From : <>
Sent : Monday, September 29, 2003 2:58 AM
To :
Subject : This is not spam
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This is not spam because it was filtered through SpamAssassin.

Well, that is not technically true.  Or is it?  The evaluation of the
truth of the above sentence is a very interesting matter.
First and foremost, consider the overall sentence structure.  It is a
compound sentence composed of two simple sentences.  For the sake of
simplicity, let us call "This is not spam because it was filtered through
SpamAssassin" sentence S.  S decomposes to "This is not spam" and "It was
filtered through SpamAssassin."
The first sentence is interesting in that it is a simple negation of the
sentence "This is spam."  Let us label this sentence p, and consequently
its negation ("This is not spam"), ~p.  Let us further let q represent "It
was filtered through SpamAssassin."  It is vital to note here that both ~p
and q are in fact independently true.
Thus the only question remaining before we may expand S to its most
explicit form is, how should ~p and q be connected?  In other words, how
should we represent the idea of "because" as it occurs in S?
Inasmuch as "because" seems to indicate cause and effect, we will first
consider implication.  For typographical purposes, let us represent
the implication operator with the character '#'.  If we write S as ~p#q,
we are saying S is equivalent to the sentence S2 "This is not spam if it
was filtered through SpamAssassin."  This is not what we want, as S2 tells
us nothing about the spam status of this document, nor whether or not it
was indeed filtered at all.  Furthermore, whereas the truth of S is at the
least controversial, we can see that S2 is patently false, since it is
still possible for non-spam to be sent if SpamAssassin is disabled.  For
now, we assume that S is not equivalent to S2.
However, implication may still be the right idea; let us construct S3 from
S2 by swapping the consequent and antecedent.  In this case we have S3 =
"If this was filtered through SpamAssassin, it is not spam," or q#~p
symbolically.  This also seems to be incorrect, as spam can indeed be
filtered through SpamAssassin (to wit, that is of course the idea!), and
this process in and of itself does not change spam into non-spam.
Nevertheless, despite the possible lack of truth of S2 or S3, keep in mind
that either may still be the appropriate interpretation if S is false as
well.  To further analyze, let us remove any risk of ambiguity that may
arise from the connotation of the word "if" by rewriting the conditionals
as disjunctions.  S2 is identical to S2' "This is spam or it was filtered
through SpamAssassin." (pVq)  Paradoxically, when written this way, we
see that S2 is true!  By the same token, S3 becomes S3' "This was not
filtered through SpamAssassin or it is not spam." (~qV~p)  Also true!
Let us disregard S2 and S3 entirely for a moment to consider an
alternative.  The only other sensible alternative is to write S as ~p*q;
or in other words to say that S is equivalent to S4: "This is not spam,
and it was filtered through SpamAssassin."  It certainly seems to be the
case that the intention of S is to convey the information of S4!  This is
our best candidate yet, but it seems as though S carries some additional
meaning beyond that of S4.  To claim that "This is not spam because it was
filtered through SpamAssassin" does not only claim that it is not spam and
it was filtered, but there is also a connection between these two facts
indicated by the use of "because".  In other words, we should not be too
eager to represent S as ~p*q, because if we take p and q to be, for
instance "Bruce Willis is the president of Norway" and "I have a cat,"
respectively (assuming that Bruce Willis is NOT the president of Norway,
and that I DO have a cat), then we could say "Bruce Willis is not the
president of Norway because I have a cat," following the form of S!
Clearly not true.
But let us turn our attention to this new sentence.  We shall label "Bruce
Willis is not the president of Norway because I have a cat," sentence N.
Also consider the following sentence which we call M: "I am not sexually
attracted to Bruce Willis because he is a man."  Notice three very
important facts here:
1. S, N, and M all have identical sentence form.
2. The truth of the individual constituent simple sentences of S, N, and M
are completely congruous.  (Granted, we are making the arguably ridiculous
assumption that I would not have Bruce Willis' manbabies.  Conversely, it
is a well-known, widely-accepted metaphysical truth that I have a cat, of
The conclusion is that sentences of this form are not truth-functional!
This is why our attempts to analyze S using propositional logic failed.
We will have to resort to more advanced means to determine the truth of S.
If we counterintuitively disregard the truth of S, N, or M, we notice
that the structure of N seems far easier to analyze than S, despite the
fact that they have identical sentence form.  N can be interpreted to mean
that the fact that I have a cat has prevented Bruce Willis' ascension to
his indisputably rightful place as the elected ruler of the Norwegian
people.  In more rigorous terms, we would say T' "If I did not have a cat,
Bruce Willis would be president of Norway."
The complication is now elucidated: this sentence expresses a subjunctive.
The codification of the subjunctive mood (that is, the expression of a
possibility counter to fact) is a controversial topic in the field of
formal logic, because many intuitive systemizations of the subjunctive
can lead to paradoxes.
This being the case, I must admit that without further knowledge of modal
logic, I do in fact not know whether S is true or false.  Unfortunately
subjunctive modal logic is beyond my field of expertise, not to mention
the bounds of this document -- which, so it is said, is not spam, and
furthermore, has been filtered through SpamAssassin.

Live long and prosper,