On Thu, May 30, 2019 at 1:18 PM Philip Thrift
<[email protected] <mailto:[email protected]>> wrote:
On Thursday, May 30, 2019 at 9:14:48 AM UTC-5, Jason wrote:
On Thursday, May 30, 2019, Philip Thrift
<[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.
Jason
For the fictionalist, one can invent anything, including
mathematics with different definitions of sets producing a
multiverse of mathematical truths (Joel David Hamkins) and
logics that are inconsistent (Graham Priest).
Matter (the universe we live in) gives what it gives and
nothing more.
There is a story today about rare earth minerals:
https://www.cnn.com/2019/05/30/investing/rare-earths-china-trade-war/
<https://www.cnn.com/2019/05/30/investing/rare-earths-china-trade-war/>
I suppose for those who think that matter doesn't exist, a
shortage of rare earth minerals cannot be a problem. Maybe
someday we build a matter compiler that can make them.
I didn't say matter doesn't exist. I only point out that the
property you call "existence" doesn't seem to */do/* anything.
