Saturday, February 26, 2011

Existential import at Answers.com

Whenever I check the traffic for this blog, I always have a look at the Google queries that got people here. Some of them are quite eccentric, such as people asking whether it will rain tomorrow, and getting this post on future contingents, which they probably didn't want. However, those asking for Existential Import probably got what they wanted. Google ranks this blog #3. As for the second, at Answers.com, their answer illustrates perfectly the conflation that I discuss here. It says:

Existential Import: The implications of a proposition as to what exists. If a proposition entails the existence of something, then it has existential import. It should be noticed that in the predicate calculus the universal quantification (∀x)(Fx → Gx) has no existential import, since it is true when nothing is F.

This confuses the question of whether (A) a universal proposition like "all dragons are fire-breathing" implies what traditional logicians call the particular or I proposition "some dragons are fire-breathing ", and (B) whether the I proposition "some dragons are fire-breathing" implies the existential proposition "fire-breathing dragons exist". The first part of the definition 'the implications of a proposition as to what exists' is correct. But the second part (that the universal can be true although nothing is F) is too strong. Those of a realist disposition (such as Meinong and possibly the Phoenicians over at camp Vallicella) may hold that 'some things are F' may be true even when no F's exist.

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6 Comments:

Blogger David Brightly said...

Oh dear. This seriously muddies the waters. My understanding has always been that there is a standard interpretation of the quantifiers in predicate calculus such that ∀ has no existential import and ∃ does. So I see nothing with which to disagree in the quote from Answers.com.

BV has said on several occasions that he is no Meinongian. I agree that it's hard to grasp just what he is claiming with regard to intentionality at times, but to abandon predicate calculus in order to accommodate him strikes me as a disastrous move. After all, Zalta's neo-Meinongian system, which I think may be a vehicle for expressing Bill's position, is formulated within classical logic. I'd like to continue to engage with him to try to tease out what he is getting at. But he is skulking in his tent at the moment, to judge by his lack of response to our most recent comments.

2:31 pm  
Blogger Edward Ockham said...

>>My understanding has always been that there is a standard interpretation of the quantifiers in predicate calculus such that ∀ has no existential import and ∃ does.

The standard interpretation is that (x) Fx does not imply Ex Fx. That is all. The question is whether Ex Fx has "existential import". If we are allowed to quantify over non-existents, so that Ex, x does not exist, then clearly not.

>>So I see nothing with which to disagree in the quote from Answers.com.

I am disagreeing with their conflation of 'some x is F' and 'some x-that-is-F exists'. Strictly speaking, 'existential' means 'uses the term exists.

2:43 pm  
Blogger Edward Ockham said...

E.g. Google "quantifying over non-existents" and you will see what I mean. Clearly if we are allowed to do so, and nothing in the predicate calculus prevents this, then the existential quantifier, despite its name, does not have 'existential import'.

2:47 pm  
Blogger David Brightly said...

1. >> I am disagreeing with their conflation of 'some x is F' and 'some x-that-is-F exists'. Strictly speaking, 'existential' means 'uses the term exists.

This may be why I'm confused. Surely this conflation is exactly the 'Brentano thesis' which elsewhere you have advocated?

2. >> The question is whether ∃x Fx has "existential import". If we are allowed to quantify over non-existents, so that ∃x, x does not exist, then clearly not.

The only way to make '∃x, x does not exist' come out true is to equivocate on the 'exists' embedded in '∃' and the 'exists' of 'x does not exist'. I think we will agree that we want to retain the interconvertibility of ∀ and ~∃~. This ties the interpretation of the 'exists' inside ∃ to the interpretation of 'all' in ∀, giving it, as it were, the widest scope possible. Hence the 'exists' in 'x does not exist' must have a narrower interpretation, such as 'x is not real (as opposed to imaginary)' or 'x is not concrete (as opposed to abstract)'. This is what happens in Zalta's system, where the predicate 'E!' is introduced to mean 'has a spatio-temporal location'. At the moment, this is the only way I can make sense of the idea of quantifying over 'non-existents'.

3. >> E.g. Google "quantifying over non-existents" and you will see what I mean. Clearly if we are allowed to do so, and nothing in the predicate calculus prevents this, then the existential quantifier, despite its name, does not have 'existential import'.

Well, I don't think it can have any 'existential import' in any absolute sense. ∃x.x*x+1=0 is false relative to the domain of real numbers but true relative to the complex numbers.

9:03 pm  
Blogger Edward Ockham said...

EO >> I am disagreeing with their conflation of 'some x is F' and 'some x-that-is-F exists'. Strictly speaking, 'existential' means 'uses the term exists.
DB >>This may be why I'm confused. Surely this conflation is exactly the 'Brentano thesis' which elsewhere you have advocated?

I have advocated Brentano’s thesis of ‘convertibility’. That doesn’t mean I regard ‘existential proposition’ as having the same meaning as ‘particular proposition’. Indeed, if ‘existential proposition’ means ‘proposition that uses the term exist’ then they don’t have the same meaning. Perhaps I am being picky. I am saying that ‘some F is G’ is truth-functionally equivalent to ‘Some F-G exists’, i.e. if one is true, so is the other, for whatever F, G. But the second is properly existential, the first is not.

>>The only way to make 'Ex, x does not exist' come out true is to equivocate on the 'exists' embedded in '∃' and the 'exists' of 'x does not exist'.

Yes.

>>This is what happens in Zalta's system, where the predicate 'E!' is introduced to mean 'has a spatio-temporal location'. At the moment, this is the only way I can make sense of the idea of quantifying over 'non-existents'.

The trouble with this, as I have pointed out, is that it solves nothing. Zalta and co probably want to explain the consistency of “John is thinking of a mermaid, but there are no mermaids” by having the first occurrence of ‘mermaid’ as ranging over objects that may not have spatio-temporal location, and the second occurrence as ranging only over ordinary spatio-temporal objects. As I discussedhere that won’t work. Intentional cigarettes are no good to smoke, nor to want to smoke.

>> I don't think it [the existential quantifier] can have any 'existential import' in any absolute sense. ∃x.x*x+1=0 is false relative to the domain of real numbers but true relative to the complex numbers.

You are denying the possibility of unrestricted quantification then?

11:56 am  
Blogger David Brightly said...

1. >> I am saying that ‘some F is G’ is truth-functionally equivalent to ‘Some F-G exists’, i.e. if one is true, so is the other, for whatever F, G.

OK, that's good, we agree on that.

2. Glad we agree on the equivocation on 'exists'. Regarding Zalta, it's certainly his aim 'To account for the deviant logic [of] propositional attitude reports, explain the informativeness of identity statements, and give a general account of the objective and cognitive content of natural language', to quote from here. I can't say how he goes about this---I don't have access to his book (note the miss-spelling), and the stuff published on the net rapidly gets too technical for me to follow. I doubt that it follows the simple recipe you suggest for exactly the reason you give. It's not that the thinking has an abstraction as its object. Rather the thinking itself is characterised by an abstraction. If I ask myself just what thinking of a mermaid consists in, it seems to me to be a rehearsal of just those properties that a mermaid is supposed to possess, and it's just those properties that are encoded by the abstraction we label 'mermaid'.

3. Am I denying unrestricted quantification? Probably. I think we should proceed with care. We know that 'the set of all sets' gets us into deep water. At the least in any discussion we should seek to clarify what we are quantifying over. See my comments with regard to quantification over directions and the like here.

11:44 am  

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