> On 31 May 2019, at 22:27, Tomas Pales <[email protected]> wrote: > > > > 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.
Keep in mind that the consistent machine is able to prove its own Gödel theorem. That is why the ontology will admit bottom and be well-founded, but the non-bottom aspect of reality will be unavoidable in the first person perspective, somehow. > > As for the most abstract object, I would say it is "existence" because it is > instantiated in every object, including in itself. Hmm… That makes sense, perhaps, in rich ontologies à la NF (Quine’s New Foundation), where the universe (of sets) can be a set. Something similar can be emulated in ZF using anti-foundation axioms, but I avoid them, for technical reason, and because it could only be a variation of simpler things occurring in the phenomenology. With mechanism, the ontology os well-founded. > Existence is just the principle of logical consistency or identity. Almost. Peano arithmetic is consistent with the proposition that Peano arithmetic is inconsistent. Consistency is shown rather cheap, and far away from Truth, which is the key notion, but of course not a very obvious one. > 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. Here I disagree. 17 is very concrete. It the successor of 16, which is very concrete, etc. With mechanism, 0, 1, 2, 3, … are taken as the most concrete “really existing” object. The moon, and yourself are extremely abstract type, having only phenomenological existence. There are reason why it needs to be like that, but I will refer, at least now, to my papers for the why. (I will have to go soon). To be continued … 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/2470590b-373e-4595-970c-40409ee19907%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/2470590b-373e-4595-970c-40409ee19907%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/10209D29-A97A-4EEC-8D0F-F69A80CE31E7%40ulb.ac.be.
