.... SYMMETRIC BEING: Logic & Language
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LOGIC, OPPOSITIONS, INVERSIONS, AND TRUTH VALUES
Logic begins with statements and propositions and their various
combinations, with how true they are, and how they function in
inferences  premises and conclusions (The dog barked; The dog is
black; so A black dog barked), and arguments. Though if all life and
consciousness is founded on perfect opposites and inversions, then the
first thing we must reanalyze in logic is what on earth we are doing
in the first place when we use logic and language, and how logic and
language are even allowed to exist; when we consider the inversion
supporting all our statements, we will have a much better understanding
of what logic is. The second thing we will do is add to logic by
creating terminology to discuss inversions and oppositions, where
philosophy is lacking in examining these things.
When we make a statement or proposition, this is allowed by a perfect
inverse statement unthought or unspoken by our invert; when we say p,
we necessarily imply unp (not "not p"); that is, p if and only if
unp; a proposition about half the story implying the other half as
well. (And besides its perfect inverse, p may also require and tear off
many other statements, a similar but not exact inverse of p, and
working outward from the exact opposite, p might be related and
sustained by all other statements, creating a new map of all logic
might be selfreliant and selfdependent, but I've not discussed this
possible sea of connections in this thesis yet).
Now the existence of unp creates doubt about what the truth of p is.
If I state something true about what's going on on my side, then might
not everything on the other side contradict what I state? Do both sides
fight about the truth I'm trying to state? Or might I consider both
sides an individual event, two things going on. If there are two
statements, is one true whenver the other is false? When I say that it
is true that the frog lept, then conversely it is false that the
unfrog unlept? (And is saying that the unfrog unlept is false just
another way of saying it's true from an inverse point of view?) Or
might we say that both things are true, that there are two tears in two
directions, that it is true that the frog lept and also true that the
unfrog unlept?
It is odd that from one point of view, if p is true then unp is false,
and from another, p and unp are true and false together (p if and only
if unp), these are two opposite views. This grayness arises much in
the metaphysics, logic, and epistemology of selfsustained Being. We
get confused as to what's going on: is a thing a subtraction from
nothing, the other thing an addition, or v.v.? Or are both additions or
subtractions to or from nothing?
There's a concept we will use in such situations to clarify what's
going on, the absolute value of mathematics. The absolute value of 8
and 8 are both 8, this is saying there is something to do with 8 (a
distance of 8 from zero, whether one way or the other). If propose that
2 + 3 = 5, supported by the unproposition that un2 unplus un3
unequals un5, we might see that we're saying the same thing from two
angles, a mathematical truth, whether we've taken nothing and created
substance  added to nothing  by the positive somethings 2, 3, and
5, or subtracted from nothing with the negative concepts un2, un3,
un5, which are almost the same thing as 2, 3, and 5. (5 is our
term  our understanding  for the total inverse idea of 5).
If we say there exists dog, or the dog barked, we consider the
unification or doubling with the inverse dog, and inverse unbarking,
going on. We can say dog/undog, where we're revising our proposition
of something going on on one side, to include both what's going on on
one side, and what's going on on the other (keeping in mind this
unification, this proposition of something going on in two directions,
requires the ununification concept of two things ungoing on, so we
must consider whether we're actually getting closer to the truth of
what's happening, or just going to war even more with the oppositte
logic).
But there is still some confusion with "true" and "false." They seem to
be opposed to eachother, hence supporting eachother as inversions. But
if I say there is not blue, I am not saying there is inverted blue (or
orange), but rather I am saying there is a tear in neither direction.
Not blue means I have not torn a tear from nothing in the blue
direction, so I have not torn a tear in the orange direction. "Not
blue" (or nonblue) implies nonorange as well, not "inverted blue" which
would be the confirmation of orange. Nonexistence does not imply
inverse existence. (We will put this confusion off for awhile while we
consider a related topic, the relation between opposites and
inversions).
Most opposites are basically inversions. Most opposies tug on
eachother, tear and feed off eachother, require eachother. If I only
exist because of my perfect invert, each subtracting or each adding to
nothing depending on our point of view, then black only exists because
of white. They are not contrary things that just happen to both exist,
but one is exactly the other's cause, Nothing tearing apart to create
two colors, the existence of each totally depending and requring the
other. So hot requires cold, feeds off it. And guilt, innocence, etc.
But what is the difference between cold (hot's opposite) and unhot
(hot's inverse)? Between black, and unwhite? Cold and unhot (and
black and unwhite) are actually essentially the same concept. The only
difference is how we refer to what it is and what it applies to. In
saying uncolor we're just pointing out a little more than usual that
this attribute has been torn from color, supporting it. In english we
might have forgone naming all opposites and simply said "negative
white" for black, the way we say "negative one" for a number we might
have just given a name to (or inverse 1). This is what we are doing
when we say unblack, we're saying "the color that has been created,
supported by, and feeding off of, the original color."
The other difference is the usage. We tend to apply white and black to
a human or to an object in our realm of Being. The ball is white or
black, hot or cold. We're temped to say the unball is (respectively)
unblack or unwhite, but we could just as well call the unball white
or black (as I usually use colors to refer to both sides because we're
more familiar with them as such than saying uncolor). A man and unman
can both see red, it's the same color, the same sensation. I will see
red when my perfect inverse sees green, and my invert will see red when
I see green.
Hence we will call the opposite (red vs green) the "existent inverse"
or "existent opposite", or positive inverse/opposite, for our tendency
to use it more for things on our side, and for the derivation of its
name: a regular name just like its opposite. We'll call the word we use
prefix un for the the "unexistent opposite" or "unexistent inverse,"
or negative inverse/opposite, the inverse via pointing out its
inversion obviously by saying "negative of some other thing", and for
our tendency to use it a little more often for inverted being rather
than being, for an unball rather than a ball.
Thirdly, we need a word for a negative spin on the original thing, a
way to refer to thing as an inverse of something else, not an inverted
or negative inverse/opposite, but an inverted or negative idea of thing
itself, and also a word we'll use a little more to talk of the original
word in relation to inverted things. We'll call this the negative or
unexistent compliment of word. Hence unwhite is black's negative
compliment, the exact same color except for usage, and the method by
which we've refered to the color, by naming it or referring to it by
the opposite of some other thing. Lastly, just for consistancy of all
four, we'll give a term for the first thing itself, we'll call any
original word without an un prefix a positive or existent word.
So black is an existent word, unwhite (same thing) is its existent or
positive compliment, white is black's opposite (what we usually call
it), or more specifically in our terminology, the existent or positive
inverse/opposite, the thing allowing its existence, and unblack
(basically also white, the thing supporting its existence) is black's
negative or unexistent opposite/inverse.
There are cases that already use a negative term for a positive
inverse, such as the term "negative one." This is almost exactly the
inverse of one which supports its existence, but the difference is it
is a positive inverse, vs unone, the negative inverse. We might even
consider giving the inverse of one a special name because it's such a
lower number, the way we have a special word for a multiple of two or
three (double, tripple). We might even name to all four, such as one as
one, "eno" (one backwards) for the existent "negative one," "neg" for
the negative inverse of one, and "gen" for one's unexistent
compliment. We can express these numbers or any opposites on the
following chart:
[image description: black, white, unblack, and unwhite, in four
corners, with lines illustrating which are sameside opposites, opposed
opposites, and opposed compliments]
Sometimes we will not have a defined word for the opposite or inverse
of a word. In this case we shall bring in another prefix to create one.
We shall use anti to create the positive inverse of word. Hence the
existent inverse of a chair is the antichair, an inverse of chair that
we often think of existing on our side, or the inverse chair in
inverted being that we refer to as a thing, and talk about (in the case
we're referring to what has happened when nothingness tears itself
apart as two additions to nothing, two somethings) rather than calling
it an unthing. And then the only way of referring to the existent
compliment of chair will be to say unantichair.
When I first started to create terminology for inverse being, I
developed these existent and pure inverses: The antidog (an existent
thing) is, and the undog (subtractive tear) unis. (We may or may not
use unthe or antithe, as an existent thing is our tendency to refer
to it with our positive language, and negative inverse is only our
tendency to refer to it with unwords. When we use language we will
almost always use "the", as we're more familiar with it, and only use
unthe when we want to create a totally opposed proposition: unthe
undog unis). When I began to be confused as to which to use and why I
even had two words, I eliminated this duality and decided simply to
distinguish between positive and negative inverse by context. Hence
"The undog is" would be positive or existent, and "The undog unis"
would be negative.
But then I when I realized opposites were basically inversions, I saw
that there were already existent inverses in the english language,
already creating the duality and confusion with anything we prefix with
un. So to classify these relationships and be very clear and precise
what the difference is, I revived this terminology and the new prefix
anti, which allows us to have existent and negative inverses of any
word. When there is any doubt, simply understand unthing and
antithing as almost the exact same concept. It is only an issue of
being precise that we have made a very subtle distinction.
We will at times bump into words which already use the prefix anti or
un. These are similar to our invertd concepts, with the exception of
where un is really being used as non. (Unblue is orange (requiring
blue as well, so unblue is orange and blue), and nonblue is anything
but blue, or no color at all, neither orange nor blue). Consider the
defined word unmask, which is almost exactly the same thing as our
unmask (we will use a hyphen to distinguish the difference, and use
context to distinguish when a defined word with anti or un utilizes
the hyphen by definition). We will consider unmask the existent inverse
and unmask the negative inverse. Unmask referring more to an action
going on in being, unmask in inverted being, but basically the same
thing.
As an example where un is being used as non (and hence not an inverse
of any kind), consider undependable, or unreliable. This is saying
nondependable: not dependable vs inversely dependable. If I cannot rely
on someone for money (unreliable), then this does not mean that I'll
expect them to take money from me, the inverse action of giving
(Theiving the existent inverse of charity). So undependable is not the
inverse of dependable at all, athough there is some opposition involved
here: for instance, it is generally good to be reliable, and bad
(inverse of good) to be unreliable, or nonreliable.
When we decide whether to use an existent or negative verb to use with
a negative inverse (whether the undog is, or unis), we only have a
decision to make when we're using what we'll call a grayarea verb.
Some example of grayarea verbs are to be, to exist, to become, to do,
to go, to see. These are verbs which are often very similar to their
inverses. In some ways to exist is very opposed to unexistence (when
we consider the tear in one direction a positive and the tear in other
direction a negative), but in some ways we're saying the same thing
(when we consider both tears to be an addition to nothing; or the gray
area of unexist  when it refers to both sides  is when we consider
both subtractions, the union of which we might call an
addition/subtraction, something similar in either direction), that all
tears everywhere in whatever direction, have cause
existence/unexistence (either or both, we don't really care which) all
over the place.
Often, the dog and undog are doing some kind of becoming, are both
becoming something. Consider "The dog became his invert, and his
inverse became him." Here we have an action that applies to the
transition between thing and unthing, a transition and action that is
happening the whole time to both beings. If we say the dog barked and
undog unbarked, we might say they are both doing something. Though
bark itself is not a grayarea verb. To unbark is to do something
completely opposed to barking, as white is opposed to black. Remember
even grayarea verbs can seem totally contradictory. The only
difference between grayverbs and nongray verbs is that the
contradiction of verb and unverb can at the same time be the same
thing. Addition vs subtraction vs two additions or two subtractions.
We can also have grayarea nouns like thing, color, being, existence,
soul. We might say that all life are souls. That all things and
unthings are still things, that the undog is still a thing, a tear in
a direction. The term "color" can be gray (not the colors themselves)
in that we often don't care whether we're calling unblack a color or
uncolor, it's still the same as white. Colors themselves are very
opposed: black to white, red to green. The only colors that are
grayarea are actual shades of gray, almost the same color.
Let us return to our confusion of truth values of propositions. In some
ways true seems the opposite of false, and until now all our examples
of opposites have been almost the same thing as inversions, things
feeding off of eachother, two tears; false or "not true" (the logical
use of not, that not true implies false, not the standard use, which
would imply we could have no truth value at all) at a first glance does
not seem to be the same as "inversely true": Not blue or nonblue means
lack of blue (hence also lack of orange), but also says we might have
any other color, or no color at all, where inverse blue means we do
have orange, a contradiction with "not blue" (but not a full
contradiction. In both cases we can have other colors, though we cannot
have no color in the case there is blue).
Here is our problem. The truth value of p is not the same as p itself;
saying "it is true that there is blue" is not the same thing as saying
"there is blue." If false is indeed an opposite or inversion to truth,
then saying "it is false that it is blue" is saying "it is inversely
true that there is blue," not "there is inverse blue." Our inversion
applies to the truth value of the sentence only, not the sentence
itself. Consider that the tearing in one direction of nothing has
created something positive where there would have been nothing; plus
one thing, plus one color or proposition. The inverse action wouldn't
be the lack of creating (not creating), but rather inversely creating
what we have done, or putting the tear back. To pull a door open vs
shutting it, not to have not have opened the door at all. We are not
doing nothing, but are contradicting something we have created. We pull
apart nothing, then push it back. This is a way in which examing
inverted being gives us a better understanding of logic: what truth
values really are, and what supports them.
Now we'll introduce a new type of proposition, that which conveys the
extra information contained in p, which we'll call ext(p) for extended
or extra or existent information, that which it implies about the
inversion going on. This is very similar to what the inversion of p
itself does, except that ext(p) will make a positive proposition on our
side about the negative inversions going on.
So take p "The clown juggled." For p to be thought or spoken requires
the inverse to this proposition, what we call antip (if we decide to
refer to this inverted thing in a positve way, the positive inverse),
or unp (the negative inverse, basically the same thing). This inverse
proposition is basically the same proposition with every word inverted.
So antip would be "unthe unclown unjuggled," or we might say unp
unis the same phrase, where we often use the negative of the gray verb
"to be" when refering to the negative inverse, but could also just use
"is." But when we, over on this side of being, talk of things happening
over on the other side, we use our language, we don't use perfect
inverted language. Taking unp with every word inverted, we can
uninvert those words that are grayarea nouns, verbs, etc, the words
that can sort of refer to either direction, the words that will allow
us to use our language to talk about just the inverse subjects and
actions in the sentence we really care about. In "The clown juggled,"
the only grayarea verb is the word "The." (We can say the tree or the
untree interchangably). Hence ext(p) would be "The anticlown
antijuggled."
Consider p "This proposition refers to itself." We have antip or unp
"unthis unproposition unrefers unto unitself." Antip and unp are
our terms to refer to that entire inverted thing. But to state
something more understandable about what's going on in the inverted
world, we will not use so many negatives, we will take the unwords
that could basically refer to either side and use their absolute
values. So ext(p) would be "Antip antirefers to itself." Note this
ext(p) is not antip. It does not match its form: a negative for every
exact word. Even if we said "This antiproposition antirefers to
itself," we're not really stating the antiproposition. The
"antiproposition" is that proposition which fully supports
proposition, allowing it, without which it could not be thought or
spoken."This antiproposition antirefers to itself" does not support
p. Antiproposition is our existent, positive word for the totally
inverted thing; we are calling antip a thing, rather than unthing,
and can make new propositions about antithing, including the one thing
p implies in the requirement of antip.
Note that if we did not give our statement the name "p," we would not
have a convenient subject, antip, to talk about. Usually we can just
invert the subject: ext(The bird flew) is "The antibird antiflew."
But the "this" complicates things. In stating "this proposition," we
cannot state "this antiproposition" in ext(p), because what we're
stating is not the antiproposition. If we do not name p, then we would
have to say "The antiproposition to the proposition that we are
talking about, antirefers to itself." This would not be a problem if
the sentence simply used "the proposition" instead of "this." But the
problem of length is fixed if we call the original statement p.
For another example, let us consider the p "I think, therefore I am."
That an inverse of this exists is basically our main thesis: "unI
unthink, untherefore unI unam." To make this more intelligiable,
we'll consider ext(p): "I unthink, therefore I unam." We've
unnegated our gray terms "I" and "therefore". Or if we consider "I
think" and "I am" are basically the same thing, and we reduce Descartes
to "I am," then ext(p) is "I unam," or if we consider "to be" is a
gray verb, then we've actually reduced to the exact same statement.
Note it would be something totally different to state "I think,
therefore I unam": this is our thesis, the extra thing going on we
conclude from Descartes observation.
Lastly, consider the rejection of our thesis "There's no such thing as
my unself." We're negating the existence of something, and if we
consider that self and unself are positive tears, then ext(p) of this
(what this also states about the opposition involved, assuming we are
correct in our thesis; that p disagrees is irrelevant to what p is
doing when we assume inversions exist) would be to conclude that the
inverse does not exist as well, so, "There's no such thing as me!"
Let us draw up truth tables of the relationships between p, ext(p), and
unp (or antip). Remember that there is a fuzzy area whether to call
unp true or false if p is true. If p is "there is elephant", is the
inverse supporting it also true, that there also unexists an
unelephant? Or if p is true, is unp inversely true, i.e. false? This
is not to say that the existence of the unelephant being false implies
there is not a tear in that direction (which would result in a tear in
only one direction without support, this is not what we mean at all),
but that whatever going's on on the other side is inversely true
because there's inverse stuff going on.
Recall the truth of 2+3=5. If we know this is true, then we might say
the unstatement supporting this truth is also true (both basically are
stating the same thing), or we might say that in its own way, it is
false, since its inverted, but just another way of saying it would be
true if it were right side up. This is the same problem in defining
positive and negative inverses. So we'll create two categories of truth
value: positive truth values for our inversions, and negative truth
values for our inversions. That there exists elephant and unelephant,
vs if the elephant exists is true, then we consider the unexistence of
the unelephant to be a false exisence. In either case ext(p) is true
if and only if p is true. So:
Designating the positive truth values for unp as + and the negative as
, we have the truth table relating negation, inversion, and
implication of inversion (ext(p)).
[descrip of picture if unavailable: simply a truth table where p is
true or false, not p false or true, then the truth values we've
discussed for ext(p), unp, antip, etc]
Remember antip and unp are almost the same thing, so we can replace
any unp with antip above. We might instead have defined antip to be
the positive truth value (p and antip are true together) and unp to
be the negative, if this were the case, we'd have antip T F and unp F
T. Secondly note the matching of the truth value of ext(p) to unp+.
This is saying that when we say p, we can also logically state
something about what's going on the other direction, just like the
total inversion of p  every word inverted  is also stating
something true. We also might consider the absolute value of unp (the
symbol for absolute value is "x" ), that in a way, saying an unp is
F is just a way of saying p is true (when we have some form p in some
way torn in both directions, i.e. that saying un(2+3=5) is F is just
another way of expressing this mathematical truth in inverted being).
Also, we can apply absolute value not just to truth values but to whole
propositions. The absolute value of unp itself is p, as 5 is 5. If
we propose 5, requiring inverse 5 or 5, we have some type of 5 in
either direction, so unp is p.
CATEGORICAL PROPOSITIONS AND SYLLOGISMS
Categorical propositions relate two groups, using the terms all, some,
or none. As with math when we say either side presents the truth of
math, we will reinforce the truth of logic in saying these truths
apply to whichever side we're talking about. When we create categories
like "dogs" and "animals", we will say we're creating inverse
categories "antidogs" and "antianimals" (why do we use existent
inverses here instead of un?). The categorical proposition "All dogs
are animals" is supported by a perfect inverse proposion, but as with
ext(p), we want to state something about what is going on on the other
side supporting p, not just try to imagine what a proposition with
every inverted word means. We want to talk about existent things we can
make statements about.
Hence we have:
p: All dogs are animals
unp: unall undogs unare unanimals
ext(p): All antidogs are antianimals
negation: Some dogs are not animals
Remember that inverting p is very different from negating p. Negation
is the inversion of the truth value of p, not p itself. And note that
in logic, negating p is "It is not the case that all dogs are animals,"
which means "Some dogs are not animals.". We are most interested in
ext(p), the readable statement of what's going on on the other side.
All, none, and some can be gray quantifiers, things that are basically
doing the same in either direction: when we say all, we're refering to
all of something, and with unthings our invert has the idea of unall,
which is just his way of saying "all" if those things were on our side.
Also, we've seen "to be" is a gray verb, so we can use "all" and "are"
to refer to these antithings, and say "All antidogs are antianimals."
Instead of considering the absolute value of unall, or all, we might
look at things as the union of the two splits, that all and unall are
doing the same thing in either direction, so we might rephrase p as
"All/unall dogs are/unare animals," and ext(p) as "All/unall
antidogs are/unare animals." We might even consider the union of p
and its inverse, the proposition that is going on in either or both
directions: "All/unall dogs/undogs are/unare animals/unanimals," or
p/unp.
Up until now we have only discussed propositions and their inversions
and the truth values of each. Most of logic examines inferences and
arguments, which we haven't covered and won't really cover, as there's
not much to say about them; we can apply what we've learned to
statements to all arguments and logic. For example:
(using '/' as therefore):
All dogs are animals.
All puppies are dogs.
/ All puppies are animals.
For the total inverse of this argument, we would simply invert every
single word, the unargument supporting it. Though utilizing gray areas
to talk about what this argument implies about its inversion is more
useful:
All antidogs are antianimals.
All antipuppies are antidogs.
/ All antipuppies are antianimals.
And likewise for all categorical syllogisms. There's no point to
examining all syllogisms, as there's nothing new left to say about
them. As for validity, the argument is valid if and only if the
ext(argument) is valid.
Here are venn diagrams for "all S is P," it's imlpiciative compliment
ext(All S is P), not "All S is P", and not(ext(All S is P)):
[description of picture if unavailable: Four venn diagrams, with S and
P crossing over. We have "All S is P" with the crossing out of the
section of S that does not intersect with P, and then an inverted
diagram  black  with white circles for S and P, for "All unS is
unP", another normal diagram for "Some S is not P" with an X in the S
section that doesn't overlap, and and the same invered diagram except
with unS and unP]
EXTENSION TO FURTHER AREAS OF LOGIC
As for logic analysing the complexities of longer arguments, there is
not much more to say; one can see that all this arguing relies on
unarguing, and all the things talked about rely on unthings. All
fallacies are from one point of view fallacies on both sides, and from
another, fallacies create truth on the other side. Validity and
soundness balanced by validity and soundsness from one point of view,
or validity balanced by unvalidity, where unvalidity = validity.
Propositional logic also is now practically totally covered. We have "p
and q" if and only if we have "unp and unq," from a positive truth
value perspective, and if and only if we have not(unp and unq) from a
negative truth value perspective. And if p is true and q false, making
"p and q" false, then unp and unq are true and false respectively if
we consider positive truth values (hence "unp and unq" is also
false), or if we're using negative truth values, unp is false and unq
is true, making "unp and unq" true (if the proposition "unp and
unq" is false from our posive perspective, from the negative
perspective the same statement must be true. keep in mind the absolute
value of a negative truth, would be false, what we would consider the
statement).
And so on for disjunction, implication, and equivalence, and for
informal/inductive, quantificational, modal, and fuzzy logic:
quantificational: "for all x" = "for all unx"; "there exists x such
that y" = "there exists unx such that uny", etc. For modal logic, if
necessarily p, then necessarily unp. If possibly p, then possibly
unp. For fuzzy logic, using an example of Bart Kosko's, if we eat 1/3
apple, we're fuzzy as to whether we have an apple, so we say we have
2/3 apple and 1/3 not apple, and so we're also fuzzy as to whether we
have 2/3 unapple; we say we have 2/3 unapple and 1/3 notunapple
(not ununapple; not negates, un inverts).
Fuzzy logic documents gray areas, gray logic. This is a similar thing
to the areas where we have gray verbs and nouns, where we're not sure
whether to say an unthing exists or unexists, and whether to say unp
is false or true if p is true. The idea of fuzzy logic is to be precise
about where we are gray, and hence our "confusion" of where to say word
or unword is often a very precise crossover where things get gray,
not a lack of defining our terminology properly. Yet our gray areas are
more confusing than in fuzzy logic: not being sure whether we have an
apple isn't as confusing as not being sure whether something is totally
white or black  false or true, exists or unexists.
A note on contradictions and imaginary terms: a contradiction actually
creates substance for our antiself. "p and notp" cannot be to us, it
doesn't make sense, while it makes logical sense to our invert. While
dividing a number by zero creates a sort of undefined* hole for us,
this hole is sort of a real defined positive existing object to our
invert. Likewise the square root of a negative number is a defined
thing to our inverse. This shows how some things on our side are
strange, negative concepts, showing substance on the other side.
*  [i.e. “undefined” with no hyphen; undefined is a
defined English word, different from our definition undefined (with
hypen) or inversely defined, where un in the defined word is being
used as non, and nondefined is very different from inversely defined
(if this word used un the way we use it, such as unmask, we would not
have to note much difference). It’s by chance and a little ironic
that this particular clarification I'm making just happens to involve
the use of the word define reflexively to talk about the verb itself.]
CONCLUSION
In discussing the logic of selfsustained being, I hope I have not just
shown how to think about inversions of being, but also helped bring to
light what regular logic is to begin with, and how it works and
functions, revealing more of the source of the logical shadows on the
wall in Plato's cave. Also, some of what we've gone through relates
strongly to epistemology or knowledge (how we know that p becomes
clearer when we examine unp), and much relates to our metaphysics;
we've clarified the language of the terms we can now use better to
discuss all there is.
......
