Normative Slots

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The normative quadrant of The 8 x 8 Grid. Its lower left corner is closest to the origin.

Syntactic Slot

See: Syntactic Level

Proposition Slot

Also known as THINK

Propositions are semantically potentially meaningful syntactically correct expressions of language.

Recursion Slot

Also known as CHOICE

Recursive patterns involve syntactic entities that refer to themselves. Perhaps the most archetypal instance of recursion within the context of computation is a function that calls itself. The actual quality of such patterns is syntactic but within them there is a potential for the object of recursion to produce information regarding itself. The production of such information is necessary for understanding taking place within a normative context. A formal system cannot express or include information about itself without some of recursion taking place.

Language Slot

Also known as WHY?

Language patterns refer to axiomatic definitions of how to construct valid propositions.

Redundant Slot

Also known as ALWAYS

Redundant patterns refer to instances of normative syntactic conventions obscuring meaning to an unnecessary degree. More advanced syntactic conventions would express the same meaning in a more elegant way that consumes less cognitive resources to process. Algebraic expressions are simplified in order to remove redundant patterns. Computer programs are optimized in order to avoid consuming CPU processing power for redundant tasks.

It might be worthwhile to note that mere brevity doesn't always minimize redundancy. For example, sentential logic can be axiomatized using only a single axiom and a single rule of inference, but in practice this axiomatization is more difficult to use than the one produced by Jan Łukasiewicz. Analoguously, computers process compressed files slower than files that haven't been compressed even though the compressed files are smaller. Therefore, even brevity may be redundant.

Semantic Slot

See: Semantic Level

Functional Slot

Also known as REASON

Functional patterns are sets of relations between inputs and outputs.

Theoretic Slot

Also known as WOULD

The theoretic slot includes patterns that are used to "close" a language, that is, to declare certain statements invalid. Languages only contain instructions for constructing valid statements of a language. Theories define invalid statemets. For example, it is a theoretic pattern that -1 is not a natural number.

Erroneous Slot

Also known as NEVER

Erroneous patterns involve unwanted changes in the data that is being manipulated. Redundance decreases efficiency but errors may prevent the task at hand from being accomplished correctly. Errors vary in magnitude and more complex tasks may have a greater chance of error. An example of an erroneous pattern would be 1 + 1 = 5. Sometimes an error only partially prevents the accomplishment of task instead of altogether preventing it.

Non Sequitur Slot

Also known as DOUBT

Non sequitur or jumping to conclusions patterns involve a failure of inference. Even though the premises and the conclusion would be true the inference was erroneous. Ie. even though a person manipulates a proposition correctly he does so by accident instead of understanding how the operators within the proposition are supposed to work. Elimination of jumping to conclusions patterns is a reason why students in school are required to write down every step of a calculation in a math exam. In a more formal context, non sequitur patterns involve mistaken use of an inference rule while manipulating propositions.

Metatheoretic Slot

See: Metatheoretic Level

Proving Slot

Also known as TRUTH

A normative statement is proved when it has been demonstrated to be the consequence of axioms that were already implicitly contained within the statement. Proving patterns explicate this implicit containment. Proved statements derive their truth value from the truth value of the axioms. But it is possible for a person to be able to prove Gödel's incompleteness theorems without understanding the limitations they impose on what formal systems can accomplish. This is why the actual value of proving patterns is less than the actual value of understanding patterns: it's possible to make a proof that implicates something important so that the one making the proof, however, doesn't notice said important implication.

Delusional Slot

Also known as MAD

The delusional slot includes patterns that appear to reflect deep normative truths, at least for someone, but have no more wisdom in them than an arbitrary syntactic convention. When contrasted with erroneous patterns, delusional patterns involve errors that partially prevent the accomplishment of a task so that the one trying to accomplish said task doesn't notice he failed to accomplish the task because of the error.

Delusional patterns include "insanity" or "madness", such as believing falsehoods to be true and truths to be false so that the result is dangerous. Mentally ill people can torment other people. They may believe that they need to kill someone, burn something down or injure themselves. They may believe they need to die. It's difficult to judge instances of such behavior from a logical or mathematical perspective but generally speaking some instances of madness are madder than others. Whatever the case, they qualify as delusional if they completely prevent the person from living a normal and productive life. Acute psychosis is a delusional pattern.

From a spiritual perspective we may call psychoses some kind of "hard enlightenment" but that notion is impervious to the rational and dogmatically assertive mindset. Even if a priest could assign some meaning to a person's psychotic beliefs they would be the product of an associative and contemplative mindset and intended to be merely useful in the situation at hand instead of manifesting the immutable static truth of a theorem. At least this is the case unless the priest happens to express an exceptionally good idea.

Obsessing Slot

Also known as MUST

Obsessing patterns are such although they don't obstruct the elementary syntatic-level processing of reality, they manifest as misguidance of such processing. They don't implicate an existence of a flaw in the interpretation of reality that completely prevents normal functioning of individual. They don't necessarily involve a conspicuous inability to perform tasks or conform to expectations in a manner that other people justifiably require.

It doesn't necessarily require special training or particular character to interact with obsessed people but their obsessions manifest so that they find meaning in things that appear meaningless to others so that others have a good reason to deem them as meaningless. As will all identifications, there are and will always be differences of opinion whether a particular activity is meaningless or not but this only makes the AMOQ useful. People already have these kind of problems but the AMOQ makes it possible to input them into a mathematical model that could be the theory underlying a future artificial intelligence.

Confusing Slot

Also known as LIE

Confusing patterns are potentially less immoral than obsessing patterns because whereas the obsession squanders mental resources, confusion could at least potentially be created for a good cause. However, unfortunately, the negative consequences of confusion are potentially great, though not as great as those of obsession. The ability to get confused or confuse others implies an ability to discern important activities from unimportant ones in such a way that no room is left for obsession, which inherently is a consistent but partial failure to enforce such a separation. Madness, on the other hand, would be a consistent and total failure to separate the important from the unimportant.

Analogic Slot

See: Analogic Level

See Also