My daughter was counting hooks in a line, but she did something interesting. As she counted hooks, she counted the spaces between hooks, so that the next space had the same number as the previous hook. Perhaps the ordinary way to think of the space between hooks is the same—as zero—that doesn’t change the count, but she felt, quite unprompted by me, that each space was unique in its place between 1 and 2, 2 and 3, etc—That it had an identity. Normally identity in math is denoted with “=”. Expressing the identity of 1 is done by writing “1=1” or . A space is the opposite of an object, but the difference between hook 1 and hook 2 could be thought to have an identity, because it can be identified with its context between hook 1 and hook 2, for example, and could be written  . It was in Plato’s The Sophist that it was offered that not-being be the spaces or differences between beings. The inequality, or difference, between 1 and 2, , or between 2 and 3 are such spaces.

I am contrasting a definition of number as a difference with a common belief that a number is a class or likeness of members. Normally the number three is essentially a set of three members, where the members of the set could be any three things we wish to collect or associate. However, we run into difficulty when five year old children count spaces instead of objects. What do the spaces have in common, how can they be identified, except as differences between objects? And in that case, how are we to deal with the idea that three “spaces” share a likeness, when all they are is purely a difference?

The point of this is to argue that different differences (or inequalities) are different from each other. Put simply

As argued in a previous post (https://questionsarepower.org/2015/01/31/degrees-of-difference/), the difference between 1 and 2 is different from the difference between 2 and 3, even though 2-1=1 and 3-2=1, we have to keep the context of the first and second subtractions with their results.

To return to that argument briefly, observe how the difference between age 1 and 6 is much greater than the difference between age 40 and 45, even though the distance between each set is 5. Further, one difference between and circle and a square is that the square can be triangulated while the circle cannot, but this difference can be turned into a similarity between a square and a strict rectangle. This would suggest that a difference “=” a likeness. Back to our inequality above, that we could denote the first difference “2-1” with ,and the second difference “3-2” with ,. If we were to lose these contexts and allow both to be reduced to the same “,” contradictions would follow. For example if we were to lose the contexts in the inequality

by writing simply

In English, the idea that something “does not equal ”, reduces to “=”, so we replace two of the “not-equals” with one “equals”:

Now, what is  equal to?

Since we already know , it cannot be that . That would be a contradiction, but the alternative:

Is also a contradiction.

So we cannot lose our context for differences, and must be aware of the difference between differences. The symbols “” and “1”  are misleading because they erase their contexts including if “1” is a difference or identity. This means, apart from the current context-wanting misuse of the inequality sign, that difference, variation, diversity are not universal, they cannot be generalized. Instead difference is always special to its context. Difference is not a neutral term, because it always implies a discrimination between particular persons, places, or things.

Complementary to this vein, and in defense of its pedagogy, an aging Augustus De Morgan wrote an essay in which he tried to generalize the “=”. (Augustus De Morgan, “On Infinity and on the Sign of Equality,” Trans. Cambridge Phil. Soc. 1871, II:145-189.) The problem he faced was:

On generalizing and replacing 0 with x we run into some trouble. De Morgan’s philosophy and historicity of mathematics was such that he felt great mathematical progress was found in “mangled” (Pickering 2006) algebra. (Richards, 1987) The trouble was not that the steps were incorrect, but how to interpret the steps so that the symbols were about something. Understanding a generalized = is one thing, and it may be that the can be generalized as above and then interpreted so that it is still about something, but I’d contend that the nature of inequality is that is is the opposite of generalization. Generalization, like an umbrella or a set, asserts a higher likeness within its domain. To assert a set A, for example, in which each of its members had some difference or other with the other members, would be like the power set of everything. Finding a contradiction or two in this set (of course it would contain Russell’s Paradox) shouldn’t be too hard.

So I’ll do it here: the set A, whose members have some difference from all the other members of the set, must contain itself (A in A), since A, the set, is not like any other member of A. This means that the property that defines the set and that the members of A share, that of being different, is not shared by any member of the set. -><-

Read more here: https://questionsarepower.org/wp-content/uploads/2016/03/many_roads_from_the_axiom_of_completenes-2.pdf

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People often think that vagueness is bad, a kind of darkness that can never be fully dispelled, while distinction is hailed as the clarifying answer to vagueness. Here is how the reverse is also true: Vagueness is the light and distinction a darkness.

The distinction I pick is not random, but an important part of all other kinds of logical distinction—the distinction between the “if, then”: “→” and the “conclusion” symbol: ⊢. ⊢ is ambiguous, however, and can mean other things such as assertion that a proposition is true and not just being named, or to assert in a metalanguage that the following is a theorem in the object language. Used in our sense here, the good property of the “→” is “true” and the good property of the “⊢” is “sound”. The distinction goes back to Aristotle. The main point is that if we do away with this distinction, call these two symbols the same, an interesting insight can be made—that a sound argument:

A
A→B
⊢B

Can be represented without the ⊢ as follows: [A AND (A→B)] is logically equivalent to [A AND B], so that the conclusion [A AND B]→B is merely a deduction of A from [A AND B]. Allowing a vagueness between → and ⊢ reveals what logical deduction is—it is a cut from a larger whole, e.g. logical deduction is the act of drawing a distinction from the larger [A AND B]. With the introduction of the distinction between → and ⊢ this is concealed:

A
A→B
⊢B

cannot be collapsed into [A AND B]→B. As promised, vagueness reveals and distinction conceals, but not just any concealment, here we have a concealment which allows distinction to reveal, since this distinction is at the root of any further logical distinction.

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A paper about vagueness in paraconsistent logic (Weber, Z. 2010) gave a rhetorical example of the interaction between vague terms and real analysis. Imagine walking down the largest mountain in the known world. Olympus Mons on Mars has a very gentle slope or declivity, so that you can start by describing yourself as “high up” but as you walk down you become unsure if you are “high up” or “not high up”. This is graphable on an xy coordinate system with 0 at the top of the mountain and 1 at the foot of the mountain. The interval of “high up” points has a least upper bound (of x values) called “sup” and the interval of “not high up” points has a greatest lower bound called “inf.” Now we will suppose, as this is a presentation of vagueness, that “sup” is also “high up” (which is reasonable since all the points less than it are also high up) likewise “inf” is “not high up”. We encounter a contradiction in all three possibilities: If “sup”=”inf” then “sup” is both “high up” and “not high up” if “sup” > “inf” then by density of the reals “sup” > z > “inf” with z both “high up” and “not high up”, likewise if “inf” > “sup”.

Now we can put the blame on the vague term “high up” which is clearly not very technical, and go on to fantasize a perfectly precise world of mathematics that should not be sullied by vague words, but such a world is more difficult to defend than the fantasy suggests. But stripping the vague term away does not save us — it only moves the problem inside the formalism itself. First of all, mathematical equations with no tie to real world meanings are widely regarded as ambiguous, a term usually distinguished from vagueness. Ambiguous means there is more than one possible meaning or interpretation. Hesse points out that Socrates’ famous straight stick in water, the apparent bend in the stick was meant to represent falsehood. Now the bend can be represented with an equation involving the theory of refraction:

“sin(alpha)/sin(beta) = Mu”

can be interpreted in other ways besides that alpha and beta are angles and Mu is a constant about air and water— “They might, for example, be the angles between the Pole star and Mars and Venus respectively at midnight on certain given dates; why would not this be a confirmation of the formalism we have mistakenly called the wave theory of light?…” (Hesse as cited Structure of Scientific Theories Suppe 1977, p 100-101)

Now suppose I invent a word that means ambiguously “tall” and “not tall.” Similar words are found in language, for example the Thai “Krup” means “yes” but also does not mean yes. It is used because yes is too strong and seen as insulting a person’s intelligence, and “krup” rather is a polite sound indicating the speakers faith that the listener can figure it out for themselves. I could invent a word “snook” that can mean “tall” and “not tall” in different situations. Is the word ambiguous when it is applied to the one of these borderline cases when “tall” is vague? or does the ambiguity of the word capture the vagueness of the phenomena? Is this a vagueness between ambiguity and vagueness? What does that mean for ambiguity in mathematical equations?

The mathematical part of the wave theory of light, if it is to correspond to reality at all, is vague. Even if we were to abandon mathematical application to science, pure mathematics still uses words such as “continuity” “completeness” and “integral” which are vague notions. In fact, a standard text in analysis will show how mathematical definitions fail to perfectly capture the idea of continuity, with fuzziness in functions getting past the definition, and being allowed to be called technically “continuous”. Without this sparse collection of vague words, math texts would be hopelessly meaningless. The vagueness of the words continuity and completeness are in fact very important to being able to learn and understand analysis. Vagueness is not what mathematics tolerates despite itself — it is part of what mathematics thinks with.

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The following is a stroll through the interconnections between a locus of concepts: vagueness, clarity, possibility, questions, and belief. The result is an offering that vagueness belongs to possibility while clarity is closer to an opposition from possibility, which goes against some thinkers on the topic of possibility, including Descartes.

“I must confess that it makes very little difference whether we say that a stone on the bottom of the ocean, in complete darkness, is brilliant or not—that is to say, that it probably makes no difference, remembering always that that stone may be fished up to-morrow. But that there are gems at the bottom of the sea, flowers in the untraveled desert, etc., are propositions which, like that about a diamond being hard when it is not pressed, concern much more the arrangement of our language than they do the meaning of our ideas.” (C.S. Peirce ed. Houser and Kloesel 1992, p 140)

First, contrast with Kuhn:

“As the problems change, so, often does the standard that distinguishes a real scientific solution from a mere metaphysical speculation, word game, or mathematical play. The normal-scientific tradition that emerges from a scientific revolution is not only incompatible but often actually incommensurable with that which has gone before.”(Kuhn 1962, p. 103)

The “meaning of our ideas” can be shifted fundamentally, so that what was a mere mathematical play (such as in https://questionsarepower.org/2014/08/) suddenly is taken seriously. What is a joke and what is serious changes, the grave becomes light, uplifting wonderment gives way to cold sadness, and with it our world shifts.

Peirce’s quote is interesting because it brings up the relationship between possibility and realism. Diodorus defined the possible, in perhaps the first definition of its kind: “a proposition is possible if and only if it either is true or will be true.” (Mates 1953, p. 6) Under that assumption, the realist question “If a tree falls in the forest where no-one hears it, does it make a sound?” is relevant; but here we must modify the question to be more difficult. Ask: “If a tree falls into the ocean and is washed to the ocean’s bottom, is it burnable?” The two questions are more related than they may seem. In the second question we have to ponder the meaning of possibility. Are things possible even if they neither are nor will be? In the first question we are asking if something is when its being can only be inferred, not experienced. We associate sound with the falling of a tree to the point of inference, that is how we can make the realist claim that such things happen without our experiencing it. But inference depends on our definition of the possible. For Diodorus, beginning with his restriction on the possible (we may, for arguments sake, suppose that the tree at the bottom of the ocean is neither burnable nor will be burnable) took his own definition of inference from it.

“a conditional proposition is true if and only if it neither is nor was possible for the antecedent to be true and the consequent false.” (Mates 1953, p. 6) Such a definition is more strict than the material implication, so strict that it rejects the realism of a tree falling in the forest and making a sound. With this definition, both “If a tree falls in the forest, then it makes a sound” and “If this tree falls into the ocean, then it is burnable” are false, because it is possible for a tree to fall and not make a sound (maybe a small tree fell a small distance on many feet of snow?), and when I say possible I must use Diodorus’s definition, and say that “at some point either now or in the future, a tree will fall in a snowstorm and make no sound.” This means that realism is entangled in a consideration of possible futures. To say that, at the very least, being able to imagine and execute our next step in our stroll is a least part of this entanglement of realism and possibility.

Also there is the problem of genera. For realism does not exactly refer to actual objects, but to the general principle that things occur “out there” without anyone experiencing them. Stoics seemed to think that genera, such as “a (any) tree” were neither true nor false, since “…the generic Man is neither Greek, (for then all men would have been of the species Greek) nor barbarian (for the same reason).” (Mates 1953, p 35) This puts realism outside the consideration of logical truth and falsehood.

Pierce, on the other hand, uses his idea of possibility to assert his idea of truth and realism. “Our idea of anything is our idea of its sensible effects…”p132 Peirce asserts realism, but says that “the meaning of our ideas” is sensible effects. However, possibility enters again:

“Who would have said, a few years ago, that we could ever know of what substances stars are made whos light may have been longer in reaching us than the human race has existed?…And if it[scientific investigation] were to go on for a million, or a billion, or any number of years you please, how is it possible to say that there is any question which might not ultimately be solved?” (C.S. Peirce ed. Houser and Kloesel 1992, p140)

So that “Reals,” as he calls them, guide our inquiries toward them in such a way that any question is answerable, and questions that are not answerable—such as Zeno’s questions or the Liar, are merely the product of language arrangements. They are not “living doubts” that drive a real investigation towards something real.

Circling back again to Kuhn, what was a mere language game can become a serious crisis for someone: “…the new paradigm, or a sufficient hint to permit later articulation, emerges all at once, sometimes in the middle of the night, in the mind of a man deeply immersed in crisis. What the nature of that final stage is must here remain inscrutable and may be permanently so.” (Kuhn 1962, p 90)

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“House-builder, you’re seen!
You will not build a house again.
All your rafters broken,
the ridge pole destroyed,
gone to the Unformed, the mind
has come to the end of craving.”

-Siddhārtha Gautama (the founder of Buddhism), upon his reaching enlightenment (Dhammapada)

It was speculated by Thanissaro Bikkhu that the house meant selfhood or perhaps entity-hood in the commentary of the Dhammapada.

I would propose a model for logic that is a house. Some logical structures are immense. The light that passes through a window would be Truth, the laws that light follows as it interacts with the building would be the laws of logic, the specific form of this particular building would be the logical statements, determining the way truth(light) moves through the logical structure. The trouble is completing the logical elements- what is falsehood? Obviously it is darkness, but the building would have to have no qualities except its form- no colors, no features, just featureless glass mirrors, otherwise truth would fade as it interacts with opaque surfaces- making truth and falsehood mingle. If the walls are perfect mirrors that propagate the light perfectly, a false space would have to be totally cut off from the light. Hypotheticals would be doors, sometimes open, sometimes shut. The only danger of falling into darkness would be entering through a door and closing it, completely cutting yourself off.

The theory that comes to mind is Anaximander’s, who thought the sun was just a hole in the cosmos, where light could enter from outside the Universe. And why is this ideal of logic impossible in the real world? There are no perfect mirrors, matter has color that absorbs light, making it an intermediate between truth and falsehood. When logic from true principles is applied to real things, interacting with matter, the truth will fade into darkness as the logical statements progress, regardless of how perfectly the laws of logic are followed. If the world of logic were to be perfect, the truth could not originate from our world, or else light that is reflected back out the window of our house would fall, logically, onto ambiguous matter. Thus, passing out the window must lead to a world that looked mostly the same as the building of mirrors.

With the modern conception that words can provide totally transparent access to an object, matter would be the only medium between truth and falsehood, but words simply aren’t transparent. They grow out of metaphors, (as argued in the essay linked in my first post) the word “be” grew out of a Proto-Indo European root which also meant grow- so that someone who is aware of the ancestry of words would have resurrected the feeling of metaphor in the word “be”, coloring the word, giving it a connection that is warranted because “be” would not be what it is now without a fathering metaphor: “being is growing”.

And the design or form of this fun-house of mirrors? Would it carry nameable concepts with it, concepts one would come to know or feel by living there? It would if it had any architectural design. How is this different from allowing a word, or a sign for an idea or feeling, into our logic?

The house of logic cannot allow matter, words, or form, except in a part of the house that is totally dark and without doors- they can be allowed into the part sectioned off as unconditionally false. Otherwise we are allowing degrees of truth, qualifications of truth, and a co-mingling of truth and falsehood.

The focus of this blog (expressed in the previous post) has changed to looking for systems of truth that gradually and naturally falsify themselves. What if we allowed matter in our house, and accepted gradations of truth? How could Aristotelian logic be modified so that each “step” in a logical progression reduced the amount of truth it propagated? The goal would initially be a logic that is calculable, so while we could take our lessons on how the logical system would be set up from how light interacts with matter, the resulting system would not be realistic initially. Following the logical system leads you out of the logical system, however, since the logical laws are not perfect propagators of truth. The logic I am formulating here, while not realistic, leads into a real world.

Most of this blog seems to be about what I call “mystical” thinking which is offered as anti-logic or contradictory. It only seems that way. While I make claims like stupid is smart, raw is cooked, warmth is cold and any number of other kinds of nonsense, I don’t actually believe these things. The goal is to understand the failure of ideation, and so this post is a Buddhist disclaimer. Like a human body, ideas are beautiful in some ways but also stink in some places and have disgusting aspects. There is no escape from this problem except to strive away from ideation. I show paradox in the most eternal aspect of our knowledge- mathematics. It is a tremendous egoism to believe in mathematics in spite of these paradoxes. I do not think we should accept the failure of our minds and efforts to grasp the truth, but rather to reject paradox, mathematics and logic in its present state as a way to understand truth.

I would like to begin a new direction for this blog, guided by questions like “What conception of number will lead you naturally to reject the conception of number?” “How to make number imperfect in a gradual, pedagogical way?” Like the dying sound of a gong, good ideas lead you to peace of mind.

Numbers seem to march on towards infinity in a regular and perfect progression, like a straight highway to the horizon. However, the size of the highway changes as the eye looks into the distance, the distant numbers are different from the near ones. It is very much related to the relative difference between large numbers and small numbers- so that the difference between 1 and 2 is relatively larger than the difference between a thousand and 1,001. This aspect of number should not be concealed, but suggested rhetorically at every turn. The idea that numbers progress evenly and regularly is an abstraction that forgets the “size” or “numerousness” of the number. Without this context of the size of each number in the progression, the progression eventually loses cognizance of its subject – number. Eventually what the progression is about can barely be called number at all. The concept of the natural numbers, its progression of “always one more” does not live forever, but degrades and loses its meaning. Number theory is mortal.

Any reference to a self is a sticky situation in logic. Logic is an attempt to understand the laws of the world. Once laws are understood, they can be used: control over the world increases. It is often believed that when someone turns to logic or reason they gain a dispassionate, maybe even objective point of view. More effective or powerful decisions can be made.

But this rosey picture falls apart when the self enters into the equation. Is logic how one controls oneself? If so who is being controlled and who the controller? It is the problem of inventing a logical law that you decide to follow. If you can decide not to follow it, is your logical law really true? And if you can’t decide not to follow it, you are not the controller, but the controlled, and you cannot say you have control over yourself in that case.

Control over yourself, as Dr. Russell would have it (see first post), is a mystical desire- it breaks logic because it is a self-contradictory desire- it requires the freedom to control oneself and restraint not to control oneself.

People who follow logic and exclude mysticism must ignore themselves to use logic consistently. They may feel they have more control over the external world, but if logic is turned inwards on the self it begs the question: “How can I have control over external things if I don’t have control over myself?” If they decide to control themselves first, then they have to do away with always following logic.

In economic models the notion of a rational agent calculates highest self-gain and acts accordingly, but this person, who probably is assumed to use logical reasoning for their calculations, cannot control themselves to follow their own rules- and if they did, the economy would suffer and different models and agents would be necessary. This is why the idea of anarchy is not actually opposed to capitalism- it is simply the logical conclusion of rational agents trying to think about how to govern themselves.

If there is any “self”, then the logical forms that are agreeable to scientists would collapse for the same reasons. Either there are “selves” who, logically, have the power to break and reshape any physical law of matter they want, or there are no selves and logic can’t about anything- it must remain empty of any subject and ultimately irrelevant.

It comes down to a paradox we are all comfortable with- that two things can be both alike and different. Its actually a contradiction, but because we are comfortable with it, we call it a paradox. The Law of the Excluded Middle dictates that either p or not-p is true, not both. The question is, when finding something in the world, say an apple, and calling it “p”, where is “not-p”? We could pick up an orange and say this is not-p, but both apples and oranges are fruit. Since “both are fruit” is true, there is a sense that the Law of Excluded Middle fails to be true, so we must keep looking for “not-p”. We could take the compliment of space that the apple takes up and call that “not-p” but the border, the skin of the apple, is a vague grey area where the Law of Excluded Middle fails to be true. The dimension of time adds to the problem. Eventually the apple will disintegrate or be eaten, turning into millions of other things. The apple shares its physical material and energy with the world. Since the apple shares a very real likeness with the world, you cannot claim that “not-p”, a thing that is totally different from the apple, exists. The Law of the Excluded Middle is never true, except perhaps in a relative sense.[1]

Scientists assume that the Law of the Excluded Middle is true, and then go searching for it in matter. The search for the atoms or elements- the things that are not composite and are utterly different (p or not-p) is a continual discovery of how things are composed of each other. The rhetoric about atoms and elements usually conceal this conclusion. A mild example is on http://www.fnal.gov/pub/science/inquiring/matter/ “Particles called quarks and leptons seem to be the fundamental building blocks – but perhaps there is something even smaller.”

The invitation is to either accept the smallest particle is discovered, or look for the next smaller thing. The smaller than smaller things, or that there will always be a “next smaller thing”, (which would mean matter is ultimately composite, both alike and different) is not suggested, even though we keep finding a “next smaller thing”.

Everyone knows that two things can be both alike and different, you won’t be called stupid for thinking it. But if you look at two lines, one clearly shorter than the other, and call the longer line the shorter, some people will not respect that belief. The idea that the longer line is the shorter is no less a contradiction than the idea that two things are both alike and different. The question of intelligence becomes a question of which paradoxes or contradictions happen to be fashionable.

Where do we go from here? Read on to find how questions can replace the void left by disbelieving in Aristotelian logic.

[1] Thinking of “p” as “being” and “not-p” as “not-being” has its own problems discussed, along with everything in this post, in Plato’s dialogue “The Sophist”.

THEAETETUS: How, Stranger, can I describe an image except as something fashioned in the likeness of the true?

STRANGER: And do you mean this something to be some other true thing, or what do you mean?

THEAETETUS: Certainly not another true thing, but only a resemblance.

STRANGER: And you mean by true that which really is?

THEAETETUS: Yes.

STRANGER: And the not true is that which is the opposite of the true?

THEAETETUS: Exactly.

STRANGER: A resemblance, then, is not really real, if, as you say, not true?

THEAETETUS: Nay, but it is in a certain sense.

STRANGER: You mean to say, not in a true sense?

THEAETETUS: Yes; it is in reality only an image.

STRANGER: Then what we call an image is in reality really unreal.

THEAETETUS: In what a strange complication of being and not-being we are involved!

STRANGER: Strange! I should think so. See how, by his reciprocation of opposites, the many-headed Sophist has compelled us, quite against our will, to admit the existence of not-being.

http://www.gutenberg.org/files/1735/1735-h/1735-h.htm

Lets look at what a “valid” argument is[1]:

p | q | p then q | p and (p then q) | (p and (p then q)] then q
—|—-|—————|—————————|————————–
T | T |     T        |            T         |             T
T | F |     F        |            F         |             T
F | T |     T        |            F         |             T
F | F |     T        |            F         |             T

What is really satisfying is that I can complete this without learning, I just calculate truth tables. Its so easy (once you know the rules), that we can get a material computer to do it. But you know its strange, actually the fourth column of the truth table: p AND (p THEN q) is the same as just “p AND q”. Note that p AND q have the same truth values as p AND ( p THEN q) given the same truth values of p, q. (Compare truth values of 4th column above to 3rd column below)

p | q | p AND q
—|—-|———–
T | T |     T
T | F |     F
F | T |     F
F | F |     F

The idea of a valid argument is the same as:

Know: p AND q

Therefore: q.

We already knew q from (p AND q), however. All we did was take out our mental knife (or pen) and cut p out. Thats why its called “deduction”, you Take Away p from (p AND q), get q.

For example, I can teach my daughter “if you touch the hot pan then you get burned”, or I can teach her “Touch the hot pan and you will get burned”. The difference is subtle and purely rhetorical. My daughter would learn the same skill of not getting burned without the “if, then”.

So why do we do all this with our first truth table, calling a valid argument “p AND (p THEN q)” instead of just calling it “(p AND q)”? The “if, then” is reductive; it focuses the person on the result, cutting out the “fathering” premise. Interestingly, the etymology of the word “robot” has the same root as the word “orphan”. The “and” is inclusive. Because the idea of a “valid argument” persuades us that we are making “progress”. Eg. “this, then this, then this, …” The valid argument confuses us from seeing the simplicity of what we are actually doing. It is a rhetorical move. The foundations of logic are rhetorical in nature. Rhetoric is prior to logic. Saying “We know p and q, and so we know q” does not sound like progress. Logic- is it the right way to think? What is thought? The philosopher Wittgenstein decided this question could not be answered.  “Thought this peculiar being” The reason is if you “really” answer this question your thoughts become a servant of your answer, which is simply mind-control.

An attitude of skeptical uncertainty, or simply by asking a lot of questions, we can avoid and defend against overusing logic and debilitating our minds.

“Don’t go by reports, by legends, by traditions, by scripture, by logical conjecture, by inference, by analogies, by agreement through pondering views, by probability, or by the thought, “This contemplative is our teacher.””

-Kalama Sutta, translated from the Pali by Thanissaro Bhikkhu

Questions are power, what do I mean? What are questions? Power is notoriously difficult to define. The idea that “knowledge is power” or “power is knowledge” leads to a very difficult discussion about what is knowable and definable. Claim: “Questions always involve an intention towards the unknown.” If you already know the answer, perhaps the unknown is whether or not someone else knows the answer. But perhaps you ask yourself something to make yourself more aware of what you already know. So it is unknown whether questions involve an unknown. It is also problematic to describe the question as an “intention.”

“Every mental phenomenon includes something as object within itself, although they do not all do so in the same way. In presentation something is presented, in judgment something is affirmed or denied, in love loved, in hate hated, in desire desired and so on. This intentional in-existence is characteristic exclusively of mental phenomena. No physical phenomenon exhibits anything like it. We could, therefore, define mental phenomena by saying that they are those phenomena which contain an object intentionally within themselves.” (Franz Brentano)

“In-existence” is referring to the object’s existence within an intention. If I am curious about a neutron star, the neutron star has an existence within my curiosity- just as I have an existence within my curiosity. What else has an existence within my curiosity? Now, the power of this question is its ability to easily indicate as its object just about anything I’ve ever directed my senses and mind toward, including my mind itself. I have stepped outside my mind and self with this question and asked about my asking, and it was easy enough to ask. The trouble is now I still don’t know where my mind or self stops and the material world begins, since it seems I can easily push that limit to wherever I want. There are interesting and relevant claims in Buddhism about meditation. In meditation Buddhists have described a state of “infinite consciousness” which seems to have the same intention as my question which has as its object all my previous consciousness- now, is that an object? Apparently through meditation it is possible that one “enters and abides in the base of neither-perception nor-non-perception.” (Sallekha Sutta: Sutta 8 Effacement, Majjhima Nikaya p. 125 trans. Bhikkhu Nanamol and Bhikkhu Bhodi), which is a mental phenomenon that does not need an object anymore.

The question shares a likeness with power in that it is also very difficult to define.

[1] The truth table of p AND (p THEN q) THEN q is the valid argument. “q” is the conclusion “p” and “p then q” are the propositions. The notion of a valid argument must be translated into basic logic, otherwise, according to Russell’s theory of types, valid arguments must be irrelevant to logic itself since a valid argument is about logic. Nonetheless, a “valid argument” is usually introduced with any beginning set of lectures on logic, but not this way.

Logic depends on the law of excluded middle, but to exclude the “middle” we have to have an understanding of the space where we operate. Is it two-dimensional? three? more? How many variables are there in all of reality? How many verbal variables? How many essential variables? These questions can be used to determine the space where we make our division/ create our opposition. It is like Derrida and Saussure’s assertion that words (such as “p” and “~p”) depend on the whole sign-system from which the words are derived. Saying logic is the calculation of distinction might suggest that it is universal, since distinction is commonly thought of as universal, whether it suggests the identity of a thing, or the world a thing is cut out of in order to identify it. The problem is that identities are not distinguished from the entire world (universe is a rather presumptuous word for the world, whatever that is), but from a certain frame of reference(visually) or sign-system(in language). Because of this logic is not universal, and it is not essential. Logic is mainly a way to create instructions that people can understand and follow. It is not the way the world works, it is not the way our mind works, it is merely a standard form for instructions that can be communicated because it is standard.

Logic is not a form of discovery unless you break the rules in “logical play,”- you must already assume your frame of reference before you start calculations- and that assumption determines what can be identified and how. Ideas can be more difficult to learn and understand when they are formalized into logic. The act of cutting your frame of reference out “the world” is itself a kind of distinction. The question operation is a way of expressing the necessity to think outside of a logic and its frame of reference- to expand our “operating table” to something larger. This necessity is clear when someone is caught up in a paradox.