The Stromboli Puzzle

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10 responses to “The Stromboli Puzzle”

1. 

   Edward Ockham

   March 11, 2012

   1. Shouldn’t the first premiss be ‘every island volcano exists’? Otherwise how is it valid?
   2.If ‘Stromboli is an island volcano’ implies ‘something is Stromboli’, and if Quine is right, then the first premiss is indeed redundant.

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2. 

   Bill Vallicella

   March 11, 2012

   Believe it or not I woke up in the middle of the night fretting over your point (1). Recall G E Moore’s discussion of the tame tigers? With respect to ‘Tame tigers growl’ it makes clear sense to ask: all or some? But with respect to ‘Tame tigers exist’ neither ‘all’ nor ‘some’ seem to fit.
   The second argument is much clearer and does pose a serious problem for the Frege-Russell-Quine view.

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3. 

   Edward Ockham

   March 11, 2012

   Good morning Bill. It is a lovely Spring afternoon here in the ‘smoke’.
   >>The second argument is much clearer and does pose a serious problem for the Frege-Russell-Quine view.
   Do you mean the argument that “If ‘Stromboli is an island volcano’ implies ‘something is Stromboli’, and if Quine is right, then the first premiss is redundant.”?
   And if you do, are you suggesting a sort of modus tollens? The first premiss is not redundant. Consequens falsum ergo et antecendens. Therefore either Quine is wrong or the first consequence “Stromboli is an island volcano therefore something is Stromboli’ is not good. Presumably you think the consequence is good, therefore you think Quine is wrong.
   Or have I completely mistaken your meaning?

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4. 

   Bill Vallicella

   March 11, 2012

   Good morning, sir. Let me be more clear. We agree that this argument is valid and sound:
   Stromboli exists.
   Stromboli is an island volcano.
   Ergo
   An island volcano exists.
   We will also agree that the following is valid but not sound:
   Pegasus exists.
   Pegasus is a flying horse.
   Ergo
   A flying horse exists.
   In the second argument, the first premise, though false, is needed for the argument to be valid. Agree? Now given the ‘Fressellian’ view, ‘exists’ has different senses in premise and conclusion. You see that of course. So the puzzle is this: How can the second argument be valid, which it is, given the Fresselian view that general existentials feature a 2nd-level use of ‘exists’? The Fressellian view induces equivocation and that invalidates the argument.
   Your move.

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5. 

   Edward Ockham

   March 12, 2012

   >>In the second argument, the first premise [Pegasus exists], though false, is needed for the argument to be valid. Agree?
   But I don’t agree. On my view, which is not a standard view, ‘Pegasus is a flying horse’ has two meanings, a literal and a non-literal. The literal meaning is such that its truth implies that something is a flying horse. I also hold the Brentano-Quine view that ‘something’ is always ‘existing something’. Thus the argument is valid with the second premise alone.
   The second meaning, the non-literal one, is ‘In Greek mythology, Pegasus is a flying horse’, which means the same as ‘Greek mythology says that Pegasus is a flying horse’. Thus your argument, on this interpretation, would read
   Pegasus exists.
   Greek mythology says that Pegasus is a flying horse
   Ergo
   A flying horse exists.
   Which is not valid. At most, it would imply ‘some [existing] creature is said by Greek mythology to be a flying horse’.
   This is not a standard view. The standard view would be that ‘Pegasus’ is meaningless because it fails to refer. Therefore your argument is invalid.

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6. 

   Bill Vallicella

   March 12, 2012

   Forget Pegasus.
   Vulcan exists.
   Vulcan is an intra-Mercurial planet.
   Ergo
   An intra-Mercurial planet exists.
   This is valid, but only with the first premise. ‘Vulcan’ must have an existing referent for the argument to go through. ‘Vulcan exists’ is a material mode way of expressing this.

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7. 

   Edward Ockham

   March 12, 2012

   So you are denying Fa -> Ex Fx ? (I note you have started a new post above).

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8. 

   Bill Vallicella

   March 12, 2012

   It is a valid inference but only on the assumption that the individual constants and variables have existing referents.
   You say the following is valid as it stands:
   1. Stromboli is an island volcano
   Ergo
   2. An island volcano exists.
   OK, but surely I don’t make it invalid if I spell out the presupposition by adding to the premise set
   0. Stromboli exists.
   Do you agree with that? I doesn’t need to be said because it is tacitly understood, but I can say it.

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9. 

   Edward Ockham

   March 13, 2012

   You say the following is valid as it stands:
   1. Stromboli is an island volcano
   Ergo
   2. An island volcano exists.
   OK, but surely I don’t make it invalid if I spell out the presupposition by adding to the premise set
   << No it is not valid as it stands. I am saying 1. Stromboli is an island volcano therefore something is an island volcano.
   is valid as it stands. By contrast
   2. something is an island volcano. Therefore an island volcano exists
   is valid only on the Brentano (‘Quine’) interpretation of ‘exists’.
   On inference (1) you want to add the assumption that the name ‘Stromboli’ has a referent. But that is unnecessary. If ‘Stromboli is an island volcano’ is true, then clearly ‘Stromboli’ has to have a referent. For it is true iff the name refers to something, and that something satisfies the predicate ‘- is an island volcano’.

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10. 

    David Brightly

    March 23, 2012

    Bill,
    Am I right in thinking your argument is that though (1)
    Stromboli fumes.
    Stromboli is an island volcano.
    Ergo
    An island volcano fumes.
    is a valid argument, (2)
    Stromboli exists.
    Stromboli is an island volcano.
    Ergo
    An island volcano exists.
    is not valid because the two instances of ‘exists’ have distinct meanings. Argument (2) should be clarified as (3)
    Stromboli exist1s.
    Stromboli is an island volcano.
    Ergo
    An island volcano exist2s.
    where ‘exist1’ is first level and ‘exist2’ is second, and this does not have the form of (1). You ask how (3) can be valid. One answer would be to say that (3) is valid in virtue of its conformance with the (unstated) rule that governs the relation between the two existence predicates. We could say that it instances a new argument form, perhaps. This is quite independent of considerations of non-existent objects.

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