squish7.com /logic
P8metafractalscolormath
logic.....ethicsknow
brain
....
....
SYMMETRIC BEING: Logic & Language

LINKS  Wiki Logic  .  Fuzzy Logic  .  Amazon Logic Textbooks  .  Syllogisms

"We [as philosophers] demand rigidly defined areas of doubt and uncertainty."
-Douglas Adams


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 re-analyze 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 un-thought or un-spoken by our invert; when we say p, we necessarily imply un-p (not "not p"); that is, p if and only if un-p; 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 self-reliant and self-dependent, but I've not discussed this possible sea of connections in this thesis yet).

Now the existence of un-p 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 un-frog un-lept? (And is saying that the un-frog un-lept 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 un-frog un-lept?

It is odd that from one point of view, if p is true then un-p is false, and from another, p and un-p are true and false together (p if and only if un-p), these are two opposite views. This grayness arises much in the metaphysics, logic, and epistemology of self-sustained 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 un-proposition that un-2 un-plus un-3 un-equals un-5, 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 un-2, un-3, un-5, 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 un-barking, going on. We can say dog/un-dog, 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 un-unification concept of two things un-going 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 un-hot (hot's inverse)? Between black, and un-white? Cold and un-hot (and black and un-white) are actually essentially the same concept. The only difference is how we refer to what it is and what it applies to. In saying un-color 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 un-black, 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 un-ball is (respectively) un-black or un-white, but we could just as well call the un-ball white or black (as I usually use colors to refer to both sides because we're more familiar with them as such than saying un-color). A man and un-man 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 "un-existent opposite" or "un-existent 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 un-ball 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 un-existent compliment of word. Hence un-white 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, un-white (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 un-black (basically also white, the thing supporting its existence) is black's negative or un-existent 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 un-one, 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 un-existent compliment. We can express these numbers or any opposites on the following chart:

logic square

[image description: black, white, un-black, and un-white, in four corners, with lines illustrating which are same-side 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 anti-chair, 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 un-thing. And then the only way of referring to the existent compliment of chair will be to say un-anti-chair.

When I first started to create terminology for inverse being, I developed these existent and pure inverses: The anti-dog (an existent thing) is, and the un-dog (subtractive tear) un-is. (We may or may not use un-the or anti-the, 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 un-words. When we use language we will almost always use "the", as we're more familiar with it, and only use un-the when we want to create a totally opposed proposition: un-the un-dog un-is). 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 un-dog is" would be positive or existent, and "The un-dog un-is" 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 un-thing and anti-thing 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-. (Un-blue is orange (requiring blue as well, so un-blue is orange and blue), and non-blue 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 un-mask (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 un-mask the negative inverse. Unmask referring more to an action going on in being, un-mask 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 un-dog is, or un-is), we only have a decision to make when we're using what we'll call a gray-area verb. Some example of gray-area 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 un-existence (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 un-exist -- 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/un-existence (either or both, we don't really care which) all over the place.

Often, the dog and un-dog 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 un-thing, a transition and action that is happening the whole time to both beings. If we say the dog barked and un-dog un-barked, we might say they are both doing something. Though bark itself is not a gray-area verb. To un-bark is to do something completely opposed to barking, as white is opposed to black. Remember even gray-area verbs can seem totally contradictory. The only difference between gray-verbs and non-gray verbs is that the contradiction of verb and un-verb can at the same time be the same thing. Addition vs subtraction vs two additions or two subtractions.

We can also have gray-area nouns like thing, color, being, existence, soul. We might say that all life are souls. That all things and un-things are still things, that the un-dog 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 un-black a color or un-color, it's still the same as white. Colors themselves are very opposed: black to white, red to green. The only colors that are gray-area 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 anti-p (if we decide to refer to this inverted thing in a positve way, the positive inverse), or un-p (the negative inverse, basically the same thing). This inverse proposition is basically the same proposition with every word inverted. So anti-p would be "un-the un-clown un-juggled," or we might say un-p un-is 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 un-p with every word inverted, we can un-invert those words that are gray-area 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 gray-area verb is the word "The." (We can say the tree or the un-tree interchangably). Hence ext(p) would be "The anti-clown anti-juggled."

Consider p "This proposition refers to itself." We have anti-p or un-p "un-this un-proposition un-refers un-to un-itself." Anti-p and un-p 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 un-words that could basically refer to either side and use their absolute values. So ext(p) would be "Anti-p anti-refers to itself." Note this ext(p) is not anti-p. It does not match its form: a negative for every exact word. Even if we said "This anti-proposition anti-refers to itself," we're not really stating the anti-proposition. The "anti-proposition" is that proposition which fully supports proposition, allowing it, without which it could not be thought or spoken."This anti-proposition anti-refers to itself" does not support p. Anti-proposition is our existent, positive word for the totally inverted thing; we are calling anti-p a thing, rather than un-thing, and can make new propositions about anti-thing, including the one thing p implies in the requirement of anti-p.

Note that if we did not give our statement the name "p," we would not have a convenient subject, anti-p, to talk about. Usually we can just invert the subject: ext(The bird flew) is "The anti-bird anti-flew." But the "this" complicates things. In stating "this proposition," we cannot state "this anti-proposition" in ext(p), because what we're stating is not the anti-proposition. If we do not name p, then we would have to say "The anti-proposition to the proposition that we are talking about, anti-refers 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: "un-I un-think, un-therefore un-I un-am." To make this more intelligiable, we'll consider ext(p): "I un-think, therefore I un-am." We've un-negated 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 un-am," 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 un-am": 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 un-self." We're negating the existence of something, and if we consider that self and un-self 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 un-p (or anti-p). Remember that there is a fuzzy area whether to call un-p true or false if p is true. If p is "there is elephant", is the inverse supporting it also true, that there also un-exists an un-elephant? Or if p is true, is un-p inversely true, i.e. false? This is not to say that the existence of the un-elephant 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 un-statement 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 un-elephant, vs if the elephant exists is true, then we consider the un-existence of the un-elephant 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 un-p as + and the negative as -, we have the truth table relating negation, inversion, and implication of inversion (ext(p)).

Truth Table 1

[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), un-p, anti-p, etc]

Remember anti-p and un-p are almost the same thing, so we can replace any un-p with anti-p above. We might instead have defined anti-p to be the positive truth value (p and anti-p are true together) and un-p to be the negative, if this were the case, we'd have anti-p T F and un-p F T. Secondly note the matching of the truth value of ext(p) to un-p+. 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 un-p- (the symbol for absolute value is "|x|" ), that in a way, saying an un-p 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 un-p 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 |un-p| 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 re-inforce 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 "anti-dogs" and "anti-animals" (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
un-p: un-all un-dogs un-are un-animals
ext(p): All anti-dogs are anti-animals
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 un-things our invert has the idea of un-all, 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 anti-things, and say "All anti-dogs are anti-animals."

Instead of considering the absolute value of un-all, or all, we might look at things as the union of the two splits, that all and un-all are doing the same thing in either direction, so we might rephrase p as "All/un-all dogs are/un-are animals," and ext(p) as "All/un-all anti-dogs are/un-are animals." We might even consider the union of p and its inverse, the proposition that is going on in either or both directions: "All/un-all dogs/un-dogs are/un-are animals/un-animals," or p/un-p.


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 un-argument supporting it. Though utilizing gray areas to talk about what this argument implies about its inversion is more useful:

All anti-dogs are anti-animals.
All anti-puppies are anti-dogs.
/ All anti-puppies are anti-animals.

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 un-S is un-P", 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 un-S and un-P]


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 un-arguing, and all the things talked about rely on un-things. 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 un-validity, where |un-validity| = validity.

Propositional logic also is now practically totally covered. We have "p and q" if and only if we have "un-p and un-q," from a positive truth value perspective, and if and only if we have not(un-p and un-q) from a negative truth value perspective. And if p is true and q false, making "p and q" false, then un-p and un-q are true and false respectively if we consider positive truth values (hence "un-p and un-q" is also false), or if we're using negative truth values, un-p is false and un-q is true, making "un-p and un-q" true (if the proposition "un-p and un-q" 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 un-x"; "there exists x such that y" = "there exists un-x such that un-y", etc. For modal logic, if necessarily p, then necessarily un-p. If possibly p, then possibly un-p. 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 un-apple; we say we have 2/3 un-apple and 1/3 not-un-apple (not un-un-apple; 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 un-thing exists or un-exists, and whether to say un-p 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 un-word is often a very precise cross-over 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 un-exists.

A note on contradictions and imaginary terms: a contradiction actually creates substance for our anti-self. "p and not-p" 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 un-defined (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 self-sustained 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 un-p), and much relates to our metaphysics; we've clarified the language of the terms we can now use better to discuss all there is.

......



P8|meta|fractals|color|math|logic|ethics|know|brain