do know that the way this answer is structured is against the agreed notion of what is allowed and what is not, here on Stack Exchange. Nevertheless, structuring it in this way is necessary to understand the core concepts.
Content of this answer
- Direct answer to the question you asked
- Splitting down your question
- Proposed definition for "Knowledge of a single person"
- Prove of my definition of knowledge by example
- Proposed defintion for "Idea"
- Prove of my definition of an Idea by example
- Closing the Circle to your Question
- Closing words
- Ideas are self standing
- An Idea which is supported by evidence is Knowledge
- The "existence of objective structure that is independet from knowledge" or "Can knowledge exist without structure" is an idea on it's own
- If those Ideas would become knowledge in the sense of "Knowledge exists without structure" this would break the very notion of what an Idea and knowledge actually are
Where this question might come from is that we as humans "hear" only a very few percent of our actual thoughts (read about System 1 and System 2). System 1 is responsible for a majority of our thinking and only pushes thoughts to System 2 which need attention. System 1 is not fully understood yet, but well enough to create solutions (AI, neural networks) which mimic it's behavior. As those solutions are well structured i suggest that System 1 itself is also well structured. If System 1 is well structured and it's thoughts are based on electrical interactions betwen neurons, those thoughts have would need to follow the same structure the neurons provide. So thoughts and therefore knowledge can not be without structure.
Direct answer to the question you asked:
No! If there is ever measureable evidence detected that there is a unresolvable difference between knowledge and the objective structure we build knowledge on, the whole line of reasoning i had in my entire life would break down and it would put me in the most severe existential crisis that i have ever had.
If there would ever be any evidence that there actually is a significant difference between those two, i wouldn't be able to possibly explain my own structural approach on thinking and would need to question all the knowledge i have ever created or gathered, aswell as all the knowledge existing for mankind. This would basically be a death sentence for me. Nothing that's worse could ever happen to me.
It would destroy all of the notions i have why people react like they do, how knowledge is created or what knowledge even is in the first place.
As for your second question: "Are there any philosophers who have studied the (possible) metaphysical difference between knowledge objects and objective structures?"
I do not know if there are philosophers who have thought about the same question that you have. But i consider myself to have thought and researched about it enough to provide an informed opinion based on personal experiences.
Splitting down your question:
To even be able to understand your question and to answer it, one must have a very good and easily understandable definition for what knowledge actually is.
For this definition i would like to focus on the percived notion of what is understood as "knowledge of a single person" and not of what is understood to be "knowledge of mankind".
So now i ask the Question "What is knowledge?"
Proposed definition for "Knowledge of a single person"
Kowledge of a single person are the underlying ideas, the lines of reasoning and the percieved or measureble evidendeces he has gathered for a specific Topic in Question.
As you can see my definition, it contains "lines of reasoning" which essentially is the Structure of knowledge. So for me, your Question can only be answered with a definitive No.
A Person will believe that he knows about something if he has seen evidence that suggests that the knowledge he has is true.
Prove of my definition of knowledge by example
There is a very well understood Theorem in physics which has been proven to be true by experimental Data. It is about the way a "non-symetrical" body (think about a tennis racket) moves trough space when thrown with some degre of rotation. It reads like this:
"The top can spin stably about the principal axes with the least or the greatest moments of inertia, but not around the intermediate axis."
This sentence is considered "Basic" knowledge by Experts in the field of classical dynamics. It has proven itself to be true on many measureable experiments (evidence) and is underlined with structured knowledge (lines of reasoning) of how classical dynamics works. https://www.youtube.com/watch?v=1VPfZ_XzisU
Now please consider a person who has absolutely no background in physics. If you would state this theorem to this person, he would not consider it as knowledge (for him), because he does not understand it. He most likely will just read the sentence and think "What a bunsh of gibberish, physicists need to be more clear in what they mean."
I hope this is enough logical evidence for you to consider my Definition for what "Knowledge of a single person" might be, to have some trueness to it.
But now we have arrived at a different problem. My definition was:
"Kowledge of a single person are the underlying ideas, the lines of reasoning and the percieved or measureble evidendeces he has gathered for a specific Topic in Question."
So to even understand this Definition we again need to have a very good and easily understandable definition of what an Idea actually is.
Proposed defintion for "Idea"
"An Idea is a self standing statement which exists by itself."
An Idea does not need to have any evidence at all. It merely is a thought a person has which could be true or not. He does not know about the "Trueness" of his Idea in the moment where it came to his mind.
How high the trueness of any Idea actually is, is determined by the perceived or measureable evidence that support that supports this Idea. It can be completely wrong, completely right or all things in between.
But for an Idea to exist, it does not need to have any evidence at all. Nor does it need to be structured in any given way.
Actually if one thinks about it, knowledge and idea are two words for exactly the same thing. Every knowledge can be formulated in a way which makes it an Idea. The only thing how someone decides if he considers an Idea to be knowledge is his notion of percived or measureable evidence.
Prove of my definition of an Idea by example
The Physics Theorem i have taken as an example for what knowledge actually might be is of great help here again. As stated, every knowledge can be formulated in a way which is an Idea. So i will just do this:
"Could it be that the top can spin stably about the principal axes with the least or the greatest moments of inertia, but not around the intermediate axis?"
Please read this Sentence like someone who has some degree of physics background but has not understood the surrounding concepts of the particular Idea in question. He may have just thrown a tennis racket into the air and observed it's movement. For this particular person, the statement provide is just an Idea.
If he now starts thinkering about this Idea, researches it and gathers evidence if the idea might be true, he will create his own personal knowledge.
As another example consider this statement as an Idea:
"A number is equal to itelf."
This is a basic Axiom (An Axiom is nothing different than an Idea) in the mathematics area of algebra.
It has proven itself to be true by the ammount of useful knowledge that can be constructed out of this Idea, the measureable real world evidences which are obtained by this knowledge and the various ways (which are ideas and knowledge on their own) of showing that the statement can not be false.
Closing the Circle to your Question
Using the definitions of "Idea" and "Knowledge of a single Person" and their respective proves we have learned the following:
- My Defintion of what an Idea actually is is self standing, a basic axiom of my own thoughts
- My definition of knowledge is based on my understanding what an Idea is
- The Concept of "objective structures" is an idea on it's own
- If someone starts thinking about the objective structures of knowledge he is actually building his own knowledge about the Topic of "Obective Structures"
- As he couldn't even think about "Objective Structures" without an Idea what that means or knowledge that supports his thoughts, there would not be any Concept of "Objective Structures"
- Thus i conclude that there can not be a significant and unresolveable difference between knowledge and the objective structures, as they are built from the same core concept
I hope this answer has presented to you my Ideas and Thoughts, aswell as the way i have gone through to arrive at my conclusions.
This whole answer is basically nothing else than an idea of its own, based on my very own definition of what an idea is.
Based on the idea to create this answer in the first place, i have structured (basically the objective structure of my thoughts and knowledge) this answer in the given way to help you understand my thoughts.
I can see where the thoughts that there might be a difference between knowledge and the structure of it come from. As explained every Knowledge can be formulated as an Idea. And if your question would have been "Can ideas exist without structure?", my answer would be a definitive YES!. Ideas are free standing without any supporting structure.
After reading this text, thinking, researching and gathering evidence on your own, i am conviced that you will arrive at knowledge which is new and interesting to you.
I hope you had as much fun reading this answer as i had writing it.