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_W >>> orks_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/ > > > 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 -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CA%2BBCJUjs_mKEnoKeP%2B9UT2sr605H8mJ0wXD5cRJVaB54gSEEhg%40mail.gmail.com.
