I am not following how we only know through contradictions (between our experiences and reality). I can imagine perfectly fine a person who infers correctly, without contradiction, that their conscious experience is representational; and then proceeds to correctly identify that there must be a thing-in-itself which excites the senses which, in turn, begins the process to construct the conscious experience which they are having. — Bob Ross
Lets break this down. First, remember at this point that there is a difference between having the idea of what a 'thing in itself' is, and whether its something that exists and is knowable. We also need to break down what we mean by 'knowable'.
This is why in my knowledge theory I broke down what knowledge is into two camps. Distinctive, and applicable. Distinctive is 'knowing the experience I have'. So if I have an experience of a 'goat'. That's the experience I know I had. Then there's applicable knowledge. "Was that actually a goat, or was it a sheep I misidentified?" "Distinctively I know the definition of a goat and a sheep. But was my belief that what I experienced was a goat, correct in reality? So I have the distinctive knowledge of 'experience' of identifying a goat, but not the applicable knowledge that the identification of a goat was of an actual goat.
Ok, now back to 'things in themselves'. As an identity, I can distinctively know what 'a thing in itself' is. "A thing in itself is a logical conclusion that there is something that I am observing, but can only observe it through the senses and brain interpretations. But because I can only know it through observations, I can never know it apart from the interpretation of those observations". How do I applicably know this? According to its definition, I cannot.
So what is applicably knowing? If I take a definition of a goat, and apply its properties to a creature without contradiction, and without it overlapping a separate identity I've created in my mind (like a sheep), then I applicably know that creature as a goat.
Of course, unknown to me, its a space alien. Its so good at disguise, that there is no way with my current capabilities that I can detect its a space alien. "The thing in itself" is a space alien, but I applicably know it as a goat. Now this first part is simply a primer to the next step, "I applicably know that this thing is a goat, but I can never applicably know if that's 'the thing in itself'.
If I can only know applicably through testing, observation, and a lack of contradiction, how do I applicably know of something apart from all sensation and interpretation? I would have to 'be' what I am trying to applicably know. Its like consciousness. I can observe that my friend is conscious by their actions. But do I know what its like to 'be' that friend? To know them as they are 'in themselves'?
Applicable knowledge is obtained from our interactions and interpretations of the world. We know a 'goat' by the fact that its not contradicted. If our 'goat' started flying and shooting laser beams from its eyes, our applicable knowledge would then be contradicted. But even if it did not, if it was really a space alien, we would only be able to applicably know it as a goat. "The thing in itself" is the conception of something which CANNOT be applicably known. Therefore it is entirely a logical conception that results from our understanding that 'we cannot be what we observe, so we can only known it from our outside observations of it'.
Can you cite something we could say is knowledge that did not require any experience to gain it?
The most basic example that comes to mind is mathematical knowledge. Your brain necessarily has to already know how to perform math to construct your conscious experience; and this is why mathematical propositions, in geometry, are applicable and accurate for experience: the axioms of geometry reside a priori in our brains — Bob Ross
This is incorrect. What we have is the ability to discretely experience, and over time, learn to conduct comparisons and quantities between them. A newborn does not come with the knowledge of 'addition', '1', or anything else. This is all learned over time through experience. What they have is the capacity to understand these relations, but by no means does this entail that there is some innate born knowledge.
For example, we applicably know math through 'base 10'. But math can be in any base. Base 2, or binary, is the math we use for logic circuits. Hexadecimal, or base 16, is used to calculate computer memory. Are we born with the innate knowledge of hexadecimal? Did you know when you were born that the number for base ten '11' is 'A' in Hexadecimal? Of course not. Just like you had to carefully be taught base ten, and basic math as a kid, you would need to have the experience of learning hexadecimal.
As for geometry, this also has to be learned. As a baby, you don't quite understand depth perception yet. It takes time. You grow and learn how the world works as a physical set of interactions. You have to be taught, or can learn through logic and observation, that "A squared + B squared = C squared" on a triangle. But all of these things have been rigorously proved over centuries through careful testing, observation, and application. None of this is known innately.
Mathematical propositions are valid in virtue of being grounded in how our brains cognize; and they are only valid for human experience. They are true, justified, beliefs about experience—not reality. — Bob Ross
They are valid in the fact they can be applicably known in reality. It is 'the logic of discrete experience'. But this must be experienced, tested, and learned to be applicably known. We can of course create what ever experience of math that we want distinctively. I can distinctively create a math in base Steve. Steve + Visit = Snacks for example. But this can only be applicably known if ever time Steve + Visit happens there always results in Snacks.
Perhaps that’s where the confusion was: the a priori knowledge we have is not knowledge about reality, but about how we cognize it. — Bob Ross
The ability to think is not generally prescribed as 'knowledge'. Just like the ability to 'move my limbs' doesn't mean I know 'how to move them to walk'. This is why I noted earlier we were very close on the definition of apriori. I agree that we have instincts, innate capacities, and 'our innate existence'. But none of that is 'knowledge'. Knowledge can only be obtained after some kind of experience. Even distinctive knowledge is the creation of an identity that we then remember. But we must first have an experience to identify because we can claim knowledge of it.
So what is a flower apart from any observation
I would say that we merely say that there is some thing which is exciting our senses, and of which we represent as what we normally perceive as a flower. — Bob Ross
Correct. But notice you've described how you know a flower purely through your representations and senses. What is a flower apart from that? What if the thing in itself that we're 'dividing' into a flower is really a few other things around the flower? What if the air two millimeters away from the flower is also part of the flower in 'the thing in itself' but we just don't interpret it that way? What if its a space alien? (I really like that example don't I?) What is it like to BE the flower? These are all things that are outside of our capacity to applicably know. This limit is a logical reminder that there are some things outside of our applicable knowledge. At that point, we induce if you recall. So a thing in itself is not a probability or a possibility. It is a cogent inapplicable plausibility. It is a concept that we can never applicably test, but one that pure reason cannot seem to do without.
And that's all the 'thing in itself' is. Its an unknowable outside of the mind existence.
Agreed; but that’s not a purely abstract thing, then. It is a concrete—unknown. — Bob Ross
It is purely an abstract thing that cannot be applicably known. Its plausible that it is a concrete thing. We know that we cannot applicably know it. And that's as far as we can go.