Re: 3 dogs, 2 men, many arguments

[xod <xod@bway.net>]

At 2:28 PM -0700 10/20/99, Jorge Llambias wrote:
>From: "Jorge Llambias" <jjllambias@hotmail.com>
>
>No, G does not depend on any value of y, it is only a
>function of x. Replace y in that expression with any other
>bound variable and you will see that G only depends on x.
>y is not a free variable in the expression 2y: F(x,y)


I no longer understand this notation. Let me try:

3x 2y F(x, y)	ci da poi gerku re de poi nanmu zo'u da batci de
G(x) = 2y F(x, y)	broda cei re de poi nanmu zo'u da batci de

Now, by "G only depends on x " you mean broda has no place for da?


>>"For at least"..."there exists" indicates a dependency of existence. I
>>think this fact should be made explicit, and without such a marking, it
>>should mean: "There exists exactly 3 dogs, and there exists exactly 2 men,
>>such that: each/any dog bites
>>each/any man at least once."
>
>That could have been the convention: take all the existentials
>first and all the universals later when dealing with more than
>one numeric quantifiers.


That's not quite what I was getting at.


>>This is the symmetrical interpretation, free of the malglico of default
>>restricted scope.
>
>I don't see that one interpretation is more or less malglico
>than the other. What you gain in symmetry you lose in
>the ease of formula reduction. You would also need to
>specify what to do when you have for example {ro} and
>a number in one expression, {ro} and {su'o} and a number,
>etc.


Why is "formula reduction" a value? Is that the way we think and speak?


>In practical terms, I don't see how it matters much one way
>or the other, since we hardly ever will want to say any of
>those things. When speaking of groups of things it is much
>more common to refer to them collectively, in which case
>this problem doesn't even arise.


As for "collectively", what do you mean? Masses where a single member's
validity is enough? Where if at least one of the 3 dogs bites only one of
the 2 men, the sentence is true?

How would you state my sample sentence "There exist exactly 3 dogs, and
there exist exactly 2 men, such that: every dog bites every man at least
once." Do you really think this is an unlikely sentence to utter?

In these sentences we are defining a relationship between every element of
some sets. The prenex declares the composition of the sets; the bridi
defines the relationship. Why should there be another, implicit
relationship between the sets? And why handle sets enumerated by ro and
su'o differently?

The condition of element-set mapping (each element of a set listed in the
prenex in position n maps to a set of type listed as n+1) should be marked.
The implictness of this is malglico and needs to be made explicit in a
logical language.








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