As follow-on to my November "Divergence" post, exploring the divide in philosophy and science and the many complexity implications, I've done a deep dive on Kant. His Categorical Framework was first published over 230 years ago & I'm fascinated by its design as a "framework for all knowledge." It's taken a bit to get inside it. With some help from Aristotle (on intention) and Wittgenstein (on semantics) I've given it a go. http://sourcepov.com/2012/01/22/21stc-kant-convergence/ .. would love any thoughts there, blog side, or here, where another thread has opened up.
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- Some systems can be abstracted usefully.
Yes, but never absolutely, c.f. Chaitin's Omega. He's shown there is no more compact representation of any complete formal system than its enumeration. Complexity rules - but fortunately knowledge need not be complete to be useful.
Yet "useful" is a value judgment. So now we come to esthetics. Which "pure intuitions" will we choose to rely upon? Those that please us, of course. has built a model with symmetry and multiple abstraction layers, and I find it pleasing, as I expect he does also. That is ultimately going to be at the end of any search for knowledge. We will choose axioms that result in pleasing belief structures, and those beliefs will determine what we attend to and make use of, which we'll call knowledge.
I think good poetry illustrates your point. New ideas expressed in new language. Brillig language, filled with quarks...Jan 24, 2012
- Peter, beauty as the criterion for knowledge. So be it :-) But the greater beauty to me is to reject axioms and degenerate symmetry. To be orderly is to be dead. What was that RSA animation Chris posted a few weeks back? Right brain, left brain? I see far more beauty in knowledge as a Texas gusher of new patterns, constantly creating new things, rich and multifaceted, much like life itself.
Anyway, with language we have no choice. The value judgement of usefulness is all too obvious. You don't need to go as far as beauty or poetry. Until we let computers treat language as the computation of new patterns, they will continue failing to hear what we say.Jan 24, 2012
- doesn't "pattern" imply symmetry? Or at least the second-order, mutating symmetry of quasicrystals?Jan 24, 2012
- That's true. "Order" too often carries that implication. But as we know random "order" is the richest. I think random "patterns" might be the richest too.
Didn't Wittgenstein say something along the lines that all arguments in philosophy come down to misunderstandings about words? Words can mean many things, frequently contradictory. That's exactly the language problem which has led me to this idea that irregular (computable) patterns are at the root of it. It is even worse when you try to pin down "grammar".
You seem to be arguing that consciousness is inseparable from the body. This is an argument which comes up time and again recently. In linguistics it is referred to as "embodiment". Most extremely, I found a mathematician in France (Giuseppe Longo, search on "Goedelitis") who claims the subjectivity we find in even in maths must be resolved by acknowledging mathematics is inseparable from our biology!
It is hard to tease embodiment and complexity apart, because complex systems also cannot be copied. Infinitesimal perturbations change the whole system. But I think this sensitivity to detail in complex systems is enough. I don't think we need the particular detail of biology.Jan 25, 2012
- Rob your read of Wittgenstein is spot on, which is why I always seek to create semantic common ground on challenging topics like this. The more general/vague the terminology, the faster we'll run off the collaborative rails. Interesting that u guys introduce mathematics, I have been mulling a mathematical view of Lanterns's 3 rows as well ..Jan 25, 2012
- Chris. You could look at axiomatic set theory and see if there's a choice of axioms which fit yours. For me, of course, it is all about the fact there is no one set of axioms you can establish from first principles.Jan 26, 2012
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