Dear NvT,
Dave Keenan's belief (NvT#30) that nonviolence theory contains a fundamental
paradox is fortunately a false one.  Consequently his "explicitly paradoxical
version" of his Axiom of Doubt is neither necessary nor useful, and need not
haunt us further.

His Axiom of Doubt is not only self-consistent, but demonstrably true, as I
will quickly show, with the exception of its first part ("the truth is
something that we can collectively make progress towards") which is
irrelevant to the supposed paradox and in any case does not appear in his
"opposite of the Axiom of Doubt" on the same page.

So Dave's Axiom appears like this: "I can never be sure that the beliefs I
currently hold are true or that other's beliefs are false".  We can drop the
awkward "currently" - certainty about current beliefs is no different in
principle from certainty about non-current ones.  Also the distinction
between self and others is irrelevant.  Since I and others are free to hold
any arbitrary belief, the Axiom in its naked form appears as: "Given an
arbitrary belief B, it is not possible to know whether B is true or false". 
And this is the form in which Dave thinks he has found a contradiction,
because the Axiom implies that we cannot know whether the Axiom itself is
true or false.

But there isn't any contradiction here.  The axiom doesn't say that we can't
be sure about any beliefs at all, only that there are some beliefs we can't
be sure about.  And this is clearly true.  I can't be sure, for example, that
I will still be alive tomorrow morning.  On the other hand I can take it as a
working assumption, without being illogical because of that.

Dave links this into nonviolence theory by identifying his Axiom with a
"fundamental doubt" which "leads to a limitation on the kinds of acts which I
may use in attempting to convince others of my beliefs".  He feels his
principles shaken by the paradox so that he suspects his fundamental doubt of
being itself dubious.

So stop worrying, Dave, your Axiom (in its abbreviated form above) stands
firmly on the rock of Truth.  If it didn't, a lot of other theories, as well
as nonviolence theory, would be looking very wobbly indeed.
Brian Currie


Dear Brian,
Thanks for your response to my article A Paradox of Nonviolence.

I think you have failed to understand my article.  But, then again, maybe I
have failed to understand your reply.  You have completely misread my
emotional state with regard to the paradox.  In fact I don't think I
indicated it in any way in the article so perhaps you have simply projected
your own fears.

I am quite comfortable with the possibility that when you attempt to express
an intuitive or mystic insight in language it often ends up as a paradox.  I
agree that the Axiom in its naked form appears as: "Given an arbitrary belief
B, it is not possible to know whether B is true or false".

But you then say "this is the form in which Dave thinks he has found a
contradiction".  I don't claim to have found a contradiction, but a
self-referential paradox akin to the liar paradox which I gave as an example.
A contradiction is something which is necessarily false such as any statement
of the form "p and not p, just as a tautology is something which is
necessarily true such as any statement of the form "p or not p", at least
according to classical logic.  A paradox is neither true nor false.  Some say
it is both true and false and others that it oscillates back and forth or
that it is a superposition of true and false or that it is 50% true and 50%
false.  I prefer to treat "paradoxical" as a third truth value.  Whatever way
you look at it it is not a contradiction and it is not a tautology.

So I agree that there isn't any contradiction here but the axiom does say
that we can't be sure about any beliefs at all.  I certainly want it to say
so, so I would appreciate it if you could suggest wording which would make
this clearer.  In other words all beliefs are working assumptions or
"provisional truths".  I won't argue whether this is logical or illogical but
it certainly has a respectable history.  It is none other than the scientific
attitude to truth.  By this I mean the attitude to truth which is embodied in
the scientific method, not necessarily the attitude of any particular
scientist(s).

Since it says we can't be sure about any beliefs at all then since it is
itself a belief then it is saying that we can't even be sure about it.  This
does not cause me any worry since I can still take it as a working assumption
and assume a 99% (or however much I like except 100%) probability of (or
degree of?) truth.  After all, of what possible value could it be to add to
any set of axioms another which says, "These axioms are all true including
this one".  This is precisely what religious fundamentalists do.  I think it
is however useful to explicitly state that all axioms are provisional even if
some mind bending must occur when this statement is seen to apply to itself. 

We have blinded ourselves to the existence of these logical cycles for too
long. My interpretation of Godel's results is that we can't get rid of all
paradoxes so we might as well choose our paradoxes wisely and learn to live
with them.

I once wrote on a blackboard before the lecturer arrived for a quantum
physics class, "Skepticism is right, believe me".  Even a student for whom
English was a second language figured out that it was a paradox.

Yes, I suspect my fundamental doubt of being itself dubious, but no, I don't
feel my principles shaken by the paradox.  It is simply an existential choice
with no logical basis, as it always was.  I currently prefer to act on the
basis of the Axiom of Doubt rather than say religious fundamentalism but I
don't expect to convince anyone to accept the Axiom of Doubt, or Nonviolent
Struggle for that matter, by any kind of logical argument.

I don't understand how you can say that the Axiom of Doubt (in any form), or
any other axiom for that matter, stands firmly on the rock of Truth.  I
believe all theories should be considered more or less wobbly.  This is what
the Axiom of Doubt is trying to say.

Please explain the significance of the capital "T" in "rock of Truth".  What
is "the rock of Truth"?

I hope you will try again to help me understand your point.
Dave Keenan