On Fri, Nov 16, 2018 at 12:42 PM Bruno Marchal <marc...@ulb.ac.be> wrote:

> *> A practical difficulty here is that logicians used the term model like
> painters: the model is the reality*

Mathematician can use one part of mathematics to model another part, for
example Descartes found a way for geometry to model algebra, and those 2
things can have equal complexity; but that like using English to talk about
the English word "cat". Whenever mathematics tries to model something that
is not itself, like something physical, it always comes off looking second
best because mathematics is just a language, a very very good language for
describing physical law but a language nevertheless.

But, I hear you say, the numbers 11 and 13 are prime and that fact is
unchanging and eternal!  Well yes, but the English words "cat" and "bat"
rhyme and that fact is also unchanging and eternal.

> > *I alluded to the fact that you can identify (by clear definable
> bijection) a model with the set of (Gödel number) of all true sentences in
> (the standard model of) arithmetic.*

Mathematics can't even identify all true sentences about arithmetic much
less become the master of physical reality. We know  the sentence "the 4th
Busy Beaver number is 107" belongs in the set of true sentences, but what
about "the 5th Busy Beaver number is 47,176,870"?  It's either true or its
not but will you or I anybody or anything ever know which one?  Nobody
knows and nobody knows if we'll ever know, but we do know that nothing will
ever know what the 8000th Busy Beaver number is even though its well
defined and finite.

*>You already need 2+2=4 to make sense of matter,*

Recent studies see to indicate that without a working brain a person's IQ
tends to drop rather dramatically, so you've got it precisely backwards yet
again,  you need matter to make sense of 2+2=4 or to male sense of anything
at all.

> *But you don’t need silicon,*

True, carbon and carbon compounds will also work.

> > or “being made-of” to define the numbers.

You need a brain made of some sort of matter to define numbers or to define
anything at all, not that there is anything special or even very
interesting in the act of definition, you need a brain made of matter to do

> *> If 2+2=4 depends on matter, tell me how a magnetic field, or a
> electromagnetic field, or a gravitational field, or any physical field
> could pertubate 2+2=4.*

2+2=4 is a description in the language of mathematics about how some
physical properties behave. For example, the mass of 2 protons and the mass
2 more protons equals the mass of 4 protons. But 2+2=4 doesn't work for
everything, the temperature of 2 hot water bottles and 2 hot water bottles
does not equal the temperature of 4  hot water bottles. Temperature doesn't
add up in the same way that mass does, a different description is needed to
describe what's going on.

> *>computations, can be defined in* [blah blah]

Who cares??  Definitions are just a human convention, a definition of a
computation can't compute and a definition of a airliner can fly you to

> You confuse the [blah blah]

No, you confuse the difference between a cat and the word "cat" . The
difference is one can have kittens but a word can't.


> > the models/realities intended will be usually much more complex, as you
> said above.

Mathematical models are ALWAYS simpler and less rich than the physical
reality they try to represent. So why in the world would you say the
physics is modeling the mathematics when its obvious that the mathematics
is trying, with limited success, to model the physics?

John K Clark


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