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Re: [lojban] {zo'e} as close-scope existentially quantified plural variable

Jorge Llambías, On 17/10/2011 02:55:

On Sun, Oct 16, 2011 at 10:11 PM, And Rosta<and.rosta@gmail.com>  wrote:

Jorge Llambías, On 17/10/2011 01:31:


On Sat, Oct 15, 2011 at 11:19 PM, And Rosta<and.rosta@gmail.com>    wrote:


The commonest case where covert donkey sentences occur is with
conditionals:
"If you give me money, I'll spend it on drugs" = "Every possible
circumstance in which there is money that you give me is a circumstance
in
which there is money that you give me and I spend on drugs". I don't
think
your solution works for that. Applying your solution gives (I think)
"Every
circumstance is such that in it I spend all money that you give me",
which
has the wrong meaning. Crucially, the conditionals rely on restricted
quantification (over circumstances in which such and such is the case).


Why does it have the wrong meaning? Is it still wrong if you use "any"
instead of "all"?


In apprehending underlying forms, we need to get rid of "any", since it is
an English reflection of a quantifier interacting with a conditional.


I take "any" here to be the same as "all", except it is plain that it
has no existential import. I still don't see what problem you see in
"Every circumstance is such that in it, for all money, if you give it
to me I spend it on drugs" or any of its variants.


"Every circumstance is such that in it, it is not the case that there is money that you give me and that I do not spend on drugs" -- that does without "if" and sidesteps the existential import issue, and yes, it works. I remember now I'd worked that out in 2004, with much more strenuous effort than it took you, and then forgot and became fixated on repetition avoidance strategies other than simple reformulation.

Oh hang on, just remembered. "Every circumstance" is the easy case. Right, so the English example is "If you give me money, I'll probably spend it on drugs". And this reduces to "Most circumstances in which there is money that you give me arecircumstances in which there is money that you give me and that I spend on drugs". Because the quantifier is "most", you can't do away with the restricted quantification. Now turn yourself loose on solving that one!

But let's change "money" to "five quid": "Every circumstance is such that in
it I spend five quid that you give me". Wrong, obviously.


"Every circumstance is such that in it I spend *every* five quid that
you give me".


  Or try "If you
tell me your name, I'll murmur it".


I don't see that as a donkey sentence, since it doesn't even have quantifiers.


Yes, sorry. I think I was thinking of them both as nondonkey sentences that wouldn't transform in the way you proposed to transform the donkey sentences, but that wasn't really relevant to the discussion.


I think my solution would give: "For any money, if
you give it to me, I'll spend it on drugs" or "I'll spend on drugs any
money you give me".


Underlying "if" and conditionals is a logical form that is either
repretitious, "Every possible circumstance in which there is money that you
give me is a circumstance in which there is money that you give me and I
spend on drugs", or else a donkey sentence, "Every possible circumstance in
which there is money that you give me is a circumstance in which I spend it
on drugs". So your challenge is to reformulate that, without using "if" or
"any", but without the repetition (of "there is money that you give me").


I don't get why that is the challenge. In the original donkey
sentence, I did use "any" in replacement of the problematic "some":
You accepted "all farmers beat any donkey they own".


It's what I see as the challenge. Reducing logical form to fundamentals involves reducing conditionals to quantification over circumstances, and that leads to lots of structures where donkey sentences appear to be avoidable only by repetition.

Things would have been clearer if I'd originally remembered i should choose a quantifier like "most" that requires restricted quantification, because obviously those are the cases that resist reformulation to avoid repetition.

I think the issue with donkey sentences is not so much reformulating
them in terms of ordinary first order logic, which can be done by
replacing the short scope existential by a wide scope universal. The
problematic issue is explaining what's going on, since this conversion
is not licensed by any rules of logic.


I see what you're saying, but I think we have different understandings of
the quintessence of donkey-sentencehood.


For me it's that they have a pronoun whose antecedent is a bound
variable, but the pronoun is outside the scope of the quantifier
binding the variable... and yet they make sense.


Indeed -- that's the angle relevant to natural language.

I take it to be when you have
quantification within a restriction on a variable, in "for every X such that
there is a Y such that F(X,Y), there is a Y such that F(X,Y) and G(X,Y)",


That's in non-donkey form.


which might be Englished as the less repetitious donkey-sentence "for every
X such that there is a Y such that F(X,Y), G(X,Y)".


Which is a donkey sentence, because the Y in G(X,Y) is outside the
scope of "there is a Y such that", so it should not be interpretable
in standard first order logic.


I see that as the quintessence of donkey-sentencehood not because that is
how it is standardly seen in linguistics, but rather because that is the
main problem they present for a logical language.


The non-repetitious form of your sentence is:

"for every Y and for every X such that F(X,Y), G(X,Y)".

But the challenge is to explain why the apparently nonsensical form
has this sensical sense.


The challenge for a logical language is to find a sensical form that is not repetitious -- given that the essential goal of a logical language is to have sensical forms without natlang ambiguity but without greater verbosity than natlangs require.

--And.

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