Analytic Metaphysics of Quality

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The Analytic Metaphysics of Quality was originally created by me in order to resolve issues in the Canonic Metaphysics of Quality. By far the greatest of the aforementioned problems is the one involving subjective quality and objective quality. The second greatest problem is whether the Metaphysics of Quality is an intellectual pattern but it was already solved. The issue regarding empiricism and abstract symbol manipulation is interesting and important but does not threaten the integrity of the Metaphysics of Quality as much as the one about subjectivity and objectivity in Lila.

Nonrelativizable Qualities

Includes the Dynamic–static-split in Lila and the romantic–classical-split in Zen and the Art of Motorcycle Maintenance.

The romantic–classical-split is the primary split of Zen and the Art of Motorcycle Maintenance whereas Lila's primary split is the Dynamic–static-split. Dynamic Quality is the complement of static quality within Quality and static quality is the complement of Dynamic Quality within Quality. Classical quality is the complement of romantic quality within static quality whereas romantic quality is the complement of classical quality within static quality.


Static quality is the same thing as relativizable quality. Nonrelativizable quality could perhaps also be called the domain of phenomena or at least processes.

The nonrelativizable qualities are thus romantic quality and Dynamic Quality. These are troublesome for the analytic mind and the troubles may have inspired Carnap's article Elimination of Metaphysics Through Logical Analysis of Language. However, they are the only way to solve the symbol grounding problem within the Metaphysics of Quality. Without romantic quality it would be impossible to use senses to verify the Metaphysics of Quality and without Dynamic Quality the Metaphysics of Quality could not have been invented. For an example of the necessity of nonrelativizable quality consider the following.

In Aristotelian physics “force” was defined as something that causes movement. But Galileo Galilei observed that cannonballs continue to move even though the explosion, that sent them to motion, no longer effects a force to them. In order to resolve this contradiction between theory and observation Galileo formed three hypotheses which are described in F. S. C. Northrop’s 1947 work Logic of the Sciences & Humanities, which was recommended to me by Dr. Anthony McWatt. These hypotheses are:

  1. Force is proportional to the weight of the body upon which the force acts.
  2. Force is proportional to the distance through which the body moves when the force acts.
  3. Force is proportional to the time during which the force acts.

After investigations Galileo ended up with the third hypothesis, and upon doing so he created an important part of the foundations of modern physics. In modern physics “force” is something that causes changes in acceleration and velocity but is not a necessary condition for sustaining movement.

However, when Galileo was conducting these investigations, the notion of “force” was at flux. Galileo had to place the pattern “force” into a nonrelativizable epistemology for a while in order to create a new rational theory about it. For example, Galileo maybe had to think the sentence: “Force causes changes in velocity and acceleration, but is not a requirement of sustaining movement.” When he was mid-way of thinking this sentence, it looked like this: “Force causes changes in velocity… ” At this moment, which maybe lasted only for a fraction of a second, the pattern “force” was obviously nonrelativizable, because Galileo had not yet finished the new rational theory about “force” but was in the process of constructing it.

Despite their creative potential, nonrelativizable patterns can also be harmful or an indicator of a problem. In the field of philosophy the problem of induction has been studied for centuries. The problem of induction is about how to justify arguments that are based on evidence that is logically insufficient to justify the argument. I will not describe the problem in detail for now but will focus on one aspect of it.

The problem of induction has been broken down to constituent problems, one of which could be called the problem of relevance. In the problem of relevance we suppose our original objective is to arrive at ”true and/or rational predictions”, and we are to deem the conclusions of inductive arguments true if they are relevant for achieving that objective, and false if they are not.

No proper definition of relevance has ever been presented. Jüri Eintalu states so in his 2001 doctoral dissertation The Problem of Induction: The Presuppositions Revisited. Yet the problem of induction is approached as if an essential part of the problem is that relevance should be defined. The concept of relevance is also frequently used and as it has no known proper definition this usage is nonrelativizable. Is this an error or not?

The question sheds light on what is the purpose of academic philosophy. If we use a nonrelativizable pattern in the definition of the problem of induction and then attempt to solve said problem as if we rationally knew what we’re trying to do we are making a metaphysical error. We would not rationally know what problem we are trying to solve. Problems that are subjected to academic work are usually not misclassified like that. For example, in the case of the Goldbach conjecture we know what problem we are trying to solve but not how to solve it. However, if we were scholastics, solving the problem of induction would not necessarily be our goal. Wikipedia says:

Scholasticism is a method of critical thought which dominated teaching by the academics (scholastics, or schoolmen) of medieval universities in Europe from about 1100–1500, and a program of employing that method in articulating and defending orthodoxy in an increasingly pluralistic context. It originated as an outgrowth of, and a departure from, Christian monastic schools. Not so much a philosophy or a theology as a method of learning, scholasticism places a strong emphasis on dialectical reasoning to extend knowledge by inference, and to resolve contradictions.

If we were philosophical scholastics, “orthodox” works would be mostly those of Plato and Aristotle and their most prestigious successors. In this case it would already be a problem that these orthodox philosophers have spoken of a problem of which we do not know what it is. Therefore, instead of not having a problem of induction our goal would be to create one. We would have such a goal because we’d want to defend orthodoxy which says there is such a problem.

If nonrelativizable patterns are used in the definition of ”the problem of induction” at least nothing can be logically proven about said problem. Therefore, defining the problem of induction this way makes it impossible to logically argue that the problem of induction does not exist – that there is no problem of induction. Even though this does not necessarily extend our knowledge it could be the only way to “resolve” a contradiction in Western philosophical orthodoxy. This contradiction is that orthodox authors have written about a problem of induction yet the problem has never been adequately expressed.

In the context that orthodoxy may not be abandoned it is not a failure to use nonrelativizable patterns in the definition of the problem of induction. Instead, it seems like the only thing that can still be done. It will create scholars a need to define relevance. Although defining such a concept seems as impossible as defining Quality the problem of induction will at least seem to exist as long as there are people trying to define relevance and refusing the idea that relevance cannot be defined. But if orthodoxy is this pointless why should we stick to it?

On Lila Squad I encountered a strong defense of the view that Dynamic Quality and static quality have no nonempty intersection. Had there been such an intersection I would have called it romantic quality and that would sufficed in resolving the relationship between Zen and the Art of Motorcycle Maintenance and Lila. But since the solution I presented was not accepted I am content preserving the sanctity of Dynamic Quality by defining romantic quality and Dynamic Quality as nonrelativizable quality and classical and static quality as relativizable quality, the intersection between the nonrelativizable and the relativizable being romantic quality.

I understand that my solution was rejected on grounds of metaphysical shortcomings, not social authority. Introducing any kind of set theoretic structure within Dynamic Quality (ie. defining a subset of Dynamic Quality) would arguably render Dynamic Quality not undefinable. That Dynamic Quality, despite being undefinable, is a subset of both Quality and nonrelativizable quality, is not a problem because the theory of relativizability is a metatheory that does not define Dynamic Quality but renders the notion of undefinability more logically precise.

Relativizable Qualities


The word "ontology" refers to the study of existence. The ontologist asks: "What is there?" Two patterns or levels are reciprocal pairs if they share the same ontology but have a different epistemology and their moral rank is inverted, ie. if rank of A is n so that the first level is numbered 0 then rank of B is 3 - n. Two quadrants are reciprocal if they share the same ontology but have a different epistemology.

Tangible Quality

Is the subjective–objective-split in Zen and the Art of Motorcycle Maintenance.
Includes the theory of static value patterns in Lila and resolves the issue of subjectivity and objectivity in Lila.
Lovers in Tarot.

At this point our task is to merge the static hierarchy with subjective and objective quality. Pirsig's solution is not good enough because it does not apply within idealism or rationalism which are the primary competitors of materialism and empiricism. According to idealism everything is mental or exists in the mind and according to rationalism knowledge can be acquired through reason without resorting to experience. None of these doctrines – idealism, rationalism, materialism and empiricism – is inherently true or false. They are just points of view. But we are looking for a theoretical basis for divinatory engineering so want to find solve problems in a way that is agreeable in as many points of view as possible. Next, we will spend a while creating such a basis.

Lila professes emergent materialism and empiricism but Zen and the Art of Motorcycle Maintenance does not. Pirsig failed in incorporating subjective quality to the theory of static value patterns because the assumptions of materialism and empiricism preclude the subjective viewpoint. However they seem compatible with the objective viewpoint. Therefore let us assume that objective quality is the domain of Pirsig's theory of static value patterns.

In order to account for subjective quality we could construct an emergent hierarchy of subjective levels that lies beyond objectivity's assumptions of empiricism and materialism. If possible, we would like to do this so that subjectivity and objectivity still have something in common with each other. By trial and error I reached the following kind of solution.

Since levels are static and static quality is both actual (= romantic) and potential (= classical) we have the liberty to assume that levels, too, feature both actual and potential quality. Let us therefore split the objective levels into a potential and actual portion. The potential levels retain the names of the static levels whereas their actual portions will be named according to Maslow's hierarchy of needs.

Now, let us begin building the subjective static hierarchy by assuming that the subjective levels connect into the same actual portions as the objective ones but in the inverse order. From a structural point of view this means that the actual portion of intellect, the highest objective level, is the actual portion of the lowest subjective level, and vice versa. Let us arrange the potential levels and the actual portions into a table. The potential levels are numbered according to their rank in the hierarchy, with a greater number signifying higher rank.

Subjective Actual Objective
4. Revelation Sense-data 1. Inorganic
3. Calculating Lower needs 2. Biological
2. Consideration Higher needs 3. Social
1. Belief Deliberation 4. Intellectual

Abstract Quality

See also Normative Quality and Mystical Quality.
Resolves the issue of empiricism and abstract symbol manipulation.
The Chariot in Tarot.

Initially I tried to construct the normative levels as something that connects to subjective and objective quality, and not to romantic quality at all. But eventually my assumption, that normative quality does not connect to romantic quality, began to seem arbitrary. Romantic quality is the cutting edge of conceptual experience. If normative quality does not connect to that how could it exist at all and what would it have to do with the Metaphysics of Quality?

Having normative quality, that is detached from romantic quality, seemed to create a new and unwieldy category to the Metaphysics of Quality, which resembled something of a metatheory of the Metaphysics of Quality. Back then I thought the normative levels are something of an abstraction of the subjective and objective levels. They are the “form” of those levels, stripped from content. But it was troublesome that I expected normative quality to emerge from the intellectual level which is connected to romantic quality. That means normative quality was a part of the emergence chain that also includes subjective and objective quality. I found no reason why, at some part of the emergence chain, should emerging levels get stripped from romantic content. That seemed arbitrary and random. There had to be another way. There had to be some form of romantic quality I had not thought of, and if I were to search for it, I would find it.

As I could not construct the normative patterns so that they would connect to any romantic cluster, whose existence is relatively easy to infer from Pirsig’s work, I engaged in introspection to find new romantic clusters. In the rest of this chapter I will describe these romantic clusters and use them to construct four classical levels of normative quality, just like subjective and objective quality are also split into levels. Each level will consist of a classical part and a romantic part. In order to give a clearer impression of the romantic normative clusters I will call them “normative phenomena”.

The four normative levels I am going to introduce do not seem to connect to any particular romantic cluster that is even implicitly described in Pirsig’s Metaphysics of Quality, as mathematical constructs do not refer to any particular sense-datum, higher need or lower need. They could be thought to refer to deliberations but in that case the Metaphysics of Quality would fail to distinguish empirical deliberations from normative, mathematical or logical deliberations, which would be quite limiting.

Before we embark on this journey we might want to double-check whether it is reasonable. Does it make any sense to inquire about the existence and types of normative phenomena? Are there such things as non-conceptual, non-classical forms of experience that are necessary for understanding formal logic and mathematics? In order to demonstrate that there are I will assume the opposite: that there is no normative romantic quality whatsoever. What would this entail?

There are savants who are able to evaluate the properties of numbers by how they “feel”. Some of them are able to determine whether a number is a prime or not by focusing on that feeling. They may report tactile sensations associated with the numbers and in this case they are not only savants but also synesthetics. These tactile experiences are sense-data and as such they belong to a romantic cluster that is already somewhat covered by Pirsig’s existing work. But the connection between the sense-data and numbers, which are normative constructs, is not necessarily objective or subjective. It’s true that the reliability of the connection could be empirically verified by asking the savant a certain amount of questions and checking whether he managed to give correct answers. But the ability itself is not a product of empirical research so using it cannot be categorized as ”intellectual” activity in the objective sense of the word. It is obviously not a social or a biological pattern, either.

There seems to be no reason to believe the use of that ability is classical quality at all. Using language to check, whether a number is a prime, is dialectic. But performing a primality check by observing phenomena associated with synesthetic tactile sensations of numbers is not dialectic. To elaborate further: the expression “a dialectic primality check” is a reference to a dialectic argument. In case the number is 29 an instance of such an argument would be:

Because 52 = 25, which is less than 29, but 62 = 36, which is greater than 29, we should check whether 29 is divisible by numbers that are greater than 1 but smaller than 5. These numbers are 2, 3 and 4. As 29 is not divisible by any of them it’s a prime.

On the other hand, the expression “a phenomenal primality check based on interpretation of synesthetic experiences” does not refer to anything like the previous argument. It is like a reference to the word “joy”. Although the reference is meaningful it doesn’t refer to something that comes into existence by means of dialectic. One does not become able to do phenomenal–synesthetic primality checks by making some dialectic argument, just like a blind person does not regain his vision by arguing that he is not blind.

Furthermore, phenomenal–synesthetic primality checks are not Dynamic Quality. The synesthetic savant can use experience to predict whether normative phenomena associated with synesthetic sense-data about a number tell that the number is a prime. He expects primes to feel a certain way that composite numbers do not. He is already able to conceptualize the connection between sense-data and numbers.

As both classical quality and Dynamic Quality have been ruled out, the only remaining suitable category for phenomenal–synesthetic primality checks is romantic quality. If normative romantic quality were deemed as an arbitrary ad hoc fabrication intended only to bolster the credibility of the Analytic Metaphysics of Quality, phenomenal–synesthetic primality checks would be claimed impossible on no other grounds than metaphysical skepticism.

I concede that my argument may seem detached from everyday life as few people actually are synesthetic savants. But I chose it due to its extremity. It’s hard to argue against the existence of an ability that provides remarkably consistent results in a spectacularily easy way. For the purposes of providing empirical evidence for a metaphysical statement it is enough to demonstrate that even a few people experience normative phenomena. But I do believe we all experience normative romantic quality. For most the experiences are just not as clear as they are for synesthetic savants.

Mystical Actual Normative
4. Aesthetic Harmony 1. Syntactic
3. Freedom Awareness 2. Semantic
2. Cultural Significance 3. Metatheoretic
1. Coincidental Unity 4. Analogic

Epistemology: The Gnostic–Rational-Split

I would consider calling gnostic epistemology "passive" and rational epistemology "active".

There's one problem with nonrelativizable quality. If we have a theory that can account for nonrelativizable quality isn't nonrelativizable quality actually relativizable within our theory? Yes, it is. But when nonrelativizable quality manifests as a pattern in our theory it still remains different from some other relativizable patterns. Relativizability is necessary for a pattern to belong to rational epistemology. That is to say, only relativizable patterns can be found to follow some arbitrary laws of cause and effect because they are relativized to these very laws. But the Analytic Metaphysics of Quality is not exclusively rational. This is a sacrifice it has to make in order to solve the symbol grounding problem. Other disciplines such as physics make a similar sacrifice but it is obvious for an educated reader that physical entities follow the laws of physics at least most of the time so although the symbol grounding problem is present and dealt with, even an educated reader might not notice anything.

Gnosis refers to direct knowledge that is not subordinate to dialectic. If you’re sailing the Arctic Ocean and feel the cold wind you have gnosis of the coldness of the Arctic Ocean. If you’ve merely read from a book that the Artic Ocean is cold then you do not have gnosis of its coldness. You have some other kind of information about it and you can use that information to make rational preparations, such as packing a warm coat if you’re going there. But having gnosis means you’re already there – in some way or the other. I don’t find it necessary to exclude the possibility of astral projection or an out-of-body experience at this point. They do manifest as gnosis and methodically checking whether they provide correct information is beyond the domain of gnosis.

Gnostic quadrants – subjective and mystical quality – contain romantic triggers to classical associations. That’s why they do not include causality. Causality, insofar as it can be processed by human language, has to be classical quality. Furthermore, causality is always a property of the reference, not of the referent. A form of causality that has no classical quality is not expressible by means of language except metaphorically or metatheoretically.

In The Problems of Philosophy Bertrand Russell writes about knowledge by acquaintance and knowledge by description. The former is gnosis, that is, direct knowledge of something that is perceived as romantic quality. If you see a brown table and utter: ”This table is brown”, you are stating something you know by acquaintance. Knowledge by description, on the other hand, is about something that isn’t currently perceived, such as “Julius Caesar was the Emperor of Rome”. It does not feature actual observation of the object of knowledge, such as seeing Caesar sitting on a throne like an emperor.

The reason why the difference between knowledge by description and knowledge by acquaintance has been difficult to explain is that it often manifests as the problem of how mystical coincidences are transformed to objective scientific theories. After all, it was a mystery why water expanded upon being frozen before a scientific theory about it was developed. Because the objective quadrant cannot emerge directly from the mystical quadrant this process can take two distinct forms, both of which are covered by the Analytic Metaphysics of Quality.

One form is to have the objective quadrant emerge from the subjective quadrant which in turn emerges from the mystical quadrant. This means we form beliefs based on coincidences and try to find empirical verification for those beliefs in order to construct a scientific theory. The other form is to have objectivity emerge from normativity which emerges from mysticality. This means we use aesthetics to construct an elegant normative system and use this system to construct assumptions of the tangible world which we then empirically try to verify.

More generally, knowledge by description is contained in the rational quadrants of the Analytic Metaphysics of Quality and knowledge by acquaintance is contained in the gnostic quadrants. Two patterns or levels are interspherical pairs if they share the same epistemology and rank but their ontology is different. Two quadrants are interspherical if they share the same epistemology but have a different ontology.

Argumentation of this exactitude is difficult to conduct without an analytically defined framework, such as the Analytic Metaphysics of Quality. If we restrict ourselves to continental rhetoric it becomes quite difficult to argue why there would be exactly two separate ways to explain how mystical coincidences are transformed into empirical scientific theories. To be sure, my above ”solution” of the philosophical problem Russell described may still be criticised as an offhanded one. I do not go into much detail about what ”rational” or ”gnostic” epistemology mean. Therefore I will now get more specific.

Generally speaking, any kind of ”knowledge” is a pattern. The Analytic Metaphysics of Quality does not distinguish ethics, ontology and epistemology. It treats the subject matter of all these disciplines as patterns. Each pattern consists of an intension and an extension.

An intension explains, how a pattern manages to refer to something, and the extension is what the pattern refers to. For example, the intension of the inorganic pattern “calculator” would be something akin to “a hand-held electronic device that performs arithmetic operations”. That’s a dialectic definition of a calculator – in other words, classical quality. It explains what is a calculator and what is not. The extension of the inorganic pattern ”calculator” would include all calculators in the world, such as my pocket calculator, my friend’s scientific calculator, my teacher’s blue calculator, and so on. In the Analytic Metaphysics of Quality the existence of actual calculators is verified by occurrences of romantic quality.

The classical appearance of a pattern does not dictate whether it’s a gnostic pattern or a rational pattern. Of course some patterns seem gnostic whereas others seem rational – some classical appearances are so strongly associated to a certain metaphysical domain that we automatically assume them to belong to that domain without checking the context in which the pattern appears. For example, the pattern ”electron” seems like a rational pattern, because the word is often used in science. The pattern ”invocation of a spirit” seems like a gnostic pattern, because it is mostly found in mystical literature. Because people interpret these appearances somewhat consistently I usually expect the reader to understand whether some pattern is gnostic or rational without explicitly specifying it. But in theory, the word ”electron” could be used within a gnostic epistemology, and the word ”invocation of a spirit” could be used within a rational epistemology. In this case these words would be used as constituents of a different pattern than the one we usually expect.

Let us form a pattern and experiment with it in different contexts. Let the intension of the pattern be: “a number whose successor is 0”. If that pattern is used within rational epistemology, its usage is such that we know the logical context of the pattern. If the context is the theory of integers, we determine the extension of that pattern to be the number -1. If the context is the theory of natural numbers, we determine the pattern to have an empty extension, because that theory does not include negative numbers. Patterns with an empty extension could be said not to exist. For example, there are no four-sided triangles, the planet Earth doesn’t have rings, and there is no natural number whose successor is 0.

But if we place the pattern “a number whose successor is 0” within gnostic epistemology we might end up making an argument as if that pattern would refer to -1 and then making another argument as if the extension of the pattern were empty, and treating those arguments as if they had been presented within the same context. If that context is, say, Presburger arithmetic, we might consequently be able to argue that Presburger arithmetic is inconsistent even if that weren’t rationally true.

Gnostic patterns can be a nuisance in ontology and philosophy because we have a tendency to expect some degree of rationality of philosophical theories, yet gnostic patterns keep popping up when we’re dealing with philosophical issues. For example, “mind” in Berkeley’s Master Argument is a gnostic pattern. It’s supposed to be a category that contains everything. Berkeley argues that everything takes place within the mind, as some kind of thoughts, and that even the pattern ”a tree that is not being thought about” is, by definition, within the mind. But rationally this doesn’t make sense. The “mind”, that supposedly contains even “a tree that is not being thought about” is a different kind of “mind” than the mind the tree does not belong to by virtue of not being thought about. It is some sort of a ”meta-mind”.

This makes it seem like gnostic patterns are useless or even harmful. However, that is not true, because they grant us access to extensions that are beyond our preconceived notions of how things are. Let us examine the pattern ”an experience of joy”. If we place this pattern into a rational epistemology it becomes an objective pattern. It may be linked to an expectation of another person becoming happy if she, for example, receives flowers. Or it may be linked to a scientific theory about chemicals in the brain causing experiences of joy in test subjects. But such expectations or theories are based on past observations of flowers or chemicals causing joy. If we were to perceive that joy does not actually ensue when flowers are given or when the brain is in the right chemical state, the joy we would find to be absent would be gnostic. Its non-existence would have no rational explanation at the moment of being observed.

In this case we’d have the option to assume that our expectations or theories weren’t entirely correct, or the option to assume that our experience of the absence of joy was not entirely correct. Suppose we chose the latter – that is, we assume that although the recipient of flowers seems unhappy despite receiving the flowers, she must actually be happy. After all, women automatically become happy upon receiving flowers, don’t they? And since a scientific theory says someone is happy, they must be happy, right?

Of course not. It would be absurd to resort to rational expectations and theories if they have already been found not to apply under present circumstances. To dismiss our gnostic knowledge of joy – to think that we should feel joy just because a theory says we are feeling joy – would amount to holding an empirical theory derived from experience, intended to explain experience, as something that in and of itself causes experience. In the 19th century that approach would have allowed people to argue that because caloric theory does not adequately explain physical observations of heat, everyone should nevertheless try to experience heat in accordance with caloric theory instead of developing the modern, mechanical theory of heat. That would have been pointless.

Now we are familiar with intensions and extensions and have recapped what gnosticity and rationality mean. In order to do proper analytic philosophy of which Russell would be proud, let's introduce a few formalisms. Let us define a pattern as an ordered pair (a,b) so that the first element is the intension and the second element is the extension.

Each pattern consists of a classical and a romantic element. In the case of gnostic patterns the intension or trigger is a romantic element and the extension or association is a classical element. In the case of rational patterns the intension or reference is a classical element and the extension or referent is a romantic element.

Let us denote classical elements with the letters c and d and romantic elements with the letters r and s. Any rational pattern is of the form (c,r) and any gnostic pattern is of the form (r,c). All reciprocal pairs of patterns are sets of the form {(c,r),(r,d)} so that if the level of c is n, with the bottom level being numbered 0 and the top level being numbered 3, then the level of d is 3 - n. Rational interspherical pairs of patterns are sets of the form {(c,r),(c,s)} and gnostic intersperical pairs of patterns are sets of the form {(r,c),(s,c)} so that r is tangible but s is abstract. In addition to providing an analytic solution to the problem of knowledge by description versus knowledge by acquaintance these formalisms clarify the nature of classical and romantic quality and as such are integral to the Analytic Metaphysics of Quality.

The arrows in the following diagram show how intension-extension-relations are inverted within quadrants whose epistemologies are different. The rest of the links are subsethood relations.


See also