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. What exactly does "fundamental
level" mean? Does there have to be "something fundamental"?
Fundamental is often used in two senses. either as "very important". In that sense
physics and math are fundamental.
Or is the sense of "primitive", that is, what we have to assume at the start, like the
primitive symbol in a theory, intended to denote what we admit to exist at the start.
We need them because we cannot derive anything from nothing. Even in the "nothing
theories", we need the mathematical axioms to handle some notion of nothing.
There is another way that avoids assuming that there is something "fundamental". It is
a sort of ring of explanation (actually suggested by Bruno):
Of course it is objected that this is viciously circular; but I counter 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 need to postulate a
universal base. You need at least the assumption of the laws of addition and
multiplication, or abstraction and application (with the combinators). But then you
don't need, nor can use, anything else, in the ontology. Physics and psychology can be
explained from there (even easily if comp is invoked at the metalevel, but this is no
more needed "after "the UDA is understood (normally).
But you need an explanation for arithmetic. Why do we conceptualize similar things as
enumerable? Why did we invent numbers and addition and multiplication? That's the
advantage of the ring, you can start at any point you think you understand and explain
other things in terms of it. That's why we don't teach children arithmetic by giving the
Peano's axioms. First, we give them counting and examples. We're starting a "science",
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