Noneism is not Allism

In his 1990 Article in Mind entitled Noneism or Allism?, David Lewis argued against the thesis of Richard Sylvan (formerly Richard Routley) in ‘Exploring Meinong’s Jungle and Beyond’ that the existential quantifier is unnecessarily, existentially loaded in most modern ontology and logic. 

Sylvan’s noneism includes a neo-Meinongian view of the existential quantifier (let’s give it the less confusing name of ‘particular quantifier’) to the effect that it should not be defined so as to be synonymous with the property of existence – ‘exists’ being a respectable but primitive first-order predicate. Thus, one encounters a loaded particular quantifier that is sneakily restricted to entities with the property of existence, and then there is the unrestricted particular quantifier that is restricted in no respect as the name suggests. This distinction means that statements like, ‘Some men are purple and do not exist’ is true: ($x)(Px & -Ex). 

Lewis argues that, whatever Sylvan’s existence predicate is supposed to be, it is not ‘existence’ in the way that everyone else (philosophers) use the term, which is as a redundant, second-order predicate synonymous with the particular quantifier: Quine’s dictum, ‘To be is to be the value of a bound variable.’ (Aside: Now, this seems to be a definition of existence. Does it not seem obvious that such a definition is blatantly circular?) 

Anyway, Lewis says that Sylvan is just an Allist. That is, someone who believes that every conceivable thing (maximally construed) exists. Sylvan just happens to also attribute to some of these things an undefined property he calls ‘existence’… whatever that might be, who cares? 

Now, the obvious response to Lewis’ view is to first agree that arguments about definition are futile. A debate only truly begins once the disputants agree on a common definition for relevant terms. Yet, one must also be motivated to have such a debate in the first place, and most well-motivated debates concern the question of whether or not something or other exists. Whether or not certain things exist is a matter of great moment for everyone. If I may not exist tomorrow, I want to do everything I can to prevent that from happening. We can see, some of us, that the property of existence that we are all motivated to argue about is that which something may or may not possess. So, if to exist is merely to be the value of a bound variable then I would have nothing to worry about if I was an Allist… because all conceivable things would always exist. Yet, noneists are concerned about whether or not things exist, just like everyone else. It is the everyday division of things into those that exist and those that do not which means that noneists are not allists. 

… 

Mandatory thought experiment: 

Imagine two worlds, W₁ and W₂. The only things that exist at W₁ are a hen’s egg and me (David Gawthorne), and the only thing that exists at W₂ is a hen’s egg (keeping the example extremely simple). Naturally, I would rather that the actual world @ is W₁ rather than W₂. I’m sure that if you were in my position – if you had to choose between these two worlds – then you would have the same preference. I think that any rational agent would, even if s/he did not like eggs (setting aside arguments about the rationality of suicide). 

So, how do you characterise my preference? I would characterise my preference by saying I would prefer the world in which David Gawthorne exists rather than the world in which David Gawthorne does not exist. Yet, if to exist is to be the value of a bound variable then this characterisation cannot be correct because it would entail that I may be quantified over  at W₂ but that I lack the property of existence. 

Quine comes to the rescue and proposes a paraphrase: David Gawthorne is the entity uniquely characterised by the predicate ‘David Gawthorne-izes’ and it is not true that any of the things in W₂  David Gawthorne-ize. That is, the hen’s egg does not David Gawthorne-ize. Now, saying that the only thing in W₂ does not David Gawthorne-ize (with an existentially loaded particular quantifier) may be extensionally equivalent to saying that I do not exist in W₂ (with an unrestricted particular quantifier).

Yet, I could not care less as to whether or not the egg, or anything else, instantiates that property. I only care about the fact that I do not exist there. It is that things may or may not exist that keeps people up at night. That is the pivotal distinction, and not whether or not some world we quantify over will include things with some property that I possess. 

… 

So, you see, it is Lewis who had the wrong definition of existence; arguing about something that, though interesting, is not what everyone else is actually worried about in their daily lives. When Quine asks rhetorically ‘What exists?’ and answers ‘Everything’, you know that there is an equivocation going on due to the mirth that follows. The extent of this equivocation is the extent of the true difference between particular quantification and existence as a first-order predicate. 

Further (and this is not exactly Sylvan’s view), if the unrestricted  particular quantifier ranges over things that do not exist, we can say some rather alarming/exciting things about non-existent things and have a principled basis for containing those claims only to things that do not exist: 

Non-existent things are contradictory and paradoxical. 

Propositions about non-existent things do not obey logical laws. 

Propositions about non-existent things are not closed under entailment. 

We can then appeal to the difference between existing and non-existent things to justify the demarcation between things which are coherent, lawful and closed under entailment, and everything else. This can give us the basis for fundamentals such as the law of non-contradiction: defining the property of existence so that such laws are analytic (yes, I am for analyticity as well). 

Noneism gives us a paradise of intentional objects for nothing (pun intended), and especially those entities that appear to breach a logical law. All that it requires is that we give weight to a common sense distinction between that which exists and that which lacks that property.