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. ----- Perpetual Progress, Self-Transformation, Practical Optimism, Intelligent Technology, Open Society, Self-Direction, and Rational Thinking. http://extropy.com/