> On 30 May 2019, at 16:52, Tomas Pales <[email protected]> wrote: > > > > 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 > > <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. > > 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.
Agreed. Now, we could say that there is no concrete object. Concreteness is when abstraction seen from inside. But usually I consider natural numbers, or programs, as concrete primitive objects, but each soul is multiplied in the infinities of computations that we get when we assume the (natural) numbers. Bruno > > > -- > 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/f6d35c1b-dc83-465e-ad23-6ae4b84b2a47%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/f6d35c1b-dc83-465e-ad23-6ae4b84b2a47%40googlegroups.com?utm_medium=email&utm_source=footer>. -- 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/92AB0D42-CA5D-42E9-92B8-CD0306FB7842%40ulb.ac.be.
