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.

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.



Can you add an electric train to the taste of a lolly-pop?

No, but those are not numbers.




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.



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.




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.





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.




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?

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.





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.

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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