On Mar 21, 7:48*pm, Sam Wormley wrote:
wrote:
On Mar 21, 4:35 pm, Sam Wormley wrote:
wrote:
On Mar 21, 2:58 pm, Sam Wormley wrote:
wrote:
I believe the laws of nature including number are in fact part of
nature and that human world views, mathematics and physics are
approximations of those rules in human terms. If the laws of nature
were not part of nature then how would nature know to produce which
result in any event? The rules have to be part of process itself.
Think of nature as computational. The rules as well as what they
operate on must be present in the computer itself for anything to
happen.
Edgar
* *Nature didn't need humings to exist... We have devised models
* *that are good approximations making predictions about how nature
* *behaves or probabilities about natures behavior. This idea of rules
* *and laws is a human construct.
* *Edgar... to say that "nature as computational" is likely misleading
* *you.
Sam,
Then how does nature know what results to produce for each event in a
consistent manner if it is not embodying some rules that determine the
results?
* *Maybe it doesn't "know".... it just is.... We make up rules.... and
* *when we find the rules are wrong... we make up new rules.... We're
* *get'n pretty good at it!

* *Quantum Mechanics, QED, QCD, etc.
* *General Relativity
* *etc.

Sam,

Well of course it doesn't 'know' in the sense of consciously deciding.
The point is that everything that occurs occurs according to rules
therefor those rules must be part and parcel of the occurrence itself.
Thus the laws of nature must be part of nature.

EDgar

* *What rules where individual photons strike in Young's double-slit
* *experiment?

Quantum mechanics seems to be a pretty accurate human approximation of
the actual rules nature uses in this case.

Edgar

On Fri, 21 Mar 2008 16:01:00 -0700, EdgarOwen wrote:

The point is that everything that occurs occurs according to rules
therefor those rules must be part and parcel of the occurrence itself.
Thus the laws of nature must be part of nature.

Do you see a difference between an occurrence happening according to
rules and the occurrence defining a rule by it's own occurrence?

Isn't a 'rule' the observation of a subsystem which is 'ruled', or acts
in accordance with a larger or pre-existent one?

wrote:
Godel can use proof to prove his incompleteness of proof without a
problem since his conclusion is not that any particular proof, or
proof itself, is invalid, only that some valid propositions cannot be
proven.

What needs to be understood is to understand the precise hidden
assumptions that Godel's incompleteness are based upon. I believe
these include infinities and recursion. When these are removed then I
believe we can have logically complete systems. My premise is that
there is an actual physical mathematics in which this is true (laws of
nature) and that human mathematics is an abstract approximation to the
actual physical mathematics. The human version makes a number of
unwarranted extensions into infinities based on a view that nature is
continuous. Eg. that there are an infinite number of real numbers
between any two integers. If nature is discrete, not continuous then
this view fails and Godel's incompleteness no longer applies. We then
have recovered the possibility of completeness.

Thus we need to formulate what this actual physical mathematics might
entail. It seems to me that what we get is a fuzziness at extreme
scales, and the notion that the number system must be scaled somehow
to physical reality.

It also may be that this fuzziness of physical math at the quantum
scale might itself be capable of explaining certain 'fuzzy' aspects of
the quantum world as mathematical rather than physical. For example
uncertainty might understandable as an imprecision in a physically
scaled number system rather than as a strictly physical quantum
characteristic.

Edgar

I contend that 'some valid propositions' and the rest of the
propositions, are not one set of propositions but are propositions made
under different, competing frameworks.

The relationship between maths, the world, and ourselves was developed
by many philosophers. Kant proposed that all these are generated under
the same manifesting umbrella which he called understanding and reason,
generating the world of phenomena and noumena.

On Mar 22, 8:52*am, ZerkonX wrote:
On Fri, 21 Mar 2008 16:01:00 -0700, EdgarOwen wrote:
The point is that everything that occurs occurs according to rules
therefor those rules must be part and parcel of the occurrence itself.
Thus the laws of nature must be part of nature.

Do you see a difference between an occurrence happening according to
rules and the occurrence defining a rule by it's own occurrence?

Isn't a 'rule' the observation of a subsystem which is 'ruled', or acts
in accordance with a larger or pre-existent one?

One needs to explain why similar occurrences all over the universe all
happen according to the same rules. Therefor an occurrence can't
generate a rule, the rule must be part and parcel of the occurrence.

Edgar

wrote:
[about Goedel's proof]If self referentiality is disallowed his proof fails.

In no system "interesting" enough is it possible to prevent self
reference. THAT is his point. (one of them, anyway)


Tom Roberts

Michael Helland wrote:
Newton's law of gravity didn't last forever.
If GR gets over turned in the next century, does that mean it wasn't a
law of nature?

No modern scientist discusses "Laws of Nature", because we understand
that Nature is inscrutable to humans. What we do is construct MODELS of
the world. If GR gets overturned in the next century, that will occur
because a better MODEL is discovered, with presumably a wider domain of
applicability. That will not affect GR's applicability within its domain.


There are Laws, Truth, out there, but we don't know them.

Doubtful, HIGHLY doubtful. There is Nature out there, but there's no
requirement whatsoever that She behave as you want Her to behave (by
following "Laws" or implementing some "Truth").


What we know are hypotheses and theories, which were invented.

Sure. They are MODELS OF THE WORLD, not "Laws", not "Truth".


Tom Roberts

On Mar 24, 12:53 pm, Tom Roberts wrote:
Michael Helland wrote:
Newton's law of gravity didn't last forever.
If GR gets over turned in the next century, does that mean it wasn't a
law of nature?

No modern scientist discusses "Laws of Nature", because we understand
that Nature is inscrutable to humans. What we do is construct MODELS of
the world. If GR gets overturned in the next century, that will occur
because a better MODEL is discovered, with presumably a wider domain of
applicability. That will not affect GR's applicability within its domain.

There are Laws, Truth, out there, but we don't know them.

Doubtful, HIGHLY doubtful. There is Nature out there, but there's no
requirement whatsoever that She behave as you want Her to behave (by
following "Laws" or implementing some "Truth").

What we know are hypotheses and theories, which were invented.

Sure. They are MODELS OF THE WORLD, not "Laws", not "Truth".

I agree.

But does that mean there is no truth in science?

This is just a minor point, but if you define truth as:

"Absolutely and perfectly true"

Then the models are not "true"

But, if you allow truth to be tentative, temporary, incomplete and
inconsistent, then theories are scientific truth.

(Some people don't like to accept that truth can change or is
imperfect, but if truth is to be meaningful to us, it must be in that
sense.)

Leibniz differentiated between Eternal Truths (Laws of Nature) and
human truth, of which scientific theories are part.

Monotheists and Greek Monists believed something along the same lines.

says...

Perhaps you would like to give some examples of Gs that are provably
unprovable that don't involve self-referentiality?

Godel described how to construct a sentence G and gave
an argument that this G is not provable (under the assumption
that the axioms are all consistent). His proof is completely
*mechanical* in that given any proof of G, we can convert
that into a proof of a contradiction.

As to the nature of the sentence G, it is just an ordinary
statement of arithmetic. G is completely written in the
language of the axioms I gave: It only uses +, *, 0, 1, =,
together with logical operators. It doesn't directly involve
self-reference at all.

It is possible to *interpret* G as "talking about itself",
but G is perfectly meaningful as an ordinary statement of
arithmetic, as well. It can be cast into the form of
a claim that a certain polynomial equation with integer
coefficients has no integer solutions.

Banishing self-reference in mathematical proofs doesn't
make G become provable. It just makes it more difficult
for you to *see* that it is unprovable. It is like putting
a blindfold on to keep from seeing something you don't
want to see.

--
Daryl McCullough
Ithaca, NY

On Mar 21, 12:40*pm, (Daryl McCullough)
wrote:
says...



Godel can use proof to prove his incompleteness of proof without a
problem since his conclusion is not that any particular proof, or
proof itself, is invalid, only that some valid propositions cannot be
proven.

What needs to be understood is to understand the precise hidden
assumptions that Godel's incompleteness are based upon. I believe
these include infinities and recursion.

Not really. Godel's theorem applies to the following
very simple axiom system:

1. forall naturals x: x+1 is not equal to 0
2. forall naturals x: if x is not equal to 0, then there is a
natural y such that y+1 = x
3. forall naturals x and y: if x+1 = y+1, then x=y
4. forall naturals x: x+0 = x
5. forall naturals x and y: x+(y+1) = (x+y)+1
6. forall naturals x: x*0 = 0
7. forall naturals x and y: x*(y+1) = (x*y)+x

Which axiom do you think involves infinity or recursion?

None do. That's why those axioms work so well in robots.
Since the thing they didn't do in defining the naturals,
is define narure.





--
Daryl McCullough
Ithaca, NY

Michael Helland wrote:
On Mar 24, 12:53 pm, Tom Roberts wrote:
Sure. They are MODELS OF THE WORLD, not "Laws", not "Truth".

I agree.
But does that mean there is no truth in science?

We humans have no hope of every knowing any sort of "ultimate truth". We
are humans, not Gods.


This is just a minor point, but if you define truth as:
"Absolutely and perfectly true"
Then the models are not "true"

Models are either valid or not valid; "true" has nothing to do with it.
The concept of validity includes a domain of applicability, which varies
for each theory (model).


Tom Roberts