"In the case of the both universes, set A is known only to God and the demon." This is most definitely not consistent with my definition of A! Set A is the information to be explained; in the picture you present you define A as something not available to you and an explanation of information not available to you is a meaningless concept. In my definition, A is what is to be explained; A is the collection of elements being passed to you by "God" in one case and "the demon" in the other. A is the set of elements from which B is taken. From the perspective of my definitions, your division into two cases is entirely spurious. The existence or non-existence of either "God" or "the demon" has absolutely no bearing on the problem at hand.

My understanding of A is that it is the explandum. However, in the GU universe the explandum is what it is, while in the DU universe the explandum (same as in the GU universe) is filtered into another explandum (set 666). The difference between the GU universe and the DU universe is that set B' is based on set A in the GU universe, but it cannot be based on set A in the DU universe simply because we know (having God's eye perspective, in this instance) that set B is actually based on set 666 while in the DU universe. Nothing in set B in the DU universe is from set A (the original explandum).

Every element of B is an element of A by definition! "B is a set, defined to be an unordered finite collection of elements of A"

But, we already agreed that a demon lies about set A in the DU universe, so it is not possible for set B to have any element of A since the demon lies about each and every element of A, leaving the poor saps in the DU universe with only set 666 by which to construct set B.

Your question 15 is totally equivalent to presuming an explanation of "Dante's Inferno" is something to be reasonably obtained from reading "Little House on the Prairie"... I absolutely agree that an explanation not based on the information to be explained is not a valid explanation by anyone's interpretation of the definition of an explanation. And I do not propose to include such a thing as a valid member of the set of things called explanations.

So, it seems that we can agree that IF the DU universe has a set A, but it is converted to set 666 prior to the explainee constructing set B, then set B is not a valid explanation, that is, your model fails to an explanation if such a demon universe (DU) exists! So, let's cover this issue of contention much more closely:

Question 16: Can set A (the explandum) be changed to set 666 without the explainee's knowledge such that they are explaining set 666 (which they might label set A), but in fact makes their set B (and your model) totally invalid? In other words, the demon can totally dupe the explainee such that a model of explanation is impossible in such a DU universe, would you agree?

• An explnation of C is presumed to be an explanation of A. - doctordick - December 21, 2004 - 12:47 UTC