<respectful ship for space>
For example, if a typical coin is tossed
and one assumes that it cannot land on its edge, then it can either land showing "heads" or "tails." Because these two outcomes are mutually exclusive (i.e. the coin cannot simultaneously show both heads and tails) and collectively exhaustive (i.e. there are no other possible outcomes not represented between these two), they are therefore each other's complements. This means that [heads] is logically equivalent to [not tails], and [tails] is equivalent to [not heads].[/U]
Garrette dealt with this very situation in his excellent post about the 6-sided die:
http://www.internationalskeptics.com/forums/showthread.php?postid=9830661#post9830661
Where you do err is in glossing over the fact that the act of assuming that one may simply eliminate results one would find inconvenient (assuming that the coin cannot land on its edge) absolutely and irreparably prevents one form claiming that what is left is either "exclusive"
OR "exhaustive".
As silly as it may sound to you, your assumption eliminates things that could, in fact, happen:
-a coin with two faces, or no faces, could have been substituted for the fair coin
-the coin could be snatched from the air by a passing
gull goose and swallowed
-the coin could have fallen down the sewer grating and been washed out to sea
-the coin could have been shattered by the well-placed bullet of an SASS devotee
-the coin could have fallen into a crucible of molten sodium and been vaporized
...and so on.
The concept to which you are resistant, and that you continue to avoid, is that, while a simplifying assumption (such as limiting the possibilities subsumed in {in fact, the very nature of})
~A may, in fact, simplify calculations, or reflect common experience, they eliminate the possibility of the
A/~A pair being exhaustive. Everything you assumed away becomes, in fact, the "red space"--the "~(
A U
~A)".
It is an error to claim that your "simplified" universal set is still universal or exhaustive. It is the error to which you continue to cling.
- Just to elaborate a little -- we could also say that if A is heads, ~A is either "on it's side" or tails. The sample space has been defined in such a way as to allow us to be more specific than "anything and everything that is not A."
And, as such, it is, in fact, closer to being actually exhaustive than your original simplification. It is by no means actually exhaustive, as you are still assuming many (even infinite) possibilities away, in order to "force" your assumed consequent.
It is still the Texas Sharpshooter, just shooting at a smaller fence...
Might I again encourage you to present your evidence (practical, empirical, objective evidence) for your belief that the "soul" exists?
ETA: ninja-ed by Garrette, and jsfisher