On 01 Jan 2014, at 21:35, meekerdb wrote:

On 1/1/2014 3:57 AM, Bruno Marchal wrote:On 31 Dec 2013, at 22:27, meekerdb wrote:On 12/31/2013 2:22 AM, Bruno Marchal wrote:On 30 Dec 2013, at 21:43, Stephen Paul King wrote:Dear LizR and Brent,I will try to go at this from a different direction. Whatexactly does "fundamental level" mean? Does there have to be"something fundamental"?Fundamental is often used in two senses. either as "veryimportant". In that sense physics and math are fundamental.Or is the sense of "primitive", that is, what we have to assumeat the start, like the primitive symbol in a theory, intended todenote what we admit to exist at the start. We need them becausewe cannot derive anything from nothing. Even in the "nothingtheories", we need the mathematical axioms to handle some notionof nothing.There is another way that avoids assuming that there is something"fundamental". It is a sort of ring of explanation (actuallysuggested by Bruno):Math->Physics->Biology->Evolution->Humans->Culture->Science->MathOf course it is objected that this is viciously circular; but Icounter that if the circle is big enough to take everything in,then it is virtuously circular.Such circles recur in the UD*, but to define the UD, you still needto postulate a universal base. You need at least the assumption ofthe laws of addition and multiplication, or abstraction andapplication (with the combinators). But then you don't need, norcan use, anything else, in the ontology. Physics and psychology canbe explained from there (even easily if comp is invoked at themetalevel, but this is no more needed "after "the UDA is understood(normally).But you need an explanation for arithmetic.

Really?

`We need to start from some non trivial agreement, and if we want`

`arithmetic, or a universal system, we have to assume it, as we cannot`

`justify it with less.`

`Then the explanation is usually provided in high school, and relies`

`without doubt to its natural implementation in our brain.`

Why do we conceptualize similar things as enumerable? Why did weinvent numbers and addition and multiplication?

`To be sure we have enough meat to the family. To survive in the`

`arithmetical reality, relatively to our current history.`

That's the advantage of the ring, you can start at any point youthink you understand and explain other things in terms of it.

`Well, that is doing a theory. We can't justify the axioms, but we can`

`believe in them. The question you ask applies to *any* scientific`

`theory, if only because they assume arithmetic at the start. The`

`result here is that in comp, we cannot even add one axiom to very`

`elementary arithmetic (à-la Robinson).`

`Our intuitive understanding of the numbers remains quite mysterious.`

`In a sense comp reduces all mysteries to that only one. How can we`

`make sense of N = {0, 1, 2, 3, ...} in a finite time is a total`

`mystery. But comp can explain why, for machines (even in a very weak`

`sense) it has to be felt as mysterious.`

`We can say: "God creates the natural Numbers". It is way to say that`

`we don't know where they come from.`

`The new point is that with comp, God did not need to create anything`

`else.`

That's why we don't teach children arithmetic by giving the Peano'saxioms. First, we give them counting and examples.

That is the best way to teach. Examples first, theory after.

We're starting a "science", empirical observation.

`Sure, then we do a theory, and we can test it by its consequences. No`

`problem with this. That is how computationalist science proceeds.`

Bruno

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