From: Brian Holtz [brian@holtz.org] Sent: Thursday, July 04, 2002 9:39 AM To: Alt.Atheism.Moderated Subject: Re: Science & atheism are cultures. "Paul Holbach" wrote: > > Every set is "purely abstract" in some sense, and for every > > world there is a corresponding logical model with a "purely > > abstract" domain set. > > OK, but you´re begging the question if you simply assume that the > empty world is one of those possible worlds. How so? It merely follows from my definition of world. You're the one who is stipulating that that a domain set is not allowed to correspond to a world if that set is empty. I see no reason for that stipulation. > Mind you, I clearly distinguish between a concrete world > and an abstract representation of a concrete world: on the one hand > there are worlds and on the other hand there are corresponding world > models. But concerning the empty world ("empty" in the sense of > containing nothing and not of nothingness!) speaking of > "correspondence" doesn´t make any sense because the existence of a > relation between A and B presupposes the existence of both A and B. You here blatantly assume that the empty world has some definition separate and independent from its correspondence with a(n empty) domain set and a (length-zero) list of propositions about objects in that set. I gave you this definition back in March; if you're going to insist on using some separate definition, then please be explicit about it. How do you define a world? > If there actually were an empty > world model the fundamental function of models would be annulled. How so? > Are possible worlds more like mobs or more like pouches? Domain sets are sets, and sets can be empty. > I´m not certain about what a physicist would > comment on the notion of zero-dimensional worlds. They have no problem with it. See "On the Dimensionality of Spacetime" by Tegmark. > That the domain of a set is empty means that there is nothing > possessing the set-defining property Huh? The set-defining property of the empty world's domain set is simply membership in that set. It's just a zero-length list. That's it. > by means of which property would you define the set of all inexistent > things?! The empty world's domain set is defined by a (zero-length) enumeration, not by any properties. > I´d really like to see your concrete "list of propositions > about the objects in that set" in the case of there being no objects and, > hence, no relations! I thought this was obvious, but here you go: Domain set D : {} Propositions about objects in D: There you have it. That is the empty world. I see no contradictions in the above. > I defy you to show me the explicit model-theoretic description of the > empty world See the above. > > In the empty world, x cannot be bound, because the domain set > > is empty. > > You´re right insofar as the binding of a variable by quantification > presupposes the existence of at least something. But in case > *nothingness* were a possible state of the world, then IT would be the > necessary existent binding the variable. You're equivocating. "Nothingness" isn't "a possible state of the world"; "nothingness" is a possible world. While some worlds may contain an object in their domain set that corresponds to the world itself, the empty world is not one of them. It violates the rules for defining a world to speak of a proposition in its proposition list as have a variable bound to something that is not in the domain set. > > Lewis may have a good reason for saying this, but until I hear > > of such a reason, I won't simply take his word for it. > > My remark is just a footnote and not intended to be an argument from > authority. I know. > > If someone asserts X, and X has no visible justification, then > > parsimony demands I not believe X. Call parsimony > > "I-don't-see-ism" or any other name, but I'll still employ it. > > My justification is clearly visible! I´ve offered you a chain of > conclusive arguments and a sound logical proof which shows that the > notion of nothingness as an ontological category is inconsistent. No, you've finally revealed that we're not even arguing about the definition of 'world' that I thought we agreed on back in March. In an argument in which two reasonably intelligent people disagree about whether a logical contradiction is present, surely you realize that a disagreement on definitions must be lurking. I'm doing all I can to get you to state your definitions, but nothing I do is working. I think perhaps my time would better be spent on other pursuits. > I´m well aware that the concept > of a state of affairs has a varied history. Which is why I'd prefer to talk about 'worlds' and their strict definitions. I've given mine. What is yours? > simply assuming that object > subtraction is feasible such that finally no object remains is begging > the question whether it´s possible to remove all objects from a world > and to preserve the world itself It's clearly possible under my definition of 'world'. You are free to define 'world' as I do except adding the stipulation that the domain set must be non-empty. (Must the proposition list also be non-empty?) However, I see no motivation for such a stipulation. > > Because it's logically possible that e.g. momentum not be conserved. > > Have you forgotten that logical possibility doesn´t entail nomological > possibility?! Have you forgotten that "nomological possibility" means possibility within our universe under its scientific laws, and that anything that is logically possible is nomologically possible in some world? > Perhaps the *material source of being* is such that > there cannot be any conservation principles other than the actual > ones. I have no idea what you mean by "the material source of being". Such a phrase sets off every nonsense alarm I have. :-) > > A world is, rather, > > anything that can be described with a non-self-contradictory model. > > OK, as long as you posit at least one object Well, you have your definition, and I have mine. I guess we're done then. > > I'm still not convinced that we can make a principled distinction > > between "positive" and "negative" properties. You never responded to > > my point that > > One expression of [a] concept might contain 'not' etc., but an > > equally valid expression of the concept might not. > > I´m afraid there are no "equally valid", ie synonymous expressions of > "nothingness" and "inexistence". I define "nothingness" as the empty world, and the word 'not' doesn't appear in my definition of it above. > > Where is the contradiction > > in the description that consists of an empty domain set and > > zero propositions about the objects in that set? > > Which concrete "description" are you referring to? See above. > And what do you mean by a "zero proposition"? I said "zero propositions"; i.e. an empty list of propositions. > Would you please be so kind as to show me the logically correct > description of the empty world. I'm not sure what criterion you mean by "logically correct", but see above. > the empty world=def the state of affairs in which all objects possess > a property incompatible with existence. I reject that definition, as it is not the usual sort of definition of a 'world' that can be used in deciding truth-values as in model theory. Also, it refers to "state of affairs", which you do not rigorously define. > You´ve tried to define "'absolute nothingness' as the situation or > state of affairs in which no entity has ontological existence". I did try to analogize it thus, by my definition of it is the empty world, as defined above. > reality cannot consist of negative states of affairs. You haven't rigorously defined "states of affairs", much less "negative" ones. -- brian@holtz.org http://humanknowledge.net