On Friday, May 31, 2019 at 11:04:53 AM UTC+2, Bruno Marchal wrote: > > > On 30 May 2019, at 14:50, Tomas Pales <[email protected] <javascript:>> > wrote: > > 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. > Yes. I didn't want to make my point about the instantiation relation too long but there is a hierarchy of abstract objects from the most abstract to the least abstract and under them are concrete objects. For example, "mathematical object" is instantiated in "number", which is instantiated in a specific number, for example in number 2, which is instantiated in the concrete relation between two concrete flowers. Concrete objects are the bottom of instantiation because concrete objects have no instances. Number 2 is instantiated in the relation between any two objects, or abstract flower is instantiated in any concrete flower, but a concrete flower has no instances; it cannot be said that the flower that is growing under my window is a property of something else.
An interesting question is whether there are abstract objects that never bottom out in concrete objects. Similarly like for the composition relation where you have a collection of collections of collections etc. ad infinitum, never bottoming out in empty collections. But I guess these infinite chains are subject to Godel's second incompleteness theorem so we may never know whether they are consistent and thus whether they exist. As for the most abstract object, I would say it is "existence" because it is instantiated in every object, including in itself. Existence is just the principle of logical consistency or identity. Inconsistent objects don't exist because they are not even objects. What kind of object is a "triangle that is not a triangle"? It's nothing. As you said, the set of inconsistent objects is empty. > 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. > Number 17 is the property of the relation among any 17 objects. The moon orbiting our planet is not a property of anything. Therefore number 17 is an abstract object and the moon is a concrete object. -- 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/2470590b-373e-4595-970c-40409ee19907%40googlegroups.com.
