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. @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/9206de65-c6ac-4fc2-9ed1-5119b410e8f6%40googlegroups.com.
