Gödel's theorem is a lesson in humility for logicians. It tells us that any logical system must be subject to at least one of the following deficiencies:
The system can't count.
There are assertions which the sytem can both prove and disprove.
There are things the system recognises as meaningful assertions yet can neither prove nor disprove.
I recently found it interesting to draw out parallels between this and some thoughts about how one conducts one's spiritual life. I wish, here, to record some of that thought, primarily for later editing, while it still lingers in my mind.
Turning each of Gödel's
deficiencies inside out, we can identify
some desiderata of logical systems; completeness might be a bit much to ask,
once one pauses to think about it, but would certainly simplify matters;
consistency is the sine qua non of logic, its absence - anathema - yields
confusion; and counting is without doubt among the things we naturally take for
granted - our unconscious desiderata, like
modus ponens (proofs
of A and of
A implies B may be combined to produce a proof of B -
implication means what it says). Indeed, completeness and consistency
once lived among those unconscious desiderata until folk came to suspect they
had found a way to formulate logic in such a way as to be able to prove that the
logic satisfied these two. This unwitting hubris came crashing down in
My parable begins by addressing a fundamental spiritual truth - though we
may strive for perfection, to presume that one has attained it would be an
imperfection. However much or little each of us sees of the spiritual world,
each has our own understanding of it. This need not be logical, but certainly
complete, as there is more to spiritual experience than
understanding. Though our understanding may be
locally consistent - in
the sense that it consists of locally coherent patches of understanding,
intelligibly interwoven - I am wary of the pursuit of
approaching it by enlarging locally consistent patches in so far as doing so
proves enlightening, being willing to split patches under the same condition,
offsetting the retreat from
global by, for instance, enabling later
enlargements of the fragments by joining with other patches thereafter in ways
more intelligible than the original.
understanding of spiritual experiance covers but one
corner of that experience. I shall use it as a mirror through which to view the
ways folk respond to reality and the spiritual issues it offers us; view the
thing itself in the light of the parable to discover such truth as may be in it,
the mirror is but a contrivance by which I come to the matter.
How shall we respond to the world ? Some roads offer rules (along,
typically, with some socio-cultural organism which sets (or has set) and applies
those rules) and call for obedience; the decision-making process turns to an
external authority, addresses it through the veil of understanding: the response
what the rules say but if the obedient misunderstand the rules, or
identifies the wrong rules to apply, still the obedient err. The obedient
delegate their decision-making: the wise review their responses in the context
of what ensued and the honest ask how their own responses contributed to the
Other roads may be found, not uncommonly by the wise and honest among the
obedient, which focus on the effects of our responses to the world. On these
roads, one identifies the responses one can see how to make to each situation,
estimates the outcome in each and choses a response based on these estimates.
The obedient, when they change allegiance, may perform a similar assessment and
choice: though this is not the only way the may come to do so. The various
roads of this style differ in how they make those choices; some involve rules
which will reject responses which produce particular kinds of outcome; some
invovle sophisticated risk-assessments associated with uncertainty as to
outcome. The honest notice the way they go about making choices; the wise study
its impact on how their chosen response affects what ensues.
Travellers on these roads recognise that if they meet a given
situation more than once, their
best choice may be different simply because of
lessons learned earlier and applied later: which can lead to them seeming
inconsistent to the obedient.
available responses using their estimated
response algorithmfalls foul of inadequacy - inconsistency - quite a good starting-point from which to tread the road towards evil incompleteness - Written by Eddy.