On Oct 6, 12:04 pm, Bruno Marchal <marc...@ulb.ac.be> wrote: > On 04 Oct 2011, at 22:44, benjayk wrote:
> > > I'd be very interested in you attempt to explain addition and > > multplication > > without using numbers, though. > > I am not sure this makes any sense. Addition of what? > In scientific theories we don't pretend to explain everything from > nothing. We can only explain complex things from simpler things. The > rest is playing with word. Why is it playing with words? We can explain simple things from complex things too. I decide to move my hand, and a lot of complicated physiological change happens. > > Anyway, even if I completely agree on these principles, and you derive > > something interesting from it, if you ultimately are unable to > > define what > > numbers are, you effectively just use your imagination to interpret > > something into the undefinedness of numbers, which you could as well > > interpret into the undefinedess of consciousness. > > Here yo are the one talking like a 19th rationalist who believe that > we can dismiss *intuition*. Since Gödel's rationalist knows that they > can't. In particular we need some undefinable intuition to grasp > anything formalized, be it number, or programs, or machines, etc. > I chose the numbers because people already grasp them sufficiently > well, so that we can proceed. I disagree. I understand what he is saying exactly. What makes numbers any more deserving than awareness of a primitive status, exempt from definition? > >>> OK. But what else is 0? > > >> Nobody knows. But everybody agrees on some axioms, like above, and we > >> start from that. > > So why is it better to start with "nobody knows"-0 > > Nobody starts with "nobody knows 0". > We start from "0 ≠ s(x)", or things like that. > > > and derive something from > > that than just start with "nobody knows"-consciousness and just > > interpet > > what consciousness means to us? > > Because 0, as a useful technical object does not put any conceptual > problem. Consciousness is far more complex. Consciousness isn't complex, it's as simple or complex as whoever it is that is the subject. In order to have 0, you have to have something that is aware of 0, but you don't need to know 0 to have awareness. > If there is 0€ in a bank account, this is sad, but is not very > mysterious. If someone is in a comatose state, the question of > consciousness is much more conceptually troubling. Humans took time to > grasp zero, but eventually got the point. For consciousness, there are > still many scientist who does not believe in it, lie some people does > not understand the notion of qualia. Is consciousness related to > matter, is it primary, ... all that are question still debated. That's only because they aren't thinking about it the right way. They are trying to fit a who and why into a what and how. That can't be done. > But > for 0, there is no more problem. Everyone agree on any different > axioms rich enough to handle them in their application. There is agreement because 0 is nothing but an agreement. It's a word for an idea, which has meanings in relations to other words and ideas of the same arithmetic type. > >>>> 1 is the successor of 0. You are confusing the number 0 and its > >>>> cardinal denotation. > >>> OK. But what else is 1? > > >> The successor of zero. The predecessor of 2. The only number which > >> divides all other numbers, ... > >> (I don't see your point). > > But what does successor mean? You are just circling within your own > > definitions, which doesn't explain anything. > > You have to study mathematical logic. yes I am circling. This is > allowed and encouraged in foundations. There are precise technic to > make such circles senseful. I agree with Ben. It's circular reasoning to say that addition and succession define each other. To me, it's clear that succession is one of the many primitive elements of sense - symmetry, reflection/ imitation, looping, association, dissociation, etc. are others. > > Yes. So you want to explain mysterious consciousness and substitute > > the > > equally mysterious numbers. Where exactly lies the explanation in > > that? > > If you can derive the mass of the proton from a theory of > consciousness, explain me how. > I have never met any difficulty about any statement I have ever made > on any finite beings constituting universal systems. But on > consciousness, humans have never cease to met difficulties. > The numbers are taught in high school. Consciousness has entered in > *some* university level course, and only with many difficulties. Consciousness can be understood in it's entirety by contemplating the meaning of the word "I", and it cannot be understood at all without understanding the meaning of that word. It's misleading to look for exterior knowledge to inform us about subjectivity. Knowledge is an obstruction to understanding in the case of awareness. > > >> I think you restrict science too much. Like I think you restrict > >> rationality.´ > > It all depends on what we mean with science, and rationality. The > > words have > > no predefined meaning, we have to give them meaning itself. > > Personally, I am > > willing to extend the meaning of science to the very act of observing > > itself, making everything science. > > That would lead to complete arbitrariness. That leads to suffering. > That leads to the defense of the special interest against the common > interest. No, it leads to enlightenment. Why do you want us to scare us away from looking at what is 'looking' scientifically Bruno? > > Comp is not a dogma. It is a testable theory, which really means only > a refutable theory, as understood by Popper. Ok, so what test would prove comp to be false? 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