Ben wrote "In sum, does a non-aristotelian approach to logic disarm an aristotelian approach to logic?

Since "non-Aristotelian" logic is an extension and enhancement of "Aristotelian" logic, that is, "Aristotelian logic" is a subset of "non-Aristotelian logic", what do you mean by "non-Aristotelian approach" and "Aristotelian approach" to "logic"?

What Ben quoted is not non-Aristotelian, it is not Aristotelian, and it is not logic of any kind.

I would say that those who repeat such stuff mistake the familiarity of an oft repeated phrase for understanding. If you say something often enough, it becomes your "truth".

But I waste my breath, as those who do respeat such stuff are not prepared to hear.

This is an example of how time-binding can degenerate into nonsense when something is abstracted by the un-initiated and passed on in altered form. The abstractions you quote are degenerate; any semblance of real substances has been lost through over abstraction. But they are repeated so often that the un-initiated think they mean something.

I'm tired of pointing out that none of those are what Aristotle wrote.

http://www.geniebusters.org/915/04e_ex01C.html

Aristotle wrote about being qua being - existence.

Read "on coming to be and ceasing to be" here: http://classics.mit.edu/Aristotle/gener_corr.html

Better yet, read all of this http://classics.mit.edu/Aristotle/

Particularly Metaphysics, the categories, On Interpretation, Prior Analytics, Posterior Analytics, ... On second thought, forget it. One who quotes such stuff would be unlikely to get anything from reading Aristotle due to preconceived notions getting in the way.

Let "A" stand for some label.

Then if a speaker shall use the symbol "A" a second time, and "A is not A", then the second occurrance can not stand for the same label as the first. Which means we cannot ever talk about anything, because no symbol or name would ever refer to one thing; "nothing repeated" can not function as language. See The impossibility of Non-Identity Language http://xenodochy.org/gs/ah/imposs.html

Language depends on repetition and association of what is repeated consistently, at least over a period of time that covers multiple repetitions.

No repetition means no communication.

There are, of coures, those who say that we never do "communicate"; that we merely act and react. What we think is "communication" is an illusion.

Words are essentially static in their shared cultural meaning - definitions - over relative periods of time. We use the word 'milk' over and over again to indicate the same class of substance. The word gets repeated.

Even the device of indexing depends on the word being indexed understood. Communications, including learning the word in the first place, depend on being able to repeat the "same" word in different contexts to indicate the same class of substance - something relevant to our survival at low levels of abstraction.

The continued repitition of the assertaion that "A is not A" WITHOUT any indices does NOTHING to bring acceptance of general semantics to the intelligent, especially those with a decent understanding of logic and mathematics.

It's pure cult-speak. The Institute has taken down Stuart Mayper's article on the place of Aristotelian Logic in non-Aristotelian reasoning.

Let's get that seminal article back in circulation.

The relationship is one of inclusion. Non-aristotelian builds on Aristotelian; it does not "replace" it. Without the so-called "Aristotelian" core logic, the extended logics are not even possible. Core logic provides for consistency, without which anything posing as or allegged to be "reasoning" becomes incoherent.

Without the core logic, theorems in mathematics are not possible. All higher level mathematics and higher logics, including multi-valued logics, probability, etc, depend on the demonstration of consistency provided by the core binary logic - which "general semantics" parochially calls "Aristotelian".

In terms of syntax and semantics "A is not A" is inconsistent and incoherent.

We can have "A₁ is not A₂" in semantics when we speak of new waters (₂) in Heracleitus's river ("A"), but without the indexing "A is not A" is both incoherent and inconsistent. It's nonsense. But it has been quoted and re-quoted by so many seemingly authorative to the uninitiated that it is continully repeated as though it means something.

It is the "oft repeated phrase" that has become so familiar that one mistakes that familiarity for understanding.

It's like the fundamentalist who knocks on your door to "convert" or "prostelitize" to you, who, when you interrupt them, can only repeat their quotes word for word; they cannot explain their quotes.

Categories are abstract, and by definition, are mutually exclusive.

Sets, however, though also abstract, may overlap as well as be disjoint.

Consistency is a binary classification applied to sets of assertions - (axioms or postulates and "theorems" derived from them.) Such a set is consistent or it is not, But if a set of assertions is applied as a map to some territory, the relationship becomes one of semantics, and semantics is governed by a relationship called "satisfaction". Indices on the terms in the language are required in such a case. Without indices the satisfaction relation cannot be tested, validated, corroborated, or disconfirmed.

When the territory is unknown, such as in the case of empiricism, it is especially important not to confuse the semantics with the issue of consistency of the assertions.

Too many who quote "A is not A" are essentially "clueless" about the distinction between consistency and satisfaction.

http://xenodochy.org/gs/gslevels.html

Ben wrote I don't see artistotlian thinking as a subset of non-aristotelian thinking, nor do I see non-artistotelian thinking encompassing aristotelian thinking. I see non-aristotelian thinking as rejecting aristotelian thinking.

This way of thinking epitomizes anti-Aristotelianism.

Ben quoted Oliver Reiser, page 51, from Logic and General Semantics:
... It is for this reason that any abandonment of the three laws of thought would constitute a non-Aristotelian logic.

How about a more complete quote, showing exactly the wording he attributes to Aristotle as the "three laws of thought".

David,

I found it interesting that you should mention the [0,1] interval as having T,F as the endpoints. This was a topic that fascinated me in my early days of mathematics long befor I ever encountered general semantics. I worked on a generalized binary operator that had its endpoint of "1" and "0" which reduced to "OR" to "AND". To visualize the space of this operator, draw a series of hyperbola segments passing through (0,0) and (1,1}. The ".5" operator becomes the diagonal line from (0,0) to (1,1). As the operator approaches "1", the hyperbolic segment rises above y=x, and as the operator approaches "0", the hyperbolic segment falls below y=x. So all the values for all these operators fall within the unit square. At 0 or 1 the operator reduces to AND and OR on the values 0 and 1. Between them, it reduces to probability, but when the operator itself varies between 0 and 1 the results smoothy evaluate between the joint proabilty and its complement. That was the concept.
1(1,1)->1; 1(0,1)->1; 1(1,0)->1; 1(0,0)->0
0(1,1)->1; 0(0,1)->0; 0(1,0)->0; 0(0,0)->0

0(.5,.5)->.25; 1(.5,.5)->.75
.5(.5,.5)->.5.; .5(x,x)->x

Then I graduated from college, and it sat in my notebooks. I never did work out explicit mathematical formulae that combined the operator value and the the two values component values.

Thanks for reminding me of that.

The article link posted by Nora is not the article I was refering to.

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quote:

THE PLACE OF ARISTOTELIAN LOGIC IN NON-ARISTOTELIAN EVALUATING
Stuart A Mayper
(After hearing Bob Pula's paper yesterday on Korzybski's origins, I realized there was a lot more I had to do on my paper. I had to Polish it.)
There is a subtitle to this paper: EINSTEIN, KORZYBSKI, AND POPPER. But ther must be a fourth person in this cast of characters, to act as Devills Advocate. So I start with him: Walter Stuermann, who was Professor of Philosophy at the University of Tulsa, and also an Associate Editor of ETC. In 1962 he laid down a challenge to General-Semanticists. He said we must reassess our theoretic foundations, particularly our claim to have a non-aristotelian system. That claim, he said, is an oversimplification; what we need is to go back to formal logic. So the title of his article in ETC. was: "Science, Logic, and Sanity." (1)
He did not think that our usual attack on a two-valued orientation should be turned into an argument against a two-valued logic because he believed that logic is "the indisensable tool by which the meaning and power of a scientific system is brought to bear upon human behavior and the world."

He considered this tool as necessary to join together the two aspects of science, the rational [The remainder of the article has too many scan errors.] @-nd tl-ie eii irical. 73y the p rational we rilean.theoretical, ii7h-level abstractions, vihi,@@h have to z)e ex@ressed i,i universal propositions, that is, of the

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Nora, Thank you! I'm glad it's still there.

Ben, If you have any problems with http://www.time-binding.org/gsb/gsb47-mayper.pdf let's bring them out here, possibly in another topic.

Ben, your attention should be directed here, and this explains why.

Ben,

I can see that you are continuing in denial to side-track any effort to get you to look at your view.

It's part of the typical process of learning general semantics; most beginners and novices go though a stage of anti-Aristotelianism. Many never get past this stage, especially those whose assimilation of mathematics and logic leaves something to be desired.

I see no utility in continuing to try to point you to in the developmental direction when you continue to avoid, sidetrack, and deny.

I'm done here, at least until you show some evidence of being willing to open your mind.

Earlier Ben quoted S&S, chapter "On Non-Aristotelian Training," pg 469:
It appears that the A structure leads to semantic states which can be formulated as the feeling of 'allness', and that, through the 'is' of identity, it leads to the confusion of orders of abstractions. Thus, for training, the program is readily sketched: we must first eliminate the 'allness'; then we must impart this peculiar stratification of 'human knowledge' which follows from rejection of the 'is' of identity; in other words, eliminate identification. It becomes also obvious that a theory of sanity cannot be separated from a [non-A]-system.


In language we have abstract categories. The rules for using categories uses binary logic in that categories are mutually exclusive and exhaustive over the universe of discourse. This is without regard to whatever the language refers to. It is a purely syntactic constraint. At this level logic - first order predicate calculus - applies in the process of insuring consistency. Only valid rules of inference are allowed - no fallacies.

But this level is as yet unconnected to what is going on. For that we need semantics, where each word has an association with presumed "putative" things via "objects" of experience. We abstract from what is going on to an object, and we further abstract from the object to what we have learned as its name - verbal level abstraction.

In addition to categtories, we have relations - another logic/syntax level structure in which "one from column A is associated with one from column B" - like the old fashioned Chinese restaurant menus. Relations cross the boundaries of categories in different ways, depending on the relation. When we define different relations, we use the level of syntax/logic to insure any such definitions retain the consistenty of our system of categories.

However, when we bring those relations to bear using our semantics - connections between objects (and hence putative "things"), we are essentially predicting that a similar relation holds among the putative "things" in what is going on.

There are two problems with this. One is that we have two levels of abstraction involved. One is from that which is unknown and unknowable in any direct way "the event level" to our objects (which are unique to each individual) and the second is from the object to a name (of a "thing" or a relation). This variability gives us two degrees of freedom (or "error") were we able to somehow compare the two-level abstraction from one individual to another. We are not able to make such a comparison. We can compare words, and combinations of words, and for this we use the method appropriate to the level of logic. But this still leaves the semantic question of the dual-abstraction-relation between any word and any possible referent open.

In our stages of development, at an early age we are typically completely unaware of this multi-level abstraction process. We learn names as near instantaneous reactions to our objects, so well that we "identify" these levels. An early stage of general semantics teaches "the word is not the thing". Most come to understand this distinction without benefit of general semantics, so the phrase seems obvious when we hear it. But contiued practiced awareness of the distinctions is another level of skill (consciousness of abstracting).

Through our language learning, the category rules of logic tend to dominate our thinking, and through the process of identification of the first two levels of abstraction, we tend to project that binary structure onto what is going on. This fails to take into consideration the problem of semantic variation as well as the "fact" that we do not ever "know" what is actually the source of our object level abstractions.

When we become sufficiently sophisticated with language we learn that the relation between what is going on and words is at least many-to-many, and we can pick many different way of describing our experiences to others. (Politicians, salespersons, con-artists, magicians, etc., become very good at picking ways of expressing that "warm the hearts" of their chosen listeners, constituents, "victims", etc.. That "the word is not the thing" becomes second nature to these persons.)

When we become conscious of this abstraction, we learn that the language classification system, which uses absolutes, cannot be made to fit what is going on, so we learn to use it "conditionally". We learn that our language system can be viewed as a map made by us and passed from generation to generation, but we also learn that because of the variablity in the dual level abstraction just to names as well as the unknowability of the source of the abstraction and therefore the nature of the relation between any "real things" and our objects and the variability between our objects and names, that whatever may satisfy any assertions or propositions has no guarantee. In short our nice neatly categorized system of langauge only approximately fits our experiences as abstracted.

We build cognitive models from a portion of our language system that allows us to navigate our environment on the basis of acting on expectations, which most often are satisfied, but occasionally are not. When they are not, we learn to alter our language system so that we can better expect (predict) what we will subsequently experience.

Some do this better than others.
Some can be taught to do this using the system of general semantics theory and practice by developing their undersanding of many point of the model.
Mathematics, Logic, Semantics, Consciousness of abstraction, map-territory analogies, the history of science, and many more things.

General semantics deals with modeling, navigating using the model, detecting errors in the model, and revising the model, through learning the model, and learning how to use and apply each part of the model.

Binary logic and strict category structure is used to insure consistency of the model and the ability to make predictions consistent with the model. It is also the basis of translating when a prediction is not semantically satisfied into an error in the model (modus tolens [Popper]).

Without this strict binary logic, our models would be incoherend and unreliable. Unfortunately, a great many humans have no or only rudimentary skills at the logic level.

Their primary means of functioning is essentially trial and error - which now-a-days we might call genetic epistemology. All the bits and pieces of stuff we think we know get all mixed up and put together in different ways, like recombinate dna, and we try something out, discarding what does not work, and keeping what seems to work while it does work. This hodge podge of evolution, together with time-binding knowledge works amazingly well, up to a point. But it's error potential is greatly reduced when strict consistency is enforced using binary logic. Then a great many combinations are eliminated without being tried, because they don't fit the category structure. Because the category structure, as passed down through time-binding, works pretty well, the elimination of know inconsistencies from being tried makes for significantly increased efficiency.

Korzybski asks us to apply scientific methods and the formal mathematics and logic to enhance our efficiency and reduce error. He called failing to do so "un-sane".


Let's look at the quote with the above background:

It appears that the A structure leads to semantic states which can be formulated as the feeling of 'allness',
We use language with our learned category structure, so we "feel" that sense of "completeness" in a category - when we apply this to "the world" outside. [Mixing or confusing the logic category level with the semantic reference level.]

and that, through the 'is' of identity, it leads to the confusion of orders of abstractions.
Applying the category to the semantics. I'm inclined to think that early learning and development simply reflect the lack of experience at distinguishing words from referents rather than any "leading to". It's more "we haven't got there yet".

Thus, for training, the program is readily sketched: we must first eliminate the 'allness';
This now speakes about applying to the semantic reference level. The allness of the categories cannot be brought through the reference relation to the putative things in the world, because as noted above, we do not have any direct knowledge of either what is going on or how that is related to our dual-level abstraction process. In other words, we must distinguish between the category structure in our language and the semantic use of this with respect to what is going on - remember nigh always they are not the same.

then we must impart this peculiar stratification of 'human knowledge'
Distinguish between language or syntax and semantics or reference.

which follows from rejection of the 'is' of identity;
Well, it does not follow from rejecting the 'is' of identity; it follows from recognizing that there is a multi-level abstraction process between words and what they refer to, and especially that our category structure is not what it represents; that it is only an approximation (though a fairly good one based on time-binding experience).

in other words, eliminate identification.
Distinguish between levels (event and) object and verbal.

It becomes also obvious that a theory of sanity cannot be separated from a [non-A]-system.
Well, it's not obvious. Korzybsk's theory is that if we learn to distinguish carefully between the various level, keeping the logic level with its consistency process using binary logic distinct from the semantic application of the language to our environment, and use ony scientific methods of reasoning - binary logic among categories, and binary logic to relate satisfaction (semantic) failure back through to our theories as a prediction failure, and therefore a revision needed, we will efficiently and effectively deal with our model and therefore navigating the environment. He also asserts that IF we do this THEN we will be fully using our human time-binding capabilites efficiently and effectively. And he "labels" this "sanity" as distinguished from his own definition of "un-sane".

Mostly Korzybski is focusing on NOT treating the semantics of language, with its uncertain reference relation, in term of the nice neat compartmentalized language structure, and doing so by distinguishing among levels of abstraction.

This is NOT a statement against so-called Aristotelian logic. Two-valued orientation is failing to make the distinction and therefore treating the world in terms of the black and while and allness charcter of the category structre and the logic of consistency. It is a stament against using that perspsective at the level of semantics and confusing it with what is going on.

We require the category structure and binary logic to insure that the model consisting of the category structure be consistent, enabling us to make predictions capable of falsifying portions of the category structure organization and relations.

Ben, In the context of general semantics "logic" is quite specific in its use. Korzybki is speaking of VALID rules of inference that back up formal mathematics. "Logic" in use in an "argument" means a series of step using only valid rules of inference from postulates to a conclusion, which in empirical modeling means a prediction.

You are going back to complaining about your interpretation that I am not responding to your specific question. You stated that you believe that non-Aristotelian "rejects" Aristotelian. Since Aristotelian is an adjective, the missing words is reasoning, logic, laws of thought, etc.

I will tell you for the last time that Aristotelian is the core reasoning method that insures consistency of our theory and models. And it is part of non-Aristotelian reasoning. Nora has backed me up. So have others.

"Logic" is a specific and well defined way of reasoning, that in the general semantics context with Korzybski's emphasis on mathetmatics, means first order predicate calculus as evolved from Aristotle.

I don't have a "signal reaction" to your use of the term; I have a response to your denial that so-called "Aristotelian reasoning" is not a subset and a core part of non-Aristotelian reasoning. Which you stated categorically that you reject.

If your mind is made up, we're done here!

Ben wrote ... thinking in the non-aristotelian way I've outlined (i.e., non-aristotelian approach) involves rejecting the tenets of aristotelian approach.

That is another example of anti-aristotelian orientation.

Thinking with a non-Aristotelian approach means using the Aristotelian approach in the proper level, that is to insure consistency of the model and to use failed predictions to "falsify" the theory that made the prediction. Following such a failure, the theory is revised using induction, abstraction, even just plain guesswork (all essentially non-Aristotelian), but the revision must be thoroughly tested at the the theory level (syntax) - for consistency using (so-called Aristotelian) binary valued logic. Any proposed theory modifications that do not maintain consistency are rejected on the basis of the two-valued logic (Aristotelian) correctly applied. Once a revised theory is proven internally consistent, then logic (Aristotetlian) is used to make predictions. After that the predictions are tested explicitly or by use. Non-failures "corroborate" (non-Aristotelian) the theory; failures "falsify" it, and two-valued logic (Aristotelian) in the form of modus tolens carries the prediction failure back to the model. The model is no longer satisfied (model theory - initiated by Tarski) by observations (again non-Aristotelian), and needs revision again.

For the uninitiated. Words in a semantic context have a relation to "things" (objects). But in a logic level context any such semantic relations are strictly ignored. A proposition (sentence using the 'is' of identity or the 'is' of predication) is assigned a binary value "T" or "F", or "1" or "0", and the operations OR, AND, NOT, IF ... THEN ... are defined strictly in terms of these "T" & "F" or "1" & "0".

A set of propositions is consistent if no contradiction can be derived from any combination of propositions in the set. A contradiction occurs when it is possible to derive both a proposition and its negation using valid rules of inference. Clearly the set of any two propositions such that the second is the negation of the first is inconsistent.

An axiomatic system is a set of axioms or postulates (propositions) together with any formulations that can be derived from them strictly using valid rules of inference (deduction). Note particularly that such a system SAYS NOTHING about any potential semantic relations. Semantics does not enter the picture.

Model theory takes a consistent axiomatic system and attaches to it a set of objects with an assignment function that connect the words in the language (names) to the objects in such a way that the relations in the language correspond to relations among the objects. This is what Tarski developed. For those of you who have been paying attention, this develpes a "concept by postulation" intended to inform or explain our "concept by intuion" for the word "truth" in a semantic context. (But that's extra credit.)

Once we have a nice consistent theory, we can claim relations between the names in the theory, and the relations in the theory, to putative "things" in the world.

Here's an incredibly simple theory that has been talked to "death" in philosophy.

Name₁. "Swan".
Name₂. "white".
Proposition₁ "All swans are white". Stated in Quantified predicate calculus: "for all x, IF x is a swan THEN x is white". Predicate calculus gives us a way to connect individuals to the class or category.)

This is a simple conistent theory. There are no other propositions. There are no other assertions. If we assign "T" to proposition₁, we have no way to derive a contradition.
Theory is consistent.

Now, let us match this theory to the swans out there in the world. This matching ads a semantic layer. We have a set of statements (namely proposition₁) and a set of objects in the world "connected" by time-binding naming and conventional reference.

When we made this connection we sought to apply the theory. We can then apply IF x is a swan THEN x is white. So we start looking at swans.
In Europe we find a swan, and lo, it is white. This went on for a long time, and each time the theory was "satisfied" by the swan in question, because it was indeed white. Each new swan "corroborated" the theory. Note, we have not used the word "true" about the theory statement, but we can use the word "true" in its semantic or correspondence sense to the sentence swan₂₅₄ was observed to be white. Observation statements about particular observations turn out to be within the realm of Aristotelian two-valued truth values. (That is, until such time as the cultural relative invariance in the use of a name changes.)

So the theory predicts that IF you find a swan THEN it will be white. Ok, I'm going to Australia with my theory that all swans are white. When I get there I find a black swan!!!
Oops. This swan does NOT satisfy the conditional "IF x is a swan THEN x is white".
A: x is a swan
B: x is white.

Here the application of logic is a bit subtle.

We discover NOT B by empirical observation.
We have 1: A by observation.
We have 2: IF A THEN B by theory.
We have 3: NOT B by observation.
Using modus ponens on 1 and 2 we derive B.
B and NOT B are inconsistent, so 1,2,3 is inconsistent. But 1 and 3 are unasailable, because they are direct observations. Therefore 2 is "false". Taking that back to "All swans are white" which generated 2, and using modus tolens, we conclude the negation of "all swans are white" is true. But the negation of "all swans are white" is there exists a swan which is not white, and this agrees with observation 3.

All of this is perfectly developed scientific reasoning using proper Aristotelian logic in its correct place, but we do not have a two-valued relation between theory statements and "things in the world" or objects we assign to names and relations. We have two known values and one unknown value. We have known values of false (in the semantic sense of correspondence) and "possibly true" (again in the semantic sense of correspondence). We also have the unknown value "true" in the semantic sense. To quote Xenophanes, fragment 34 goes: "Even if a man should chance to say the complete truth, he cannot know that it is the truth." (circa 6^th century bce). Within the known class of possibly true we have the following sub-values: not tested, tested and corroborated to a small degree, tested extensively and highly corroborated, and these give us what we might call a conditional probability of being true, conditional in the senses of with respect to how much it has been tested. For all these we can estimate a "probability" of truth, a value somewhere between 0 and 1, which Korzybski referrs to as infinity valued "logic". (There are an infinity of possible different values between 0 and 1.)

So, in the relation between our theory and observation we can have "truth values" that range from false to true, but we can only know about those less than true. This relation is not two-valued, and we might refer to it as "non-Aristotelian". (Stuart Mayper reported that Popper denied such a characterization.)

To put this in a summary nutshell, "Aristotelian" reasoning (as evolved) applies to determining and maintaining consistency of theories, and it applies with respect to evaluating observation statements and predictions. It does not apply to the application of theories, as the relation between theory and observation is multi-valued. Theories can be proved false, in a semantic sense of correspondence, that is, that that they are not satisfied by observations. Theories can be "corroborated" in that observations to date are consistent with the thory . (Remember that observation statements may be true or false, so consistency with theory applies in this situation). But the truth of individual observations does not entail the truth of theories, because it is not possible to complete all possible observations, and this is not a binary relation, hence is "non-Aristotelian" in application.

"Aristotelian" logic, reasoning, processes, etc., are the core method of insuring we can discover that theories are not applicable, but it does not enable us to discover "true" empirical theories. For that we must have confidence level results - multi-valued, and hence non-Aristotelian - and we must live with the uncertainty of something less that known truth.

Ben wrote, Say that someone makes the argument "Miss Gypsy must die at the stake!"

This is not an argument. It is a simple assertion in deontic logic. (Logic involving "must" and other such.)

An argument must have one or more starting points, a chain of reasoning, and a conclusion. Otherwise it is simply an assertion or opinion, not an argument.

The above might be a conclusion, but the rest of the argument is missing. What is it?

The subsequent "A gypsy's a gypsy" is not shown to be connected to dying in any way. It is a pure identity statement that is unconnected to the previous statement.

Let's have an actual argument, a chain of reasoning involving one or more starting points that arrives at a concusion.

Earlier Ben wrote,
By "an aristotelian approach," I mean accepting these narratives:
- the law of identity
- the law of non-contradiction
- the law of the excluded middle

...

By "a non-aristotelian approach," I mean rejecting these narratives:
- the law of identity
- the law of non-contradiction
- the law of the excluded middle

Well, these aren't "narratives"; they are names.

Associating these laws of thought with Aristotelian and non-Aristotelian in this way represents a "flat" - non-multi-level (two-valued: accept-reject) way of thinking.

See my Laws of Thought for how to put these together in the multi-level perspective.