Monday, January 30, 2006

The Default Position

To me, the following three sentences seem identical

No mountains are golden
There are no golden mountains
Golden mountains do not exist

Brandon writes here:

> On what principles do you make the equivalence of the three the 'default' position?

I reply: on the principle that I don't understand what the other position might be. The default position is simply that I don’t understand the supposed difference between any of the sentences. There is a tendency to to assume that there is a clearly understood and definable difference between so-called 'existential' and 'quantifier' uses. I don’t understand it. Someone please explain it. (See my related posting on Alan Rhoda's attempt to explain it).

Indeed, it is difficult to have the argument unless we assume these formulations say the same thing. Brandon says 'There is a way of looking at the problem such that it's false to say that 'of course' there are no nonexistent objects'. I take him to be asserting the existence of a certain way of looking at the problem. He says 'There is a way …', and I deny the existence of such a way. I could not deny this without the default position that 'such a way does not exist' contradicts his assertion 'there is a way'.

He says that 'nothing about a quantifier requires that it import existence'. But this is itself a quantifier sentence denying the existence of anything about a quantifier that signifies existence. His point seems self-refuting, for to understand it at all is to understand it – a quantifier sentence - as denying existence.

In summary The default position is that the sentence 'there is a default position' asserts the existence of a default position. If you deny this, you have accepted the default position.


Brandon said...

It's possible to take the existential quantifier 'There is' simply to be a positing operation. If we do that, it's very easy to make sense of claims like the following:

* There is a detective in Baker Street called Sherlock Holmes; but Sherlock Holmes doesn't really exist.

* In Macbeth there are three witches who tell the future, although, of course, no witches exist.

* There is a center of gravity in the object, although there is nothing actually existing in the object that is a center of gravity.

And so forth. It is possible to give an account of these on the position you suggest, but it is very difficult. All a quantifier does is tell us how much of a given domain a proposition covers; we get existential import by restricting the domain to things that actually exist. One reason why someone might not want to restrict the domain to things that actually exist is that, if you don't, it becomes much easier to handle fictional characters. It also becomes possible to talk about pure mathematics without presupposing that somewhere in reality any mathematical object you define exists. When you don't give the quantifier existential import, all it suggests is that you are positing such-and-such for some purpose or other, without committing to whether it actually exists. So I can understand centers of gravity to be merely useful fictions; if so, no center of gravity actually exists, but I can still posit centers of gravity for a given purpose.

If I say, "All unicorns have horns," under the standard modern interpretation this universal quantifier has no existential import: it just means that, to be a unicorn, something must have horns. Likewise, one could argue that in "At least one unicorn has a horn" all that is implied by this 'existential' quanitifier is that, for any X you name, if X has a horn, that doesn't eliminate the possibility of its being a unicorn. Further, one could argue that "There is a unicorn" just means that in some (purported)domain (actual, fictional, mythical, purely possible) at least one of the elements of the (purported) domain is a unicorn.

Edward Ockham said...

But none of this contradicts my thesis, which is that the following sentences are equivalent:

No mountains are golden (except in stories)
There are no golden mountains (except in stories)
Golden mountains do not exist (except in stories)

It is of course a separate question as to whether there are golden mountains 'in stories', or what is meant by qualifying an existential statement by 'in myth/legend/the Bible' &c.

Alan Rhoda said...

Brandon expresses my point of view very eloquently. Sometimes we want to say "there is" without committing ourselves to actuality.

Edward Ockham said...

Of course, if it is possible that p, then there may be some reason (hence some 'actual' reason) why it is possible that p. Express this fact as q. So, it is the case that q (i.e. 'actually' the case), and because it is the case that q, it is possible that p. For example, we now know a lot about the structure of human DNA. This makes it possible that we could live much longer. Was that what you had in mind?

Anonymous said...

the three statements you provide are not the same.

"no mountains are golden" - is a general statement that describes these two concepts as not forming a 'unity'.

"there are no golden mountains" - is an implicit existential expansion of the first statement such that the existentiality of the general statement would be tested. hence a golden mountain may exist in the past/future, and/or may may exist
in a 'sub-domain'(a story in a book that is in my bag), such that there are no golden mountains in the highest domain shared among the debatees, but is not wholey excludible from existentiality.

"golden mountains do not exist" - this is the explicit equivalent to the second statement, such that no golden mountains can be found to exist in 'any capacity', including over all time, any domain or sub-domain. in some senses this is arguably impossible to prove...much like atheism...