> On 30 May 2019, at 20:18, Philip Thrift <[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] <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 > > <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/ > > 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] > <mailto:[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 > > <https://groups.google.com/d/msgid/everything-list/9271b101-d253-41c0-b0b2-3bb48b390646%40googlegroups.com?utm_medium=email&utm_source=footer>.
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