> On 30 May 2019, at 14:50, Tomas Pales <[email protected]> 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.
In philosophy base on the assumption that there is a primitively Aristotelian reality. Note that in math, an instantiation is when you replace a variable by a “concrete” number. With mechanism assumed in the cognitive science, the physical reality is projection in the mind of the universal Turing machine (which probably exist in elementary arithmetic). Physics is not the fundamental science, once you bet on mechanism (like Darwin did). > 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. OK. But that view can be shown inconsistent with the idea that the brain does not use magic to function. You need a non-mechanist theory of mind to make sense of this. With mechanism, physics emerges from a statistic of number dreams (so to speak, they are computations with a notion of being seen from inside arithmetic) which are (provably when assuming mechanism) realised in the elementary arithmetical reality. The number 17 is, for a mechanist, more concrete than the moon, which only seems concrete because the brain is programmed to make us feel that way. 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/a59b80c8-b58c-43f6-af87-a843735e35f8%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/a59b80c8-b58c-43f6-af87-a843735e35f8%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/946CBA95-D64F-43E6-9303-AA0AEEDA05D6%40ulb.ac.be.
