On May 9, 2:37 am, Bruno Marchal <[EMAIL PROTECTED]> wrote:
> Le 08-mai-07, à 04:27, [EMAIL PROTECTED] a écrit :

> > 'The Laws of Physics'  don't refer to human notions (they certainly
> > are not regarded that way by scientists - the whole notion of an
> > objective reality would have be thrown out the window if we thought
> > that there were no objective laws of physics since as mentioned,
> > physics is the base level of reality), but are precise mathematical
> > rules which have to be (postulated as) *universal* in scope for the
> > scientific method to work at all.
> Actually, although the current laws of physics does not refer to
> humans, they do refer to observers, if not only through the notions of
> observable and measurement..
> With Everett, the observer can be "just" a memory machine. Once a
> machine,  the laws of physics have to emerge from something else, like
> number or information science/computer science, or mathematics.
> You are perhaps confusing the notion of objective reality with the
> physicalist assumption that the objective reality is the physical
> reality. This has never been proved, and indeed is already jeopardized
> independently by both the quantum facts and simple hypotheses, like the
> finiteness of some possible representations of the observers.
> Bruno
> http://iridia.ulb.ac.be/~marchal/

Actually Bruno, been thinking a bit more and you may be right.
Shouldn't perhaps have put it like I did.  I'm still not totally clear
on the ultimate status of the relationship between the physical and
mathematical worlds - I doubt anyone is ;)

One thing I *am* sure about is that all valid mathematical concepts
map to physical concepts.  So I accept the Tegmark thesis about
mathematics in one sense: that all mathematical things are also
physical.  Again, physical does not have to imply concrete or finite.
Some physical oconcepts have be abstract.

 I can only refer you to my 'Class Diagram Of Reality' which is a
graphical representation of my latest attempt to classify all
knowledge at the highest level of abstraction.  The story behind it is
that I spent 5 years of intense focus on ontology (for fans of Vernor
Vinge: I became a 'zip-head' for 5 years in the field of Ontology) and
the class diagram is the result of that.  So it's not something I've
just put up without a *lot* of deep thought.  Here's the diagram:


The three levels of reality I've talked about this thread are
represented in the diagram along the up-down axis.  At bottom are
'Models' (The State Level Of Reality, the most fundamental).  At top
are 'Systems' (The Operational or Functional Level of Reality).  In
middle are 'Tools' (The State-Change Level or the level of
computatational physics).

Physical,Mathematical and Teleological concepts are along another
axis: from left to right.  Incidentally, the fact that there are
actually more than one ontological axis is, I believe, the source of
immense confusion in the field of KR/Ontology.   Don't confuse this
axis with the other axis I mentioned in the previous paragraph!

The Physical concepts are all represented by the left hand boxes.  The
Mathematical concepts are all represented by the right hand boxes.
You map the concepts by mapping the physical boxes to the Mathematical
boxes in the corresponding positions on the other side of the
diagram.  It can be seen that math and physics completely map to each

But you may be right that in terms of *explanatory power*, mathematics
is primary.  The 'Reality Theory' represented by the diagram is
*itself* a class - it belong in one of the mathematical boxes - the
box 'Symbolic Logic' to bottom right.  In that case it would appear
that indeed all concepts spring from mathematics.

But what is mathematics?  It's three things I think: Categories,
Relations and Propositions.  Of these, Relations and Propositions
refer to discrete (finite) knowledge.  But Categories includes the
other two, since categories can also deal with the infinite.  So it
would appear that the ultimate root of it all is *Categories*
(Category Theory).  Number Theory/Sets are general kinds of category.
Machines/Computer Science deal with finite categories.

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