Brian:
The severe limitations of "logic" have been long recognized --
which is why "real life" doesn't much rely on it.
Are you familiar with the Trivium and have you thought much about
your "system" in relation to it?
Ultimately, what are you trying to accomplish?
Mark Stahlman
Brooklyn NY
Hello Mark,
The prevailing view of logic appears to consider it 'optional'
and apart from the normal reasoning process. Perhaps this
view is equivalent to equating it with the abstract level
mathematic computations and equations for data that derive
answers from computer processors, that thought would begin
and function in terms of logical operators. A robot likely would
be capable of doing this brute-force "thinking", yet even that
remains unnatural to natural processing of logic as it exists
in the world. I cannot quite fathom the total question the
entire situation involves - the context for logic and its
various mediations - yet to me it preexists and is attached
to 'all truth' as an informational structure, which if something
actually is true, it is resolved as A = A. So when a scientist
or astronomer discovers a new cosmic detail, what is revealed
is of this context and its truth justified by the logic that it
inherently involves, as things are related to other things,
in shared structures of truth. It is not optional as a basis for
defining truth and yet it is viewed as if somehow secondary
to language. Whatever truth exists in language, it is justified
by its logic, not by the signs alone (that would be faith in
observational viewpoints versus what they are referring to).
Things ground to logic, like a circuit, and 'truth' is based within
logic, not outside or beside it. If preexisting models of truth
existed, purified of errors, then it may be possible to reason
like a computer processor does in its logical calculations - though
because it is a natural process, it is truth that is structuring and
interweaving with other truth, and how the ambiguities and errors
are mediated, dealt with. So I think in this sense perhaps much
that exists is actually not effectively 'grounded' in truth the way
it is believed to be, and this is allowed by language in its default
functioning and so rationalization can occur, function as if logical
reasoning, yet only allow for partial truth and partial exchange
as a result which then skews ideas and 'shared worldviews'
to the finite, where truth actually is the problem, managing,
controlling it, versus honoring and serving it as the foundation
of reality. In this way perhaps much thinking and many ideas,
even those of science, are 'virtually' being reasoned, yet without
the rigor of logic, the errors are the structure for the views.
And that it is proposed is how structural problems creep in
to 'pure ideas' without being accounted for, via feedback.
So until logic is the basis for determining truth, this virtual
condition of consensus language as an unreal substitute.
Regarding the Trivium, I am not directly familiar with it though
have much appreciated reading your posts and ideas and
that is perhaps how it was first encountered, though I have
heard and had conversations about similar aspects, to the
effect that the way mathematics is taught in schools removes
it as a general knowledge via equation-based abstractions,
versus the real utility it has for thinking and conceptualization.
So too with music. This could even be a question of how the
interdisciplinary nature of knowledge exists and yet cannot
be approached within existing categorization/rationalization.
For instance, music and mathematics overlap and could be
a way to teach themes across frameworks or dimensions.
An idea like 'resonance' and tuning directly relates to that
of logical reasoning (A=A) and also psychology and social
relations, e.g. zones of public and private consciousness,
if shared or unshared in a given scenario, as with Venn sets.
There are ideas involved in these realms that are of general
importance for thinking and yet absent from communications
and that is where I have wondered about a core curriculum
that could address an issue of 'missing literacy', where basic
skillsets could be developed both for children yet also for the
existing adult population. I believe part of this situation exists
as a result of not having any cultural account and awareness
of technology and its purposeful management within society,
in the sense that issues it involves are yet to be addressed.
For me it involves recognition of the role of electromagnetism
within society, which is a non-subject yet also censored data.
So society basically is founded upon a pre-electric worldview
yet governed by an electromagnetic state and its machinery.
So there is that. Yet it is also an issue of science and religion,
which once were not separated, philosophy at this juncture.
So if populations are not able to deal with the 'physics' yet it
is also prevalent in the metaphysics ('new age' and so on),
so there is all this magical thinking yet very little is grounded
in the world as it actually exists, including scientific views
that edit out truth from perspectives beyond its framework.
It is a recipe for cultural madness, a technological dark age
where instead of revealing greater truth it is instead buried.
To sidestep the issue of actually be able to effect change in
this situation and finding support for the pursuit of truth, for
me it became very clear that skills of visual communication
are nearly absent from the populace to mediate ideas and
complex relations - the ability to diagram concepts and to
organize information coherently. And this is as simple as
making a list or two dots and a line interconnecting them.
It is not necessary pretty pictures or artwork and instead
about structural communications, breaking down as with
building up ideas and abstractions via conceptualization.
So diagramming to me is a fundamental skill that if shared
could enable far more than written language alone, where
it could become a primary means of sharing knowledge.
And yet 'listserv' mailing lists from the 1990s and email
software has degraded in performance for such basic
visual communication, now even email software does not
allow inline imagery and instead forces it as an attachment.
The ability to share a complex idea is forced into alphabets
or photoshopped imagery, versus cave diagrams needed
by those who primarily mediate concepts, their exchange.
So digital tools have degraded in the last twenty years and
it even seems purposeful, to limit the possibility to relate.
If you think primarily in concepts, language is a translation
from a purer form, and opens up much more ambiguity via
explanation in words, all the inherent problems it involves,
versus dealing with structures, their conceptual relations.
With the diagram, you can enter into mathematics in terms
of the numberline and various approaches to number via
its geometric relationship, say with counting systems, into
issues of language and communication (expanding the
tree-branch analysis of sentences, to ideas themselves).
So in some sense: diagrams {reading/writing/arithmetic}
And if adding symbols, it could enter into conceptualizing
not only ideas, also musical concepts if not programming
as flowcharts or whatnot. Maybe UML in some sense. It is
seemingly necessary for establishing and interacting with
pattern, also related across many fields of consideration.
A related aspect to the diagram is modeling of a circuit,
If feedback-based it is a way of evaluating the processing
of ideas and information and activity, understanding the
self or other events and how they function, and how the
decision-making process relates and is founded in logic.
Is it really true the way something functions is the way it
is modeled. And what if there are anomalies and it does
not exactly fit or work a given way in some parameters.
How to deal with that. And so circuit-based analysis and
consideration could allow for such logical reasoning. In
this way the circuit corresponds to a hypothesis, where
such thinking begins, not the law of 'theory' where it is
solidified as an established truth given the entirety of
its empirical review, a position that has to be earned
not just declared as interpretation, a result of 'signs'.
If ideas were modeled and evaluated, they could also
be proven wrong and fallible and this then could be
addressed and the truth that exists, retained, while
the falsity removed, and circuits could allow for this
in terms of concepts, whereas words and sentences
as structures are relied upon to hold up these ideas.
'point line plane' would in this shared realm extend
beyond a given author, to plot the points everywhere,
their interconnection in truth, its validity, and then the
shared plane of consciousness the grounded result.
It may happen temporarily in reading, yet collapses,
whereas in diagrams it could be a sustained field or
atmosphere, a common referent, the empirical model.
And so this modeling is presumably related both to
diagramming and also this circuitry, like in a context
of ecology and chemistry and biology at the very least.
The issue that seemingly is most vital to the present is
to teach people how to think - not what to think, though
how to go about accurately processing information and
dealing with feedback, so to manage an individual life
yet also relations with others. 'Logic' seems to be some
kind of expert system that is its own symbolic language
and that is not what is referenced here, it is a simpler
approach via the most basic observations, that it is an
issue of common sense and thinking-through ideas
in an accurate modeling, as a way of mediating truth.
Weighing it, valuing it, being able to account for it.
Much of it psychological, as bias, distortion, warping
are part of peoples lives as they are born into contexts
of others, who influence development via particular
dynamics and thus everyone has their own viewpoint
or relativisms to mediate for such a shared observation.
To account for this, an education where each child or
person would diagram themselves as their educational
project, from youngest age to adulthood as a living model
of the self and its relations and dynamics. In this way, if
error arises it can be communicated about in a grounded
context, and if in a school context, perhaps as diagnostic,
some may be better with mechanical skill in their circuitry
thus curricula shifts to their independent studies, based
on improving abilities, evaluating their growth and health
of circuitry and goal setting and basic standards, such as
contributive work, and teachers as tutors and guides then
interacting with students in this particularized context of
individual and group, and what may be possible if able
to function outside the too-simple standardized test that
oftentimes punishes all differences of all people, their
uniqueness, versus helping and fostering their growth.
So what if the circuit of self was a model of awareness,
such a boy who is preoccupied with taking apart things
may harness that in their education, or a girl who is a
fine orator and thinker, how that could be developed
as individuals versus existing institutionalized hazing.
There must be a place for poetry within education and
if there is not, what occurs besides a training regimen.
Grounded truth is need in educational systems to allow
for such an approach, and its accurate accounting such
that a person would have a right to pursue greater truth
and not be held back by teachers or guides or mentors,
given logical reasoning, evaluating the feedback circuit.
This versus the opinion of authority, which oftentimes is
requiring the student to work in its narrow framework to
proceed. Without logic to evaluate these dynamics the
power of decision-making rests with existing hierarchy.
What they say is true is true - that kind of pure tyranny.
So the idea of diagramming a life as a circuit then can
also relate to 'rights' and how they are grounded with
an individual in relation to the state. If an injustice were
to occur, it would be between the circuit of the state or
the educator and the circuit of the person, and it could
be logically evaluated and determined via shared truth
what is actually going on, versus onesided viewpoints.
If the Constitution says something, a person could link
their actions to it, which is its essential idea, whereas if
it is mediated in language, its truth can be lost amidst
surrounding noise, skewed interpretations, frameworks
that force the exchange into false views, compartments.
In this way, law & lawyers, the supreme anti-reasoning,
detached from neutral truth, virtual, mainly about power,
managing the status quo, the functioning of machinery.
Logic, as a way of accounting for truth, via its structure,
then can begin to deal with any such situation in any
such warped or distorted or biased condition, perhaps
on the level of its 'physics' in the sense of concepts that
are structural frameworks and influence these dynamics.
Ideas like 'empirical' or 'relative' can be understood via
logic such that these dynamics can be neutralized and
their truth recognized and their errors identified and in
turn accounted for, recovering & grounding what exists
in truth, and removing the falsity contaminating ideas.
So the relation between logic and concepts, as these
relate to diagrams and circuits and models, then is an
issue of basic awareness and core observational skill,
to be able to consider things in a grounded viewpoint,
defined as fallible, yet tending towards truth if following
certain guidelines recognized, yet not yet adhered to.
In this way, 'truth' instead of a standing-reserve would
be a 'standing truth' or standing wave, to achieve this,
versus each person being archaeologist at their own
excavation site, without corresponding data sets of
shared culture, the truth not adding beyond the self.
An attempt to say the relativistic perspective and the
empirical perspective can become unified within a
logically grounded observation via such modeling,
based within circuits, diagrams, as communication.
It would seem from here, an issue of patterns, about
how larger scale feedback loops within circuits, of
say 'the state' or 'society' could themselves each as
models have recurrent patterns or themes, such as
'economic bias' or 'cancer-causing chemicals in food'
or 'discrimination against women' or whatnot. Errors
within certain frameworks potentially. Also, positive
or neutral themes such as 'romance' and 'wildlife
sanctuaries' and 'population'. The thing is, it could
be a child in school who has an idea, referencing
some observational model and testing a hypothesis
that could flip certain bits and if insightful, as feedback
cause a rube-goldberg like cascade of truth across
the various logical structures, as it is accounted for
in its accuracy and-or errors. A sociologist could
run studies or a thesis against large datasets this
way, and it would be a common way of thinking,
referencing the shared empirical model of truth.
That, the result of the combined efforts of society
to model what exists as it is exists, beyond signs,
into the structures, their truth, grounded in reality.
Patterns then may be recognized as ideas, yet in
the N-dimensional realm, where it could involve
'many perspectives' at once, thus moving from a
2-D flatland version to a spherical Platonic form,
where seemingly the dodecahedron resides in
its mystery, the more and more connections in
this shared truth of observation, seemingly to
smooth out the remaining rough edges of idea.
By contrast, a CERN collider diagrams of the
particulate explosion, of sharp shrapnel rays.
Thus, it would seem such an education and ability
to communicate would require advanced models
that can only be sustained within technology if to
export such conceptualizing beyond the person,
their consciousness, brain, and logical functioning.
Thus such a future computer actually is extension
of this essential competency that allows a person
and state to govern itself toward highest purpose
and capacity, versus lowest. Such a computer is
worthless without the purposeful interacter, the
person thus is in a vital relationship with it, their
value is its same value, their logic is its logic too.
Meaning truth could be its foundation rather than
something subsequent if not non-consequential.
So the person, so society. The computer as tool.
Today its quite different. It is not even possible to
imagine interacting with technology in these terms
given existing equipment and modes of relation. A
disenfranchisement or detourned development has
occurred, leaving people out of loop of the society.
In this way, people, populations, turned into slaves
of the machinery and its functioning and routines.
Machine-based culture, politics, economics, etc.
Its reality, its rules, its priesthood, the god-head.
In this way the relativism of atheism, those who
refuse to serve nothingness as the greatest truth.
And so that is a context, my naive approach was to
believe it possible to 'reason' within society, thus to
approach questions of curricula within the goals of
electromagnetic literacy, a project for a HIOX ring,
a 16-segment LED display that would be a kit that
like a Board of Education from Parallax or other
electronics microcontroller platforms, it would be
a way to teach logic via electronic components in
a given circuitry, and also in its functioning and
operation, logic and programming. Perhaps today
a watch would allow for more to occur yet the idea
at its simplest involved language and mathematics
in a common symbol, and how it could potentially
allow a new basis for reasoning about ideas and
concepts and how things relate. All information of
this has been lost, so there is nothing to reference.
And yet such a project could encapsulate various
principles of diagrams, circuits, feedback circuits,
logic, reasoning, programming, as a literacy device.
I mean, what's it mean that an ancient symbol has
within it the alphanumeric code running the society.
It is not known what the exact structural relation
between the various concepts may be, though it
logic likely is primary, reasoning, and circuitry.
It is also likely modeling and diagramming are
involved yet how they might relate to circuitry as
subsets or supersets would need to be evaluated.
For instance, {logic, reasoning, modeling} where:
modeling {diagramming,circuitry}. I do not know.
I mistakingly started using 'set theory' structures
like the above paragraph without defining them,
so it is basically a way of modeling ideas as sets,
as groups or classes in relation to hierarchy, where:
superset {set1,set2}, which if in a traditional diagram
would be a rectangle where 'universe' is superset,
a container, for two circles 'set 1' and 'set 2' within it.
Likewise, an option for labeling exists such that the
superset could instead be referenced as 'set' instead,
and thus: set {subset1, subset2}. Doing this to give
an indication of structural relation, the left-side is a
level up. Maybe some are not familiar with this yet,
though a tutorial search on the topic could clarify.
The question of Trivium as structure then might be:
curricula { grammar, rhetoric, logic }
And Quadrivium:
curricula { arithmetic, geometry, astronomy, music }
The curricula as a 'superset' category, for various sets
else as a set, with various subsets. So my question or
a question might be how diagramming, logic, reason,
may fit into that category via its structural hierarchies.
For instance if Venn diagrams and set theory are vital to
conceptualizing logical considerations in their simplicity
that it would be a necessary subset of logic, such that:
logic {venn diagrams, set theory}
Then in this way:
curricula { logic {venn, sets}, reasoning, modeling }
And yet likely 'diagramming' exists in modeling and
'feedback circuits' in multiple categories of reasoning
and modeling, so perhaps that would move it up in the
hierarchy, given a thorough evaluation of the structures,
how these concepts functionally relate to one another.
I don't know though it is fascinating to consider.
Ultimately the purpose of the subjective mathematics essay
was to convey an idea that to me is quite evident and not
yet adequately addressed or communicated about. The
situation it defaults to requires and institutes and propels
unequal exchange, where expropriation and exploitation
occurs via biased onesided dynamics within interactions,
of people and ideas, oftentimes in the guise of 'reasoning'
yet it is to interact and mediate things within language that,
in its short-circuiting, function like a rigged slot machine or
other device that in its very use, unaccounted for in such
malfunctioning, is wrongly believed the basis for action,
when instead it is the medium deterring its possibility.
My goal was to convey that to deal with this requires logic.
That that is how the accounting occurs. And that if each
person who is contemplative thinker, who evaluates and
seeks truth, were to recognize the common condition, that
in changing the basis for evaluating 'reason', that different
set of rules could apply that are not being acknowledged,
and if they were, every just claim could be approached in
this way, in a legal, constitutional, grounded context, It is
just a matter of logical reasoning. It is a capacity and it can
be developed, given enough consideration and sharing of
basic knowledge which today is very difficult, even online,
given splintered group dynamics and technological tools.
In this moment of reflection upon the potential to say and
what is said, if there is one thing to convey, the purpose,
it is that one viewpoint of reasoning does not equate with
all truth of what it references, and is likely very minimal.
[reason 1] =/= [all reason]
So while I may reason about something, it is fractional
at best to what it references, only if all other views and
observations in truth were accounted for, would the idea
be more fully 'true' in its totality. Perhaps the word reason
stands in the way here, as a concept. Yet if every view of
some event were to occur, its every truth accounted for,
then in this N-number of observations, what is observed
may be modeled accurately as truth.
[observer] ==> [observed]
Meaning that if a single observer makes an observation,
such as within language describing something, it is not
describing 'the whole thing' only a particular view of it,
relative to its perspective and context. Observer 1 and
Observer 2 may see different things:
[observer 1] ==> [observed]
[observer 2] ==> [observed]
This is relativism, and some of what is observed may be
inaccurate, partly true, if not false, given observational
biasing, lack of knowledge, new data, whatever. So if
considering that what is observed, if it were 'all true'
and described in its entirety, this would likely involve
all observations to account for its totality of truth.
Observers 1, 2, 3... all the way to infinity (N=infinity)
then could evaluate this shared observation...
[observers 123..N] ==> [observed]
And yet if errors in view or assumption are not corrected
for, even then what is observed may not be fully true, it
could only be partially true. It would require taking all of
the observers, their observations, and figuring out what
is true and separating it from what is not. That is how the
observation would then be grounded in empirical truth,
if the bias, warping, and distortion were neutralized, the
known errors corrected and disallowed in the modeling.
By default the situation today in language is to assume:
[observer 1] ==> [observation] (100% truth)
When in the totality of what is observed, as an idea or
concept in its reality, all possible truth of its existence,
then tends to have a single finite observer contributing
a minor aspect of the totality of truth a concept involves,
such as my mentioning [society] without referencing or
distinguishing contradictions and interpretive errors,
such that in such a ungrounded reference instead of
being by default [100% true] it may be [false] or even
[0.000000000000000000001%] of its dimensionality,
yet within ordinary reasoning function as faith accompli
(typo kept for je ne sais quo factor), in terms of its not
being the 'whole accounting' for what is referenced.
A [sentence] could begin to fall into [error] as these
[things] get [out of control] as [ungrounded] [ideas],
such that [truth] may not be occurring at [100%] via
referencing [concepts] as [words] in comparison to
their [modeling] as [ideas], and instead, because of
this [lack] of [empirical] [cumulative] [N-dimensional]
[accounting], what is [referenced] as a [sign] could
instead be [minor truth] if not [infinitesimal] by default.
Such that [all truth] is not being processed by each
and every [reference] to [concepts], [100%] as it
combines with [100%] as it correlates with [100%],
thereby, I conclude [100%] is the standing[reality].
Instead, it could be [partial truth] and [minor truth]
full of [errors] and [bias] that are [structural] to the
ideas themselves, including their [origin], that is
the [fallibility] of thinkers, their [subjectivity], even
that is not [accounted for], and in continuation of
these, [0.001] and [0.00000001] and [0.000001]
in their interaction as more and more minor truth
is described and calculated, that this is not adding
up to N-dimensional modeling removed of error,
via this [observational relay] within communication,
instead it is moving towards [absolute falsity], that
is, [nothingness], by default of its lack of grounding.
Thus the more [words] relied upon to describe the
[concept] the more errors and impure frameworks
are assumed to be [neutral] carriers of [ideas] yet
it is their very recession, a receding of [truth] via
this language, hidden within the structures if not
beyond them, [forced] to [mediate] this instead,
these [signs] and this armature of [alphabetic]
[signage], that this description in itself is a unique
[perspective] that is only [partially true] at its best.
And thus its a trap, to mediate ideas in this way,
especially without a common referent removed of
known errors, all of this instead relying on a basis
of assumption - essentially 'faith' and 'belief' in the
infallible observer communicating in pure truth and
it is just not the reality. Errors are at the foundation.
This is in error, by default of writing it, as if all true.
And yet its truth, however infinitesimal - as its truth
could be all true, if corrected for, yet it is precisely
not this N-dimensional truth of each & every idea
that is referenced. It is of dust within the cosmos.
Unless empirical models were to sustain 'truth'
and this instead was referenced as the basis
for exchange and sharing of hypothesis, views.
Where error would be removed by requirement
so only the pure concepts would be mediated,
not the noise, not the distortion, not the biasing,
which seems to function almost as if categorical
style, sociodemographic or institutional aura, etc.
To sum up the basic idea, and maybe this diagram
is not effective to do so, yet it attempts to model the
situation, it is that a single observer is not observing
this N-dimensional truth by default:
[observer 1] ==> [N-observed]
Whereas if the observer was made empirical, then
together our observations would combine into a
single shared viewpoint, as N-observer, such that:
[N-observer] ==> [N-observed]
And if this, the accumulation of all views was itself
the position of an observer, what is observed would
be of the panoptic, every available facet evaluated
in its truth and inaccuracies, not just the observed,
also every observer observing every other observer
such that in their correlation and resolution of views,
the observer is removed of their own errors prior to
and along with other observational errors, such that
a defect in the eye could affect what is seen, so too
inaccuracy in thinking could effect what is observed,
and therefore others can account for these errors in
observations between us, so to capture the truth of
a particular view or observation while removing it
of distortions or biasing or whatever is not true.
Without this correlation and correction, any number
of observers could lead to a miniscule truth if their
observations do not accurately add up, such that
they may cancel eachother out via contradictions,
where shared frameworks becomes arbitrary...
[N-observers] ==> [0.00000000000001 truth]
Wheres if errors were accounted for, this same
scenario could be grounded in a shared empirical
model, where together the same group of observers
could have the 'truth' they know, correspond to the
observation in its shared modeling of the concept...
[N-observers] ==> [100% truth]
While such observation may remain contingent, and
actually involve remaining unknowns and unknown
errors, 'know errors have been accounted for' and
are not allowed to continue in the shared processing,
if falsified, to whatever degree. Perhaps remaining
around as junk DNA or in the realm of potential data
that could be further reinterpreted via other hypothesis.
And here is the point, that N-observers in their combined
efforts, can then become a single observer who is able
to reference the shared model in its truth, such that:
[N-observer] ==> [100% truth]
That would require a new kind of computer as the
basis for communications, and yet, to say this or that
each of these referenced [concepts] could be instead
empirically grounded to a shared model removed of
falsity and tied into its structural interconnections, say
as a [concept] may relate to an [idea] and having a
model with the best working hypothesis of why this
is so, and running viewpoints through these 'forms'.
The thing is, today, in this language, by simply being
able to type at a keyboard, it could be assumed that
the person is doing exactly this, that it is to reference
a 100% truth by referring to an [idea] from what is a
unique perspective, ultimately, as a finite observer.
And what that is by comparison is the very opposite:
[observer 1] =/=> [100% truth]
The observer does not tend towards absolute truth,
via the uncorrected for relativistic assumptions, it is
instead to tend to highly particular truth, enframed:
[observer 1] ==> [00.0000000001 truth]
If an observation is true it may actually be 100% truth,
if it were removed of its errors, except the context is:
[observer 1] ==> [99.9999999999% falsity]
If considering the truth in its actual N-dimensionality,
such that the observation is so small, it is not even
equivalent to the entirety of what is referenced. In
this way, ungrounded observation tends towards
absolute nothings and total falsity by default.
[observer 1] ==> [total falsity]
In this way, the false perspective and false reality,
language propping up a virtual realm of 'reason'
as if it inherently corresponds and is guided and
managed by language, mediated it by it, versus
the way [truth] is removed, replaced by [power].
Logic, the requirement to resolve this condition.
An idea such as [ideology] has been referenced
here as negative many times, yet it is potentially
neutral, a function of [answered questions] that
may be [working models] of [grounded beliefs].
Yet if an ideology is based in bias, warped and
distorted thinking, it can function against truth in
its deterministic answering, closed-minded and
not allowing feedback to correct for its errors. In
this way, [everything], subtle & in superposition.
Any given view, only partial, likely a contradiction
in absolute terms (N-observed), and only partial.
Like these ideas and my viewpoint versus those
of others, to correct my errors and distortions and
to correlate and add additional observations and
views and greater truth. Without that, whatever is
here collapses back into the undifferentiated, as
it cannot be sustained within language, its signs.
The truth is not in these words, it is beyond them.
And in that way, a contradiction annihilates itself.
---
Brian Carroll
Minneapolis MN
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