On 5/30/2019 7:14 AM, Jason Resch wrote:
On Thursday, May 30, 2019, Philip Thrift <[email protected]
<mailto:[email protected]>> wrote:
On Thursday, May 30, 2019 at 7:50:37 AM UTC-5, Tomas Pales wrote:
On Wednesday, May 29, 2019 at 10:15:46 PM UTC+2, Jason wrote:
Appears to predict the arithmetical reality:
"There exists, unless I am mistake, an entire world
consisting of the totality of mathematical truths, which
is accessible to us only through our intelligence, just as
there exists the world of physical realities; each one is
independent of us, both of them divinely created and
appear different only because of the weakness of our mind;
but, for a more powerful intelligence, they are one and
the same thing, whose synthesis is partially revealed in
that marvelous correspondence between abstract mathematics
on the one hand and astronomy and all branches of physics
on the other."
https://monoskop.org/images/a/aa/Kurt_G%C3%B6del_Collected_Works_Volume_III_1995.pdf
<https://monoskop.org/images/a/aa/Kurt_G%C3%B6del_Collected_Works_Volume_III_1995.pdf>
on
page 323.
Jason
In philosophy, the relation between abstract and concrete
objects is called "instantiation", for example between the
abstract triangle and concrete triangles. It is a relation
whereby the abstract object is a property of the concrete
objects and the concrete objects are instances of the abstract
object. The instantation relation is regarded as primitive,
similarly like the composition relation between a collection
of objects and the objects in the collection. The
instantiation relation may appear more mysterious though,
because while it is quite easy to visualize a collection, it
is impossible to visualize an abstract object.
Abstract and concrete objects are existentially dependent on
each other, because there can be no property without an object
that has the property, and there can be no object that has no
property.
In the fictionalist philosophy of mathematics
https://plato.stanford.edu/entries/fictionalism-mathematics/
<https://plato.stanford.edu/entries/fictionalism-mathematics/>
there are no such things as abstract objects.
So such troubles do not arise.
Let's say reality is composed of two sets:
1. The set of all existent things
2. The set of all non-existent things
If nothing existed at all, then set one would be emtpy, while set two
would contain everything.
Now take the nominalist position. Set one would contain the physical
universe while set two would contain all abstract objects:
arithmetical truth, executions of programs, histories of non-existent
universes, etc.
What puzzles me, is that in the program executions and in the
histories of non-existent universes you will find worlds where life
evolves into more complex forms, you will find the risings and
fallings of great civilizations, you will find literature written by
the philosophers of those civilizations, their treatises on ontology,
on why their universe is concrete while others are abstract, on the
mysteries of consciousness and strangeness of qualia. If all these
things can be found in the abstract objects of the set of non-existent
things, then how do we know we're not in an abstract object of that
set of non-existent things?
Does it matter at all which set our universe resides in? Can moving an
object from one set to another blink away or bring into being the
first person experiences of the entities who inhabit such objects, or
is their consciousness a property inherent to the object which cannot
be taken away merely by moving it from one set to another?
Much to think about.
You're equivocating on "existent". The set of all non-existent things
is empty because non-existent things don't exist in one sense of the
word. But then you switch to the other sense of the word so that
"non-existent"="imaginary" and conclude that there are lots of imaginary
things and therefore lots of non-existent things.
Brent
Jason
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