From: Brian Holtz [brian@holtz.org] Sent: Saturday, July 20, 2002 10:00 AM To: Alt.Atheism.Moderated Subject: Re: Science & atheism are cultures. "Paul Holbach" wrote: > > 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. > > Claiming sort of a "truth by definition" and repeatedly blaming one´s > opponent for alleged stipulations seems like a rhetorical strategy I do no such thing. I assert one definition. You assert a similar one with an extra stipulation, and then complain that my definition violates your extra stipulation. All I ask is that you justify your stipulation. > We´d better spend a minute on the meaning of "domain set" Yes, I know what "domain" and "range" mean in mathematics... > In our case of world models the domain is simply the > totality of the concrete world itself, the entirety of all individual > things Bzzt. We're using 'domain set' in the definition of 'world', so you can't use 'world' in the definition of 'domain set'. That's circular. I ask you again: please state your formal definition of 'world'. If it's any help, I'll repeat the definition I gave back in March: a world is that which corresponds to or can be represented by (a domain set and a list of propositions about any objects in that set). > > 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? > > World models do not correspond to sets but to worlds! I said: (empty world) corresponds to (domain set and proposition list); i.e. (empty world) corresponds to (world model). Not only do you not have a formal definition of 'world', but you haven't yet understood mine. > Generally, a world is a concrete system of objects and relations > between the latter. What work is 'concrete' doing in this definition? If you remove it, then your definition is just an informal restatement of mine, with the possible exception that by using 'system' instead of 'set' you may be trying to stipulate that the number of objects must be non-zero. There is nothing self-contradictory in such a stipulation, but it's ludicrous to claim that your stipulation creates a contradiction in the version of the definition that omits your stipulation. > The fundamental function of models is representation. If there´s no > original, then there´s no representation of what doesn´t exist. Let's call the "bh-empty-world" that which is represented by or corresponds with my definition of the "empty world". Now, the only way you can decide that the bh-empty-world cannot exist is if you have some new way of defining worlds that is independent of the old domain-set-and-prop-list technique. If you have such a way, then please publish it so we can all dispense with the old technique! > > > Are possible worlds more like mobs or more like pouches? > > > > Domain sets are sets, and sets can be empty. > > You´re being evasive, No, you're just naively assuming that worlds are something other than what they are said to be by the only rigorous definition on the table (i.e. mine). > the only reason you offer regarding the possibility of an empty world > is that because sets could be empty, worlds could be empty too. But > such a leap isn´t justified by anything! It is plainly justified by the only rigorous definition of 'world' on the table. > as I´ve mentioned above the "domain" of a realistic > world model is a number of worldly items! Bzzt. It's circularly to use 'worldly' in a definition of 'world'. Dropping 'worldly' leaves "a number of items", and it is only by your stipulation that this number could not be zero. > you´ve been > equating empty sets with empty worlds, and already many posts ago I > stated that this is an unwarranted act of reification. You're confusing an act of reification with an act of definition. If you have an alternative definition, is there any way you can think of for me to successfully get you to state it? I'm out of ideas on this score... > I gather from everything > else you´ve said that you belong to the pouch-ists. Sorry, but I reject your fallacious assumption that the concept 'world' must be either like a mob or like a pouch. It isn't like a mob or a pouch, it's like a model. (Specifically, it's that which corresponds to a model.) > > The set-defining property of the empty world's domain set > > is simply membership in that set. It's just a zero-length list. > > What do you mean? Defining a set by specifying a certain property > decides which entities become members of that set and which don´t. Its > intension determines its extension. Sets can be defined by extension as well as by intension. > > 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 think it´s become more than obvious that you regard worlds as > "domain sets" and, analogously, empty worlds as reified empty sets. No, I don't "regard worlds as 'domain sets'". As I've been saying since March, a world is that which corresponds to or can be represented by (a domain set and a list of propositions about any objects in that set). > But while sets are abstract, purely conceptual entities, worlds are > totalities of concrete, interrelated entities. You've merely changed the problem of defining 'world' into the problem of defining 'concrete'. Surely you're aware that this definitional path is not going to lead to a satisfactory definition of 'world' as it is used in discussions of possible worlds. > Furthermore, even if > the empty world were analogous to the empty set, you couldn´t succeed > in establishing an ontological category *nothingness* because the > empty set refers to nothing, not even *nothingness*. You misunderstand my position if you think that I have a goal of "establishing an ontological category *nothingness*". I seek merely to establish a rigorous definition of 'world' that helps me think about possible worlds in general, and the most minimal (empty?) possible world in particular. > That the empty set has nothing as its member doesn´t mean that > it has *nothingness* as its member! Of course not; you're the one who has been reifying 'nothingness' in this way, in order to invent a contradiction in my definition. > But a model that refers to nothing, doesn´t represent > anything and so is no model at all! When you say that the bh-empty-world counts as "nothing" and cannot be the correspondent of a model, what is the source of this knowledge you have about the bh-empty-world? You again are obviously importing some naive intuition about worlds that is not based on any rigorous definition of them. > What is more, there would be at > least one true proposition about D: "There are no objects", which is > equivalent to "Nothing exists.", which is equivalent to "Everything > doesn´t exist."; and oops-a-daisy we´re stumbling again over the very > same self-contradiction I´ve revealed! Your point here is already rebutted by a paragraph that you snipped: 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. > Worlds are like mobs and not like pouches! Worlds are like neither. > It´s fallacious to assume that if one says > nothing ("zero-propositions"), one doesn´t say anything wrong. ;-) Wittgensteinian nonsense, whose insubstantiveness isn't excused by your smiley. > I think there´s reason enough to presume that the empty world is a > pseudo-model that isn´t capable of introducing an acceptable > conception of nothingness. You obviously have a preconceived notion of how nothingness should be conceived, even though you lack a rigorous definition of it. That sounds like a personal problem of yours, and not like a problem in my definition. :-) > Since I´m sure that, unfortunately, you´re going to refuse to agree > with me on that, we´ve indeed drained this thread´s cup to the > dregs...but it´s been worth it in my opinion... :-) I agree, on both counts. > > 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? > > If that were so, then there´d be no discernible difference between > logical and nomological possibilities any more False: nomological possibility within a world would still be quite distinct from logical possibility -- and within the actual world (or the set of possible worlds with the same scientific laws as ours) is precisely the context in which "nomologically possibility" is used. > > I have no idea what you mean by "the material source of being". > > Such a phrase sets off every nonsense alarm I have. :-) > > "Vagueness is at times an indication of nearness to a perfect truth" "Don't confuse vagueness/generality with vagueness/nonsense." [Brian Holtz, 2002] -- brian@holtz.org http://humanknowledge.net