Academic Philosophy

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Justified True Belief and the Gettier Problem

According to a certain philosophical stance, knowledge can be defined as ”justified true belief”. Edmund Gettier demonstrated in 1963 that this is a troublesome stance, but his paper is not universally accepted. What does the Analytic Metaphysics of Quality say about this issue?

According to the Analytic Metaphysics of Quality, knowledge can be rational or gnostic. For example, in the analytic Metaphysics of Quality you are allowed to be able to predict the future with Tarot cards if this only means that whatever the future will be, you expect to believe it was foretold by Tarot. In this sense Tarot’s ability to predict the future is merely an accurate report of your beliefs. This approach differs from traditional Western philosophies which only consider rational knowledge proper. From such traditionalist viewpoints the addition of gnostic knowledge, such as divination by Tarot, transcends both the notion of knowledge and that of justification. What could be a notion of justification that is common to both gnostic and rational knowledge?

The issue of justification is traditionally thought to be about questions such as why do we consider modern thermodynamics more advanced than caloric theory. It is not really thought to be about why do people believe Tarot to predict a certain kind of future but not another kind of future, as any future predicted by Tarot is condisered equally devoid of justification. But in the analytic Metaphysics of Quality the caloric question and the Tarot question are both considered an instance of a justification issue, only within a different epistemology. The analytic Metaphysics of Quality generalizes the traditional notion of justification as the notion of excellence, which is analytically defined but its application is partially gnostic. Hence the ”justified true belief” turns into the ”excellent true belief”.

What, then, is ”truth”? It would seem to point at something epistemological, that is, related to knowledge and knowing. But the analytic Metaphysics of Quality does not differentiate truth from existence or moral value. That is to say, the analytic Metaphysics of Quality does not introduce an essentialist belief in entities which are known but do not exist, which exist but aren't known, which are known but are not evaluated or which exist but are not evaluated. Similarly, the analytic Metaphysics of Quality doesn't introduce any entity that cannot be thought of as a belief, because beliefs are the fundamental ontological substance of the subjective quadrant, which implicates any static thing can be thought to emerge from beliefs. Hence, the notions of ”truth” and ”belief” can be synthesized into the notion of ”pattern”, and this way ”excellent true belief” is simplified into ”excellent pattern”. Do, then, Gettier's criticisms of justified true belief apply to excellent patterns? Let us examine his arguments from Wikipedia. Case one:

Smith has applied for a job, but, it is claimed, has a justified belief that "Jones will get the job". He also has a justified belief that "Jones has 10 coins in his pocket". Smith therefore (justifiably) concludes (by the rule of the transitivity of identity) that "the man who will get the job has 10 coins in his pocket". In fact, Jones does not get the job. Instead, Smith does. However, as it happens, Smith (unknowingly and by sheer chance) also had 10 coins in his pocket. So his belief that "the man who will get the job has 10 coins in his pocket" was justified and true. But it does not appear to be knowledge.

Case two:

Smith, it is claimed by the hidden interlocutor, has a justified belief that "Jones owns a Ford". Smith therefore (justifiably) concludes (by the rule of disjunction introduction) that "Jones owns a Ford, or Brown is in Barcelona", even though Smith has no knowledge whatsoever about the location of Brown. In fact, Jones does not own a Ford, but by sheer coincidence, Brown really is in Barcelona. Again, Smith had a belief that was true and justified, but not knowledge.

Let us translate these cases to the language of the analytic Metaphysics of Quality. Case one:

Smith has applied for a job, but, it is claimed, has an excellent belief that "Jones will get the job". He also has an excellent belief that "Jones has 10 coins in his pocket". Smith therefore (excellently) concludes (by the rule of the transitivity of identity) that "the man who will get the job has 10 coins in his pocket". In fact, Jones does not get the job. Instead, Smith does. However, as it happens, Smith (unknowingly and by sheer chance) also had 10 coins in his pocket. So his belief that "the man who will get the job has 10 coins in his pocket" was excellent and true. But it does not appear to be knowledge.

In this case we should first ask what is the quadrant of Smith's supposedly excellent belief of Jones getting the job. If the quadrant is subjective, the rule of the transitivity of identity is irrelevant and the case is closed: excellent patterns are knowledge even if they are subjective. But let us suppose the belief is actually a social or an intellectual pattern of the objective quadrant. That is to say, the belief is backed up by some evidence such as statistical data of what kind of people does the employer hire. In this case the excellency of the ”belief” merely means that Smith has compelling objective evidence for the case that Jones gets the job. Smith himself getting the job is a pattern, that would have existed but could not have been known at the moment Smith makes the objective assessment, and the Analytic Metaphysics of Quality does not introduce such patterns. Therefore Smith excellently believed Jones would get the job (meaning that this subjective belief emerged from trusted intellectual quality by means of strong emergence), and it may have been gnostically true that Jones would get the job, but Smith was rationally wrong, and Jones didn't really get the job. To state that this is impossible – to require the existence of static knowledge that cannot be wrong – is just a delirious essentialist fabrication that is contrary to the scientific method. Scientific theories are open for revision, and even if Smith isn't a scientist, he is employing the scientific method to the best of his ability when making the objective assessment that Jones will get the job.

Case two:

Smith, it is claimed by the hidden interlocutor, has an excellent belief that "Jones owns a Ford". Smith therefore (excellently) concludes (by the rule of disjunction introduction) that "Jones owns a Ford, or Brown is in Barcelona", even though Smith has no knowledge whatsoever about the location of Brown. In fact, Jones does not own a Ford, but by sheer coincidence, Brown really is in Barcelona. Again, Smith had a belief that was true and excellent, but not knowledge.

If Smith's belief is subjective the normative operation of disjunction introduction cannot be applied to it in a rational manner. Furthermore, according to the mystical quadrant Smith is capable of clairvoyance if Brown really was in Barcelona when Smith used a disjunction introduction to figure this out. However, Smith could have as well used Tarot cards to attain such knowledge.

But let us suppose Smith objectively believes in Jones owning a Ford. This still does not entail that the rule of disjunction introduction applies to Jones owning a Ford, because that rule is a normative construct. We cannot jump into the conclusion that simply because the normative rule of disjunction introduction exists, it applies to every objective pattern. Instead, we should empirically verify such a hypothesis. If we performed a sufficient amount of experiments, it would probably dawn to us that although Brown may be in Barcelona when Smith uses the rule of disjunction introduction to assert so, correlation does not imply causation, and furthermore, we have no evidence of causation.

It is possible to construct infinitely many axiomatic systems with different properties that would contradict each other, and there is no objectively excellent (supposing that we aim for maximal excellency, that is, intellectual quality as opposed to inorganic, biological or social excellence) way to select a random normative rule and assert it to apply to objective patterns without relying on any experimental data. Therefore Smith cannot excellently conclude that Jones owning a Ford means Brown is objectively in Barcelona. Such a conclusion would be a bad objective vector, not an excellent one. The vector would be bad because it does not have classical justification within the objective quadrant. In fact, the essential meaning of case two seems to be that it is obvious that the conclusion does not have enough classical quality. If it were not obvious, Gettier wouldn't have written case two like this in the first place.

More specifically, the bad vector would be an oppressive, failing or disastrous vector. Other slots are not appropriate because this objective vector necessarily has intellectual potential but neccessarily fails to realize it, thus becoming bad.

The article Objective Slots defines oppression as:

The oppressive slot includes patterns that threaten to deteriorate intellectual patterns into social ones. For example, if a scientist is forced to work in slavery, or encouraged to forge, plagiarize or exaggerate results for the sake of career advancement, the criteria of oppression are met.

To assert an objective state of affairs one must have an objective reason for doing so if the discussion is conducted on the objective quadrant. If there is no excellent objective reason the best possible reason to believe it would be the social authority of the one who says it. And that person could be lying or wrong. In case the report of said state of affairs would be wrong and people would suffer because of that there would be an objective reason to suspect that the social authority of the one who made the report would have potentially damaged an intellectual pattern. In practice this might mean things like the state censoring important information because it wants to preserve the reputation of officials who have engaged in misconduct. Or Smith not believing excellently but because someone has cheated him.

The real state of affairs could be even worse as the reason to believe a state of affairs could also be a biological one. Ie. someone believes anything she is told because she wants to have penetrative vaginal sex and condoms, which would make the act socially rather acceptable, are unavailable. Suppose any contraception, even retroactive, were not available. Smith could believe something like: "I'm/He's gonna pull it out and we're both clean" without having any rational reason to do so. Although there may be exceptions, it seems fair to say that seems like a failing pattern which is worse than an oppression pattern.

According to the AMOQ an even worse kind of failure could be that of disaster. That would mean that messages are malformed so that no living being benefits of this. An example of such a thing would be Smith believing things about Jones because of brain damage. Such a way of believing does not count as excellent in the objective sense of the word. Of course, under some circumstances even that could have aesthetic quality so if we did permit changing context mid-sentence without mentioning it, ie. relativing the discussion to a different quadrant on the run and expecting the audience to just "get it", then even this could be excellent. But in the simplest and most straightforward interpretation it is not excellent.

I conclude that although knowledge cannot necessarily be defined as ”justified true belief”, the analytic Metaphysics of Quality replaces ”justified true belief” with ”excellent pattern”, and knowledge can be defined as an excellent pattern in a way that spans multiple epistemological and ontological contexts.

Knowledge by Description versus Knowledge by Acquaintance

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.

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 that Russell might appreciate, 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.

Knowledge a priori and Knowledge a posteriori

Seems like the justification of normative things is knowledge a priori. The justification of subjective things appears to be knowledge a posteriori. Justification of an objective or mystical thing could be either. The interesting question here is: does justification correlate with emergence? In other words, is it true that an objective or mystical pattern emerges from a normative pattern if it is justified a priori? And does an objective or mystical pattern emerge from a subjective pattern if it is justified a posteriori? I like these hypotheses.

On the other hand, is it possible for an objective or mystical pattern to emerge from a normative or subjective pattern so that it doesn't have justification? I like the hypothesis that this isn't possible. That is to say, strong emergence from the subjective or normative quadrant manifests the same thing as the notion of justification. But strong emergence from the objective or mystical quadrant isn't justification. It's just emergence.

Phenomena and Noumena

Normative quality that isn't emergent seems to comprise the domain of noumena - a reality present to reason alone - whereas other quadrants would seem to qualify as phenomena. At least this seems to apply to how Kant used these concepts. It is my understanding that after Kant these concepts have changed somewhat in meaning, with "noumena" turning similar in meaning with "abstract patterns that aren't emergent".

It is true that, for instance, mathematical theorems emerge from an objective reality involving a paper on which the theorem has been written, and that Kantian noumena aren't "pure reason" in that sense. However, it is also true that once the theorem has been understood and memorized it has been made accessible to cognition so that no written instructions are needed. It is in this sense that Kantian noumena are present to reason alone.

Utilitarianism versus Ethical Code

See section Ethical and Moral Implications in Excellence, Decency and Badness and Nonrelativized Slots.

The Problem of Induction

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 gnostic. Is this an error or not?

The question sheds light on what is the purpose of academic philosophy. If we use a gnostic 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 would be 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 gnostic 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 gnostic 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.

Abandoning Essentialism

Nowadays a lot of people make the offhand remark that they oppose “dualism”. This seems to mean they oppose the doctrine that only one defined philosophical doctrine is correct and others are false. There are various other names for a similar if not identical oppositionary way of thinking. The ones I can come up with are:

  • Emptiness in Buddhism
  • Rejection of essentialism and nihilism
  • Rejection of subject–object metaphysics in Pirsig’s Metaphysics of Quality

As far as I can tell, all of these ideas advocate rejection of what I’d call rationalistic essentialism – the doctrine that reality is essentially rationally processed classical quality. This doctrine may seem easy to dismiss at first glance, but when people stumble into metaphysical questions they seem to accidentally presuppose rationalistic essentialism and consequently make errors or at least limit their imagination. The domain beyond rationally processed classical quality is not without structure, and that structure can be differentiated from classical quality.

Whenever one sees a bunch of rationalistic essentialists trying to do something impossible, one is kind of compelled to present them an argument that implies the existence of Dynamic Quality. Dynamic Quality is a very profound concept for someone with little philosophical understanding. It will take some time to stomach what that means. Understanding the meaning of that concept makes it impossible to be an essentialist. But I would like to express the controversial idea that after Dynamic Quality the concept is understood it becomes dull and trite. I don’t think it’s very interesting to keep affirming the existence of Dynamic Quality with various rhetorical devices long after it is already understood. Because Dynamic Quality has no attributes the conscious will can’t use it for anything. Rather, the conscious serves as an instrument of Dynamic Quality.

The concept of Dynamic Quality isn’t the only gateway for abandoning essentialism. Arguments related to the refutation of essentialism seem to constitute an entire branch, if a neglected one, of philosophy. Whether this branch should be named is a difficult issue. If it could somehow be conveyed to people that it’s bad to adhere to essentialism, they might report having abandoned essentialism in spite of not understanding what that means. They might be inclined to do that simply in an attempt to be popular and well-liked. The Buddhists have protected their tradition by requiring well-known opponents of essentialism – their llamas and such – to live a profoundly different life than ordinary people and by requiring monks to meditate instead of just wildly doing anything they want like I do. This detachment from an ordinary lifestyle allows them to oppose essentialism without the common public caring about it. Consequently, the principles of Buddhism have not been adulterated by disinterested goons who only want to climb up the social ladder.

This is not how philosophy is conducted in the West. A prestigious academic is not only able to live an ordinary life. If he is a professor he is likely to be wealthier and more powerful than the commoner. Wealth and power are desired by commoners so if abandoning essentialism were set as a requirement for being a prestigious philosopher many people would try to seem like opponents of essentialism without understanding what that means. Hence, it would be risky to publicly acknowledge the opposition of essentialism as a venerable genre of philosophy. However, because the modern West has not apparently even tried this I think the risk could be taken.

Most notable works of mysticism and some philosophical works operate beyond essentialism or approach its limits. Some notable such works and ideas include:

  • The Diamond Sutra
  • The Fundamentals of the Middle Way, Nāgārjuna
  • On Certainty, Wittgenstein
  • Confirmation Holism, Quine
  • The Metaphysics of Quality, Pirsig
  • The Structure of Emptiness, Priest

Carnap’s The Elimination of Metaphysics Through Logical Analysis of Language seems to belong to this genre, but doesn’t. Instead of denying essentialism Carnap opposes all metaphysics, which makes him a nihilist. This, in turn, makes him an essentialist. Carnap overinterprets the metaphysical implications of his logical argument, which properly only entails the rejection of rationalistic essentialism. I want academic philosophy to be extended to include the study of Buddhist emptiness and the opposition of essentialism, which are pretty similar things.

The Structure of Emptiness

a short paper by Graham Priest called The Structure of Emptiness, published in 2009. The paper attempts to explain Buddhist thinking with mathematics and as such is obviously something I should comment. The Metaphysics of Quality has taken a lot of influence from Eastern philosophy, and the analytic Metaphysics of Quality is also mathematically or logically somewhat refined.

I have to give merit to Structure of Emptiness for being bold in its weirdness. Graham Priest is a Boyce Gibson Professor of Philosophy at the University of Melbourne and a Distinguished Professor of Philosophy at the CUNY Graduate Center. He begins desribing his theory by presenting the Śūnyatā – the Buddhist notion of emptiness – as a doctrine according to which there is no thing that has intrinsic existence. He alleges this view to be orthodox in Mahāyāna Buddhism and to be defended by the ancient Nāgārjuna in his work The Fundamentals of the Middle Way. I cite chapter 15 of that work:

  1. It makes no sense to say that essence arises from causes and conditions. If essence were caused or conditioned, it would not be essence.
  2. Essence cannot be created or otherwise come to be. Essence is not artificial, nor does it depend on another.
  3. If there are essences, then there are real differences between things . . . .
  4. Are there entities without essences? Then there are no real differences between them . . . .
  5. If we cannot find an entity with an essence, that does not prove the non-existence of such entities. Some say that an entity that changes is a nonentity.
  6. Those who think in terms of essences and real differences, and who cannot recognize entities without essences, do not grasp the truth taught by the Buddha.
  7. The Buddha . . . counseled against saying “it is” and “it is not.”
  8. If only entities with essences [really] exist, then there is no non-existence, nor can anything change.
  9. Some will say, “If there are no essences, what is there to change?” We reply, “If there are essences, what is there to change?”
  10. To say “it is” is to be attached to essentialism. To say “it is not” is to lapse into nihilism. Therefore, judgments of “it is” or “it is not” are not made by the wise.
  11. “An entity with an essence cannot not-exist.” This is essentialism. “It existed before, but now it doesn’t.” This is nihilism.

Here to ”have essence” probably means to have intrinstic existence. Verses 5, 7, 10 and 11 seem intended to mean that the intrinsic existence of entities is not to be affirmed or denied. Hence, it’s a bit strange of Priest to deny the intrinstic existence of entities.

Priest argues later, that assuming entities to have intrinsic existence makes it possible to break any dialectic object into constituent parts, which in turn are broken to their constituent parts, and so on. This decomposition cannot be proven to end at some specific point, and at first Priest finds this to entail nihilism. This is what most Western readers probably would think so it’s possibly wise of Priest to follow their way of thinking before presenting an alternative.

Immediately afterwards Priest comes up with an alternative interpretation of the result of his skeptical thought experiment: that nothing determinate exists. He reports the Vimalakīrti Sūtra to explicitly recommend to tolerate “the groundlessness of things” yet he seems to have difficulty understanding what that means: he finds the debate to become “murky”. Priest wonders whether existence can be indeterminate. He expresses some sort of bewilderment about the idea.

I no longer see what’s difficult to understand about Dynamic Quality, although I used to have difficulties with it. The essential lesson to be learnt here can be studied from the Stanford Encyclopedia of Philosophy article Logic and Ontology. It is also a central thesis of Quine’s confirmation holism. It is in no way particular to Buddhism or the Metaphysics of Quality. I think even Rescher knows it. The point is simply that dialectic systems cannot justify themselves from the “outside”, that is, from beyond their own dialectic content. That is what “groundlessness” means. Even science is not subjectively true for someone who does not believe in science. To make a person believe in science would amount to having him accept the scientific method. Only after that would scientific arguments convince him. But if he has some problem – I don’t know what problem – with the scientific method, then he will not accept that kind of arguments. And there is no one method of argumentation that is known with certainty to make any living person accept the scientific method. Hence, science is “groundless” beyond its own context. The old Wittgenstein, too, knew this.

Priest proceeds to present a mathematical model of relative existence. He defines an object to be “empty” in the Buddhist sense if it exists as a locus in a field of relations but does not exist in any other way. At this point it could have been relevant to note, that no locus can be determined not to exist in the form of Dynamic Quality. Instead of doing so, Priest engages in what seems like an attempt to deny the existence of Dynamic Quality: he defines a converse closure condition. According to this condition every locus is in the domain of some relation. This is similar to the Metaphysical Autology Principle in the CTMU.

Priest’s paper concludes that reality is a non-well-founded set which contains non-well-founded sets. This is a bit funny given that the converse closure condition seemed intended to deny the existence of Dynamic Quality and yet here we have a notion of “non-well-founded set” that has no static mathematical meaning. Furthermore, if reality indeed is a non-well-founded set what was so bewildering about existence being indeterminate or unspecific? That’s a logical conclusion of Priest’s own work. Maybe the bewilderment was a rhetorical device employed with the expectation that the reader would, in fact, be bewildered about the claim that existence is indeterminate. Priest’s conclusion amounts to saying that reality is Quality, which cannot be determined to mean anything specific. I have no problem with that conclusion.

The Structure of Emptiness demonstrates what hopefully should be a trivial metaphysical point for all readers even though it unfortunately probably isn't. It makes this demonstration in a way that brings Western and Oriental philosophy into dialogue with each other.

See Also