On 20 Dec 2012, at 17:53, meekerdb wrote:
On 12/20/2012 1:29 AM, Bruno Marchal wrote:
People agree that 2+2=4 because it is a simple truth which follow
from simple definition.
But that makes it conditional on the definition (axioms).
Usually we prefer not see a definition as a condition, but logically
you can do that.
We prefer to say that 17 is prime, instead of "if p->(q->p), if (p->(q-
>r))->(p->q) ->(p->r)), if ..., and if s(x) is different from 0 for
all x, and if x = y when s(x) = s(y), and if if x + 0 = x, and if x
+s(y) = s(x+y), and if x * 0 = 0, and ..., and ... then 17 is prime".
We assume we are OK on the prerequisite.
And it is not such a simple truth. Two raindrops plus two raindrops
makes one big raindrop.
Raindrop and clouds are bad model for what we mean by natural numbers.
Come on. You could demolish Einstein special relativity with remark
"--Mister Einstein, we member of the jury are not convinced by your
thesis. There is a definite lack of rigor. Clearly E = mc^2 will not
work with 2 interpreted by 2 raindrops. FAIL."
One bridge teams plus one bridge teams equals three bridge teams.
The simplicity of the truth comes from abstracting away all the
particulars of reality. So people are agreeing about words and
definitions and meanings - but not about facts.
That is why I am a theoretician. Notably. I say that if comp is true,
then physics is given by <this theory>. Facts confirms, but I let to
talented experimenters to decide or refute it in fine.
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