On Sunday, October 21, 2018 at 11:16:29 PM UTC+2, Brent wrote: > > > > On 10/21/2018 7:11 AM, Tomas Pales wrote: > > I am generally sympathetic to Tegmark's mathematical multiverse idea, but > I have two comments/criticisms to it: > > 1) I am not sure whether Tegmark is aware of the so-called "instantiation" > relation. In philosophy, the instantiation relation is the relation between > a general and a particular object, where the particular object is an > instance of the general object. In other words, the general object is a > property of the particular object. Example: general triangle (or triangle > "in general") is the property of any particular triangle, and any > particular triangle is an instance of general triangle. Another example: > number 2 is a general relation that is instantiated in the particular > relation between any two objects. I am not sure whether Tegmark realizes > the difference between general objects and their instances, because he said > something like: when we probe matter we only find numbers (and hence > reality is just mathematics). But numbers cannot be found in our world; you > cannot find number 2 sitting on a tree or in the atomic nucleus. You can > only find instances of number 2, as relations between particular objects. > Mathematical objects are usually thought to be general objects, but in that > case there is more in reality than mathematical objects: there are general > objects *and* their instances. And in our physical world there are *no* > general objects, only their instances. If we want to say that there are > mathematical objects in our physical world, we should include among > mathematical objects also non-general objects, that is, objects that have > no instances. (By the way, there is a hierarchy of generality: more general > objects are instantiated in less general objects and those are ultimately > instantiated in non-general objects. Non-general objects are often called > "concrete", while general objects are also called "abstract".) > > > This appears not to be a well-order hierarchy. The thing I am sitting on > is an instance of a chair, and it's concrete. But it's also an instance of > a matter, i.e. a collection of particles of the Standard Model (which may > or may not be the most general category). It's also an instance of things > I own. >
Yes, it is not always possible to say that one object is more general than another. Matter (the property of being a material object) is more general than chair (the property of being a chair) because the set of chairs is a subset of the set of material objects. But the property of being a chair is not necessarily more or less general than the property of being a thing you own. > > > 2) While I agree with Tegmark that reality contains all mathematical > objects (both general and non-general), I think there is also a > non-mathematical aspect of reality. That's because mathematical objects are > relations or structures of relations, but relations cannot exist without > objects between which they hold. While it is true that relations can hold > between other relations, there should also be objects that are > non-relations, which ultimately make sense of all relations. These > non-relations are the non-mathematical objects and they (or at least some > of them) may be the qualities of consciousness (qualia) - because (1) they > have an unanalyzable/unstructured nature, and (2) they stand in relations > to other objects (relations or non-relations) that we call "correlates of > consciousness". > > > Can you clarify with some examples? > Relation is an object that holds between other objects. (By the way, all relations are instances of the similarity relation, which means that the objects between which a similarity relation holds have some same property and some different property.) But how could there only be relations between other relations that are relations between other relations etc., just relations? It seems that the definition of all those relations would be infinitely postponed; they would never be defined. And if you wanted to make a finite structure of relations that is ultimately cyclical, where relations are defined in relation to each other, every relation in that structure would end up being defined as a relation between *itself* and other relations. Which is another nonsense, because a relation holds between *other* objects than itself. -- 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
