From xod@xxxx.xxxx Mon Oct 25 16:43:21 1999
X-Digest-Num: 266
Message-ID: <44114.266.1443.959273825@eGroups.com>
Date: Mon, 25 Oct 1999 19:43:21 -0400
From: xod From: "Jorge Llambias"
>
>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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