On Thursday, May 30, 2019 at 9:14:48 AM UTC-5, Jason wrote: > > > > On Thursday, May 30, 2019, Philip Thrift <[email protected] <javascript:>> > 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 >>>> 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 >
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/ 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. @philipthrift -- 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/9271b101-d253-41c0-b0b2-3bb48b390646%40googlegroups.com.
