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Maybe reality is an onion with layers. As our understanding of the universe is unfolding the onion, we are growing closer to the tearful core. While each layer is uncovered we are seeing an onion segment. The segment is an abstraction of the whole onion but it is a segment nonetheless.
To define our notions as subjective because they cannot describe reality precisely or the connectedness of reality is arbitrary. It is a philosophical construct which is not useful in the realm of a rickety old chair. If we get closer to the core your notion of human abstraction will be more useful. On the other hand, like the tootsie pop commercial says, the world may never know.
I can't explain Tammet, but I think I can explain why math is an abstraction. First of all, most people aren't really clear on what an abstraction is, or rather they simply have a different definition, since there is no such thing as a concrete notion. But my notion of abstraction is that, as limited humans, we focus on a particular property that our system has discerned, and we think about it in exclusion of the rest of the properties with which it is associated.
For instance, the barking of a dog does not exist in the absence of dogs, but we can think about just the barking because our system has a limited capacity for awareness. Likewise, we can think about quantity, in exclusion of things which we perceive to have quantity. Math was first developed as a simple accounting tool, and its creators were thinking about quantities of grain and rice and berries, but in exclusion of the grain and rice and berries themselves.
What I am saying is that there are not actually discrete entities in reality. Everything is somehow effected by everything else (or it simply is not called real), and to discuss things as separate entities is only to abstract certain notions from what that thing really is, disregarding the rest. And any notions we build using such abstractions are not truly representative of reality. They are only representative of those aspects of reality which we perceive. They are subjective knowledge; the knowledge that an aware system has of its own experience.
John, If math is an abstraction, not a real entity, how does Daniel Tammet, the new rain man do it?
He solves complex math problems without calculating. How is it that integers have distinct shapes and colors? What would you think if other rain men had the same description of the integers? Will the omniscient man in your matrix see his landscape in synesthesia?
Okay, look, I don't want to get off a productive track here. I will address each of your points, but it's important to note that all these disagreements we have stem from one thing, for me. It's your certainty.
I use all the same methods of observation, abstraction, classification and logical determination that you guys do. I know it sounds like I'm attacking them all, but its only your certitude that I am attacking. It's only when you say that you know something for sure that I am compelled to disagree. And, Michael, it doesn't work to flip the script and ask me to prove my assertions because my assertion is that we can't make assertions. Yours is that we can, so you're the one who has to prove any assertion you make. That's the Aristotle and the sophist argument I was talkin about earlier.
I have made quite a study, as I can tell you have, of the foundations of philosophy, science and even religion. But while I marvel at the ingenuity (or sometimes the stupidity) of each method of observation; each perspective of consideration, I am not completely convinced by any of them. I can see a flaw in you saying that you know 2+2=4 because of the same point DS made in your Jan 25th post - math is an abstraction, not a real entity. We abstract qualities like "line" from all the things the length of which it has become useful for humans to measure, but there is no such thing as a "line" in reality. Likewise, there is no such thing as a "2," floating out there anywhere either, and there are no two things that you could say are completely equal anyway, to know that adding them together equals exactly twice either of them. Trying to apply such abstract concepts to reality reveals their inadequacy as accurate descriptive tools. They are approximations, and you cannot have certainty with approximations.
Michael, you want to dismiss all these minor incalculables as insignificant and only applicabale to the subatomic scale, but that doesn't mean they don't apply to the macro scale. On the contrary, in many cases it means they are magnified exponentially by the sheer number of their re-occurence. Math has had to develop concepts like limits and fractals and chaos theory to get around some of realities unknowables, but because they are still approximations, certainty is still an illusion for humans.
However, I can conceive of one way that humans could overcome that limit of reality and become effectively omniscient. I don't know that we'd actually want that, but there could be a way: if we design a virtual reality, and can transplant our consciousness into, or convert our matter into energy and "plug in," matrix style, then we would effectively know the initial parameters and limits of the system in which we live, and could make accurate valuation judgements about the nature of reality. We could possibly have objective truth/ knowledge in that situation. I'm not really sure though.
Perception is not flawed. If it is quite easy to prove (reduce to perceptual evidence) that perception is flawed? Do it! I would like to see you use your powers of reason to disprove an implicit necessary quality or proof. Again, perception is not our knowledge base. It is our means of receiving information. Perfection is not necessary, objective definition is. And the definition of knowledge is concepts that are integrated without contradiction. If you cannot or do not do this, you cannot have knowledge and any point you make is arbitrary.
The law of identity and the concepts that follow are not numbers. Numbers are different. Again you are mixing metaphor with reason.
You have not shown me how one can properly doubt the law of identity. The law of identity is what makes possible you seeing anything to begin with and distinguishing it from something else. If borders do not exist, then what the fuck are you looking at? Quantum soup?
I know my conclusions I make from the integration of perceptual evidence are valid because they can be integrated into my knowledge base without contradiction. You have zero knowledge that this world is a virtual representation of another world and even if it was, that would not change that this world, our knowable universe, is subject to causal law. Causal law is what makes knowledge possible, without it you would not be able to form a sentence, let alone get very confused about the fact that quantum theory has no role to play in epistemology.
How is it that you know knowledge is not possible?
I refuse to contemplate how the definition of chair wouldn't change if gravity were taken away.
One does not require all knowledge to have some knowledge. Again, please answer, how it is that you know that knowledge is unobtainable? Not just a list of metaphorical nonsense. Specifically, how is it that you are sure? How is your point of view validated?
It matters not at all that people have been wrong about what they know. 2+3=19. That's wrong and I know it because I have knowledge of mathematics. The presence of an error in addition does not negate addition itself.
There is absolutely a core concept of a chair. It is what allows humans to recognize when something is a chair and when something is not a chair.
Knowledge I possess:
The capitol of Illinois is Springfield.
Humans need oxygen to live.
The sun is in the center of our solar system.
The english alphabet has 26 letters.
Earth is older than 6000 years.
Circles have no right angles.
You are confused.
No one used the internet in the 19th century.
My name is Michael.
China's land area is much bigger than Italy's.
The sun is made up mostly of Hydrogen and Helium.
Oh wow, you have a really special way of looking at things, Michael. You contradict yourself so much it's hard to know where to start. First of all, when you start by saying "There is only the noncontrictory integration of perceptual evidence. To be valid, a concept must fit without contradiction into your knowledge base both:...." you are saying that perceptual evidence is our knowledge base. But it's really quite easy to prove that perception is flawed, and that memory of perception is flawed, so even if you had some rock solid knowledge base (whatever that is), you would not remember it perfectly, nor communicate it perfectly, so this knowledge base is already full of holes.
Second, you insist that the Law of Identities and all the concepts that follow, are some infallible set of numbers with which you can mathematically build knowledge up from that special knowledge base you were talking about. But I have already showed you how the Law of Identities can be easily doubted, so all the building you do with it is just castles in the sand, my friend. Can you prove you are not in a virtual reality? That everything you see, hear, taste, touch, smell and think aren't just programmed to feel that way? Can you? Then how do you know any of the conclusions you make from your evidence are valid?
Third, you insist again that sophism is a self-defeating premise, but that is because your definition of knowledge is inadequate, not because knowledge, being impossible, therefore makes it impossible to conclude such a thing. It's the very innability to prove anything that shows the impossibility of knowledge. The onus is not on me to prove my point because you cannot give me any examples of this rock solid thing you call knowledge. I can give examples all day, until I'm blue in the face, of people thinking they knew something and winding up wrong. I can deconstruct any argument you make, right down to the fundaments of your concepts, and show that you never knew what you were talking about at all.
There is no core concept "chair;" nothing that can be clearly and completely defined as a chair. Did you not listen before when I explained this? Your Science God says the chair has gravity that pulls on everything else that exists. If you took it away, everything would behave differently; have different qualities, however slightly. If you do not know the exact nature of all of its interractions, then you do not know what "chair" is. And since it would require omniscience to know all that, you will not be gaining anything called knowledge anytime soon.
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