On 03 May 2013, at 17:09, John Mikes wrote:
Never argue with a logician!
I try to insert some re-remarks into '&'-induced lines below
John
On Fri, May 3, 2013 at 5:52 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 02 May 2013, at 18:03, John Mikes wrote:
Bruno asked: "are you OK with this?" - NO, I am not OK:
as I follow, 0 is NOT a number, it does not change a number.
0 * 1000 = 0.
& read in English: 'zero times thousand is zero, - which is
&-funny: it is not additional/subtractional only states that if I
&take the '1000' NOT AT ALL I get nothing. You are right: I &have
no problem with 0.00089, 0s as "position markers" for &the order of
magnitude of the 89. I have problems if (some &of the) 0-s are NOT
zeros, like 0.20489: to use NUMBERS &as position-markers (the dirty
trick of a decimal point -<G>)
Well, I have to say you are the first to refuse to 0 the number
status, with the notable exception of the greeks, but they did not
really discovered it.
I am sure you have no problem with expression like "the
concentration of this product is 0.00089 cc". It uses the number 0,
which is very useful in the decimal or base notation of the natural
and real, and complex numbers.
But how do you " A D D " a number to another one if it is not
identified as a quantity?
"quantity" is already part of some interpretation, but you can use
it, it is very well.
&so you do not IDENTIFY, you just INTERPRET? (and do &so
'practically')
Yes, and if we are cautious enough, the reasoning and the conclusion
will not depend on the interpretation. It is not well known, but this
has made clear by Gödel, Henkin in the frame of the first order
predicate logic.
Can you add an electric train to the taste of a lolly-pop?
No, but those are not numbers.
&How would you know, if you do not know what NUMBERS &are? So far
(my) 'Ding an Sich' can be anything.
We might not know what numbers are, and be pretty sure what they are
not.
You speak about 'axioms' (- in my words they are inventions to
prove a theory's applicability.)
They are just hypotheses that we accept at the start for doing the
reasoning. Nobody ever says that an axiom is true, except in some
philosophical context.
&does that mean that 'an axiom is untrue'? if it is 'not true',
&why should I accept the hypothesis based on it? Maria said &I lack
a proposal substituting the accepted reasoning. &Pardon me, I am not
smarter than those zillion wise men
&who so far used 'numbers' - yet I have the right to question.
We don't know if the hypotheses are true. That does not entail that an
hypothesis is untrue. It means that we are agnostic. This should not
prevent us to reason as IF they are true, in case the theory
(hypotheses) shed light on some subject.
So no reversing please: proving the theory by axioms.
We never do that. We always prove FROM axioms, and we always know
that "proving" does not entail truth or knowledge. Only pseudo-
scientists believe that we can prove things about some reality.
&I am not for 'proving', do not accept 'reality' and 'truth'. I am
&just a simpleminded agnostic who asks questions.
And I am a simple minded agnostic who try to answer them. The point is
that proving does not mean at all "making true". Proving just shows a
shatable path (for good willing people readu to do some work) between
hypothesis and consequences. It does not mean that the hypotheses, nor
the consequences, are true.
May I repeat the main question: is YOUR number a quantity?
Natural number have both. A quantity aspect, and an ordinality
aspects, like in the first, the second, the third, etc.
so you can add (two = II to three = III and get five = IIIII) ??
That's correct.
&Now I really do not get it. You marked the quantity-aspect &by pegs
- au lieu de anything better.
? you did.
So WHAT is that
& NUMBER TWO marked by 'II'? Do you COUNT them?
&(what?)
In the theory I gave, two is the successor of one, and one is the
successor of zero, and zero is that unique number which is such that
when added to some number, it gives that number.
If THAT is your axiom then numbers are quantity specifiers.
You can see it that way, but we don't need to agree on this, as long
as you agree with the axioms given. Agreeing in science does not
mean that we believe those axioms to be true, but that we can
understand them and use it to develop some other theories.
Now 2+3 = 5 was not an axiom, but it can be derived from them easily.
&As an agnostic I cannot "agree in science" or it's axiomatic &bases
just to submerge into a conventional belief system,
&which includes the interlaced assumption-conclusion mass &we call
'science'. Numbers, or not.
Science is agnostic. (well, before Nobel Prize and before pension, and
out of the coffee room, actually). When science is not agnostic it is
pseudo-religion or pseudo-science.
We may AGREE on that, but then numbers are indeed the products of
human thinking applied as humans think. Q E D
In which theory?
&Maybe in the overall 'belief' that we can understand the &world.
That needs an act of faith in some world, and some act of faith in our
own capacity to understand.
I do not assume the humans as primitive, I try to explain them in
the theory which assumes that human can be Turing emulated. The
result is that the physical laws evolve from the relation between
numbers, and this in a testable way. the advantage is that we get an
explanation (perhaps wrong, of course) of why we have consciousness
and qualia.
&Please do not forget all those knowables we may acquire &later on
That's why we build hypotheses, and are open to change them in case
new informations refute them, or make them doubtful.
- they may change the 'physical Law' of yesterday
I have never buy them. The physical is just an appearance of reality,
not reality. provably so in the mechanist theory of mind.
&even the "Turing emulation" of the 'HUMAN'.
The result is that IF human are Turing emulable, then Aristotelian
physics is no more defensible.
Which raises &again the question how reliable the "numbers" may be.
(If &we agree in their identification).
Never identify. Just agree on some axioms, and reason from them. Or
propose other axioms.
Bruno: "...That's very good, but we can also develop general
statement. We would not have discover the universal number (the
computers) without agreeing on those principles."
That's a practicality and very fortunate.
It is also a conceptual very deep discovery. Before it,
mathematicians thought that no epistemiological concept (like
computability) could have a universal nature. They believe we could
use Cantor's diagonalization to refute all prtendion to universality
in math, but computability seems to be an exception (cf the Church
Turing thesis).
Does not enlighten the problem of what 'numbers' may be, if not
quantifiers.
The problem is what mind and matter are. The numbers are tools that
we use, and we don't even try to explain them, if only because we
can already explain (in the comp theory) why it is impossible to
understand what they are from anything simpler than them.
&My common sense feeling bows before that.
&I would leave out mind, matter, consciousness
Well, that is what I am working on.
and accept &the numbers as (simplest) tools in a certain aspect.
Good.
Unless &you want to include the 'computation' term for non-math
i.e. &analogue or else not even thought of) topics (logical?) when
&I may see trouble again. Complexity of the world is beyond &our
capabilities (infinite?) to comprehend.
That is why I favor clear hypothetical deductive approaches. We can
learn by being refuted, and suggest new theories.
Bruno
&- John
BrunO :)
JOhn
On Thu, May 2, 2013 at 4:54 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 01 May 2013, at 22:09, John Mikes wrote:
Bruno asked why I have problems how to figure out 'numbers'.
In his texts (as I remember and I have no quotes at hand) the
"world" can be construed from a large enough amount of numbers in
simple arithmetical ways (addition-subtraction). Also: numbers do
not mean quantities.
If his older post with pegs (II=two, IIII=four etc.) is OK, the
'words' two and four DO mean quantities. If not, as 'numbers' they
are meaningless combinations of letters (sounds?) we could call
the series any way, as well as e.g.:
tylba, chuggon, rpais, etc. for 1,2,3 - or take them from any
other language (eins,zwei,drei, - egy, kettő, három) as they
developed in diverse domains/lifestyles. The 'numbers' would be
like "Ding an Sich" (German) however used as qualifiers for
quantities if so applied (see Bruno's 'pegs' above).
The terms we are using are not important. All we need is some
agreement on some theory.
Most things we need for the natural numbers can be derived from the
following axioms (written in english):
any number added to zero gives the number we started with (= x + 0
= x)
0 is not the successor of any natural number
if two numbers are different, then they have different successors
a number x added to a successor of a number y gives a successor of
the sum of x and y.
Are you OK with this?
In science we know that we cannot define what we are talking about,
but we can agree on some principles about them.
Bruno: "...We would not have discover(ed) the universal number (the
computers) without agreeing on those principles."
To have discovered the 'universal number'(?) (i.e. computers)
is fine but that does not imply understanding on numbers:
like "numbers are such as to be applicable for..." etc.
My agnosticism needs more than that. Sorry.
More reasonably sounds the idea of my wife, Maria, who assigns the
primitive development of quantities originally to proportions:
"larger (amount)" - "smaller (amount)" evolving in some thousand
centuries into the process of 'counting' the included units.
That's very good, but we can also develop general statement. We
would not have discover the universal number (the computers)
without agreeing on those principles.
I published on this list my thought for developing the Roman
numbering signs. I started with 2 - a PAIR of hands etc. (not with
one, which means only the existence) and branching into 5 (as
fingers, as in pentaton music) already as 'many'.
OK.
I still have no idea what description could fit 'number' in
Bruno's usage (I did not study number - theory - to keep my
common sense (agnostic?) thinking free).
See above.
Bruno
John
John Mikes
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