As to irreducible levels of order, Wittgenstein put it like this: We could try to understand what is happening in a room by describing all that is going on that can be observed. We could observe a man sitting in an elevated wooden bench, and several other men sitting at table opposite him. There also exist 12 individuals paying attention to each person as they speak in succession and another near the front transcribing everything, and etc., etc., etc. We could describe the entire scene in exquisite detail, but unless we already knew what jury trial is, it would be a complete waste of time. There is no amount of description that can allow us to understand what is happening. Kauffman makes the same argument about biology. We spend so much time with a reductionist approach, but perhaps we can never in principle discern how these findings relate to the organismal level, which results from essentially infinite interactions smaller units on many different length and time scales. I would totally agree with you if you said "Numbers are the only form of absolute Truth". I just don't think they can always provide a useful description of the world.
> Greek thinkers; most were extremely disinterested in observation. Of course, but they had at times supremely penetrative insight. Consider Democritus and the Atom. > Pythagoras believed in a highly idealized world "Number governs the Universe" is the shared thought. That school was a comprehensive order governing all aspects of life, including mores, hygiene, etc. Anyway, that school only knew of {N}. I am talking {Z} and harmonic systems: http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN235993... http://www.wolframalpha.com/input/?i=e%5EiPI+%2B+1 To frame it by more contemporary terms, my philosophical views regarding Mathematics are likely close to Constructivism/Intuitionism: I reject the "excluded middle" [1] as a universal truth, and, more fundamentally consider the entire edifice of time-space (and all objects therein) a construct of mind, a side-effect of cognition. (Recall our previous conversation.) I assert that knowledge requires effort, at a fundamental level and is but the fruit of computation. While I personally like Ludwig far (far) more than Alan Turing, it would appear that Turing (an "empiricist" you should note) was correct and our dear Ludwig was merely philosophizing. [1]: Of course (!:) I have a wonderful proof 'showing' this, but the internets is too small to contain it ...
I assert that knowledge requires effort, at a fundamental level and is but the fruit of computation. I agree with this statement, but where I don't agree is that the brain can be treated as a Turing machine. How real neurons respond to real environmental cues is still not entirely clear, and our understanding is becoming more complex year upon year. For example, it was recently shown that the firing of an action potential is not a mere superposition of the inputs to a neuron, as was previously thought, but actually is highly dependent on the order in which the inputs are received. That is, in neurons, logic gates are not the same as the logic gates in an electric circuit, which I believe is the underlying assumption in a Turing machine. I suppose our divergence is that I don't think of LW as "merely philosophizing". I am of the opinion that good philosophy underlies good science. To me, he was showing us how to think, and thus, how to understand the world around us.
It is a temporary condition, I assure you. Truth is eternal. This material life is a crucible: The 'foam' rises to surface and is wiped away; what remains is what is. Like shall be with like: Light with light; darkness with darkness. (Harmonic systems ...) > How real neurons respond to real environmental cues is still not entirely clear, and our understanding is becoming more complex year upon year. For example, it was recently shown that the firing of an action potential is not a mere superposition of the inputs to a neuron, as was previously thought, but actually is highly dependent on the order in which the inputs are received. That is, in neurons, logic gates are not the same as the logic gates in an electric circuit, which I believe is the underlying assumption in a Turing machine. I didn't hear about that, but your conclusion is incorrect: A neuron is modelled as an FSM [1]. You are perfectly correct that a simple logic gate is an inaccurate model for our new understanding of the neuron. But a temporally ordered selector set across n input feeds can be trivially modeled with a multiplexer front-end and a demultiplexer back-end. (In other words, the organic neuron is cleverly O(1) given the permutation set of threshold exceeding event based on a temporal ordering of the input activations, whereas the model will be O(n) -- in terms of space.) It remains a Turing Machine. > I suppose our divergence is that I don't think of LW as "merely philosophizing". I am of the opinion that good philosophy underlies good science. To me, he was showing us how to think, and thus, how to understand the world around us. I have deep respect for Wittgenstein's mind. Let's discuss TLP:4.1252 [2] [1]: https://en.wikipedia.org/wiki/Finite-state_machine [2]: http://people.umass.edu/phil335-klement-2/tlp/tlp.html#bodyt...
Anyway, neurons are a convenient example because they're so well known, but there are many other factors that lead me to believe the brain itself can in no way be construed as a Turing machine. Namely, the contribution of glial cells to neurophysiology, which is largely ignored by most people who espouse their ideas on the deterministic nature of the brain (which, if the brain is a Turing machine, it certainly is deterministic). However, we need look no further than the tripartite synapse to see that the behavior of many neural mechanisms is often stochastic. The tripartite synapse is so named because there are three essential components: the axon terminal (pre-synaptic terminal); the post-synaptic terminal; and a psuedopod of an astrocyte. The role of the astrocyte is to provide neurotransmitters and other bio-molecules that can vastly alter long term depression and potentiation. This makes a non-neuronal cell, that does not fire an action potential, integrally important to the normal firing of action potentials. I don' believe there is any such analog in computers. Furthermore, there is biomolecule sharing between oligodendrocytes and axons that drastically alter the properties of the axon, such as the ability of the axon to produce neurotransmitters, to grow and to conduct current. These, and many other, properties are stochastic, not deterministic, and cannot be ignored when developing a complete picture of the brain, but they often are by those who are trying to model the brain and those who are writing about the deterministic quality of the brain (John Searle comes to mind). I believe this is history's influence on neurobiology. It was thought for many years that astrocytes provide structure and nutrients and oligodendrocytes provide myelin; end of story. This is as far from the truth as claiming the world is flat, but is still ignored in so many arguments. I will need to brush up on the Tractatus to have a meaningful discussion about it. I take PI to be divine words, but I've always read that LW himself rejected a lot of the Tractaus later in life, so I haven't paid nearly as much attention as it probably deserves. I appreciate the free link though; definitely going to bookmark.
Yes, his life is parted in the middle. I am strictly a fan of the young, fearless, and spiritual Wittgenstein. TPL is inspired thinking. > I take PI to be divine words !!! b_b, you have some explaining to do! :)
When we focus on the same set of ideas and come to different conclusions, I think it speaks to our underlying assumptions about the world, which can't be dictated by reason or logic. One feels X, and another feels Y. Like our materialist vs. non-materialist conversation the other day. This type of belief can't be shown to be true or untrue; we just pick a side based on some internal criteria, and it can dictate how we feel about many things.