On 30 Nov 2010, at 16:51, Pzomby wrote:



On Nov 29, 7:25 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 28 Nov 2010, at 21:18, Pzomby wrote:

On Nov 27, 10:49 am, Rex Allen <rexallen31...@gmail.com> wrote:
On Thu, Nov 25, 2010 at 7:40 PM, Jason Resch <jasonre...@gmail.com>
wrote:
On Thu, Nov 25, 2010 at 3:38 PM, Rex Allen
<rexallen31...@gmail.com> wrote:

The same goes for more abstract substrates, like bits of information.
Rex

Assuming that by using the term ‘abstract’ it means ‘non-physical’,

But abstract does not mean non physical. "F = ma" is physical yet
abstract. It is a true (say) abstract relation that we infer from many
observation, and which can be instantiated in some concrete
relationship between bodies, for example.

Would not the context of this discussion, referring to ‘abstract
substrates’, as opposed to physical substrates (quarks and electrons)
indicate that ‘abstract’ (in this case) is not of the physical?  Some
of the contents of human consciousness are non physical (not of the
five senses). ‘Curiosity’ for example is a non physical trait.
http://www.chompchomp.com/terms/abstractnoun.htm


Not bad :)
But as you might guess, such a difference between abstract and concrete can be theory dependent. Is time, or even a moment, an abstract or a concrete: I cannot see it, I cannot hear it, I cannot smell it, I cannot taste it, and I cannot touch it ... unless there is particle of time (chronon, that exists ... in some theories!).
What if we discover 'curiositon' :)



is
it possible for information or anything to be ‘more’ or even ‘less’
abstract.  Are not the physical and abstract realms pure unto
themselves with no possibility of being more or less abstract or
physical?  In other words ‘abstract substrates” could be
incongruous.

This is theory dependent. Natural numbers are usually considered by
number theorists as being very concrete (yet immaterial) objects.
Relations between numbers are more abstract, and relations between
those relations are still more abstract. In math, algebra is
considered as more abstract than arithmetic. category theory is known
as very abstract. Lambda calculus contains a "concrete" abstraction
operator (indeed "lambda") capable of constructing more and more
abstract objects. It replace concrete/token immaterial object like
numbers (or strings) by variable one.

Bruno

Yes, ‘theory dependent’ human constructs.  No doubt number theorists
have agreed upon terminology and understandings that describe the
functions and results. Are what they are really referring to, is that
which is ‘finite’ (having natural boundaries or limitations) rather
than concrete?

The basic objects of number theorist are the numbers, but they are interested in functions, properties, relations, which are always infinite objects.


Are not category theory, algebra, etc. representing
things that have ‘finite’ rather than ‘concrete’ properties?

No their objects are usually infinite. The category of sets is so big that it is not even a set. It is bigger than all the Cantiorian infinties. That *very* big.



If a
mathematician or scientist presumes the brain is the mind

That is a direct category error. I can see, smell touch, ... a brain. Not so for a mind. yet a mind can be said concrete like whenh I talk about my mind, or some precise people mind in some situation.




as in
physicalism, materialism etc.,

They do association. identity theses are not all category errors.



he of course, will have little choice
but to describe everything (including human consciousness) as
concrete.

That is the reason to make distinct the duality abstract/concrete from immaterial/material. My mind is concrete, moments are concrete, numbers can be considered as concrete, more generally the object of the structure are concrete, as opposed to their possible relations. My (human) consciousness is concrete, (even if it is immaterial and different from my brain).
Human conciousness in general is an abstract notion.
Notions are abstract, dispositions are abstract, and concreteness will depends on theories, current paradigm, ontological choice or reality, etc.


Bruno
http://iridia.ulb.ac.be/~marchal/



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