On Monday, October 22, 2018 at 1:41:23 PM UTC+2, Bruno Marchal wrote:
> > The computable universe hypothesis cannot make sense. To define > “computable” you need to assume arithmetic. But arithmetic executes all > computations, and the measure problem will have to involve infinities. > So the correct passage from “mathematical universe” to computationalism > consists in > > 1) distinguish well the ontology and the phenomenology. Restrict the > ontology to the finite and computable finite objects, > In his paper, Tegmark included in CUH only mathematical structures defined by halting computations. So I guess this would include only finite computable objects? > > 2) allowing the infinite in the phenomenology, where indeed the physical > universe will appear. > > The infinities ruins physics only if they are put in the ontology. This is > explained in details in basically all my papers (on this subject). I can > give the reference (again) if you are interested. Tegmark missed the > mind-body problem. > > How do you include the infinite in the phenomenology when you only have finite objects in ontology? I imagine that we cannot really experience or perceive the infinite, but we may infer it inductively from finite objects. And this inductive inference may perhaps give us a kind of feeling or sense of "the infinite", but it would be a feeling from the inferential process rather than from the infinite itself. Anyway, I should tell you that I am no mathematician, so I am afraid I can't digest the technicalities in your papers. I am not even a physicist or a professional philosopher, I just dabble in philosophy. In my ontological musings, I try to get to the bottom of what is necessary and avoid arbitrary assumptions. First, what is existence? All definitions of existence should follow the principle of logical consistency, or in other words, the principle of identity: an object (that which exists) should be identical to itself. It should be what it is and not be what it is not. This also means that the object should be defined consistently in relation to everything else, otherwise its identity would be violated. I know there are people who believe in the existence of inconsistently defined objects (dialetheists), but that seems like craziness to me, sorry. Moreover, unless you arbitrarily block logical explosion, such an inconsistency would render all ontology meaningless, erasing even the difference between existence and non-existence. So, logical consistency is a necessary criterion of existence. Is any other criterion necessary? I don't think so. Adding any other criterion seems like an arbitrary restriction on what exists. If an object is identical to itself, then it is something rather than nothing and so it is there in some sense. Instead of excluding some consistent object from existence, we can talk about the way in which it exists. And so, we can *identify* logical consistency with existence, as the property of all existing objects (there are actually no non-existing objects because such objects would have to be inconsistent and therefore they would not be objects but nothing). Next, I find that if there are objects, then there must also be relations between them, as a special kind of objects that hold between other objects. Relations are just as necessary as the objects between which they hold. And while relations also hold between other relations, there must also be objects that are non-relations, as I explained in this thread earlier today. Next, I find that the most general relation is "similarity", because it is a relation that holds between any two objects. It means that the two objects have some different properties and some same properties. Which gives rise to another general relation called "instantiation", which is the relation between a property and its instance. The instantiation relation is a special kind of the similarity relation but less general than similarity since it doesn't hold between arbitrary two objects. Finally, any objects can define a collection of them (for example based on their common property, as long as such a definition is consistent), which gives rise to another general relation called "composition", which is the relation between a collection and its part. The composition relation, too, is a special kind of the similarity relation but less general than similarity since it doesn't hold between arbitrary two objects. So, the similarity relation, together with its special kinds - instantiation and composition, defines all possible relational structures. And all these three relations come together in set theory, the foundation of mathematics (instantiation is the satisfaction of a property/predicate by a set and composition is set membership or the derived relation of set inclusion). More accurately, by "set theory" I mean all consistent versions of pure set theory. What all versions of pure set theory have in common is the concept of set as a collection of objects that can be defined by listing those objects (set members) or by specifying their common property. As it turned out, not every definition via a common property is consistent, and since it would not be very useful to define sets only via listing of members, one must also specify with axioms what common properties can be used to define sets. Which gives rise to uncountably many axiomatic versions of pure set theory. The relational aspect of reality is therefore defined by set theory and in this sense is mathematical. That's where my ontology is the same as Tegmark's mathematical universe idea. But in my ontology there are also non-relations, which constitute a non-mathematical aspect of reality. I propose that these non-relations, or at least some of them, are the qualities of consciousness (qualia), thanks to their non-relational (unstructured, unanalyzable) nature, which is nevertheless inseparable from their relations to other objects, some of which we call "correlates of consciousness". In view of this, why do you restrict your ontology to finite arithmetic and how do you get qualia from it? -- 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.
