On Thursday, May 30, 2019 at 3:32:41 PM UTC+2, Philip Thrift 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. >
If there is no abstract triangle then there is no concrete triangle either, because what would it mean that there is a concrete triangle? That seems more of a trouble. -- 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/f6d35c1b-dc83-465e-ad23-6ae4b84b2a47%40googlegroups.com.
