Variation on the Argument from Marginal Cases

I have recently thought of a puzzling, but potentially revolutionary variation on the Argument from Marginal Cases. I am not exactly at the stage where I can conclusively say that this variation establishes its conclusion, but it has given me great pause.

The standard form of the Argument from Marginal Cases is well known. It runs as follows:

PREMISE 1: Assume that some trait T, such as intelligence, moral agency, the ability to appreciate art, the ability to feel romantic attachment, etc, is the sole determiner of moral status.

PREMISE 2: Some humans as a matter of fact do not possess the aforementioned trait.

CONCLUSION 1: Some humans (i.e. marginal cases) do not have moral status.

PREMISE 3: But, the aforementioned marginal humans actually do have moral status.

PREMISE 4: If the aforementioned marginal humans do have moral status, then trait T is not the sole determiner of moral status.

CONCLUSION 2: Trait T is not the sole determiner of moral status.

The obvious intention of this argument is to demonstrate that many proposed determiners for moral status are insufficient, because there will always be some humans who we intuitively believe to possess moral status who will be classified as not possessing such status as a result of applying this argument.

But, as people who follow debates on Animal Rights are all too aware, those who propound this argument do generally agree that there is in fact a sole determiner for moral status that is not susceptible to the argument. The criteria, of course, is that of sentience. Sentience, i.e. the ability to have subjective experience, is said to be the key that unlocks the gateway to moral status.


The usage of this argument, and the eventual appeal to sentience as the criteria,  usually leaves the opponent with one of two options:

1. He can define moral status as being determined solely on the basis of species membership.

2. He can accept the conclusion of the argument and follow the Vegan lifestyle.

Option 1 is obviously recalcitrant, since it is just an example of speciesism, and thus embodies the same sorts of prejudices as racism, sexism, ageism, classism, etc.

Option 2, though indeed the sensible conclusion, is also considered recalcitrant because of the personal sacrifices that the Carnist must make.


This is all standard fare to those deep among the milieu of animal philosophy. But what I want to bring under consideration is the notion of sentience as the criteria for moral status. For, as should be clear enough, not all humans are sentient.

Quite apart from such trivial cases as dead and not-yet-born humans, there are real instances of living humans that lack the property of sentience. The most obvious example is people who are comatose, but certain severe and profoundly disabled humans might also  lack sentience. But there is a universal instance where living humans lack sentience, namely, when they are asleep. We will refer to all humans who fall under these instances as "Non-S Humans."

Let us test this criteria by formulating a new version of the Argument from Marginal Cases with it in mind. We might formulate it as follows:

PREMISE 1: Assume that sentience is the criteria for the possession of moral status.

PREMISE 2: Non-S Humans do not possess sentience.

CONCLUSION 1: Non-S Humans do not possess moral status.

PREMISE 3: If Non-S Humans do not possess moral status, then it is morally permissible to treat Non-S Humans in any way we please (for instance, to rape them).

PREMISE 3: But it is not morally permissible to treat Non-S Humans in any way we please.

CONCLUSION 2: Non-S Humans do possess moral status.

PREMISE 5: If Non-S Humans do possess moral status, then sentience is not the criteria for the possession of moral status.

CONCLUSION 6: Sentience is not the criteria for the possession of moral status.


As we can see, this argument operates essentially on the same sort of principle as the standard AMC. We propose a criteria for moral status, but then we note that this criteria does not apply to all humans, and that the humans it does not apply to do seem to really possess moral status.

But just why is this argument so revolutionary? Well, if it is correct, then it would at the very least strongly point us to the notion that all living things have moral status merely by virtue of the fact that they are living. This fact in turn, would imply that the typical sentiocentrist ethic of the Vegan movement is radically mistaken, and that we Vegans need to move toward a biocentric or an ecocentric ethic.

In addition, this would also seem to have implications for the question of abortion. For some fetuses, especially early term fetuses, appear to lack the property of sentience

Now the we have laid the argument out and hinted at some of its possible implications, let us think of how we might respond to it. There is one obvious objection, and that concerns those Non-S Humans who are normal humans that are just currently asleep. In this case, the objection would be that the Non-S Human in question has an Aristotelian potentiality of sentience, in much the same way that a person with their eyes closed has an Aristotelian potentiality for seeing.

So far as I have been able to tell, this objection seems plausible. But we must note that it is not so easy when it comes to the other sorts of Non-S Humans, viz. the extreme cases of severe and profoundly disabled people and the comatose. But even in these cases, we can put forth a modified objection. We would say, not that they possess the Aristotelian potentiality for sentience, but that they possess the potentiality simpliciter for sentience, in much the same way as I possess the potentiality simpliciter to read and understand a graduate-level string theory textbook.

However, we still have a defense. We can posit that the Non-S Humans under consideration do not possess the potentiality simpliciter for sentience. This obviously leads us into a consideration of the different types of modality in order to determine just what sort of potentiality is at issue. I don't think that we can say that it is either logically or metaphysically impossible for these Non-S Humans to possess sentience. Physical impossibility is I think much closer to what we need, but I am not prepared to go quite that far. I think what we are after here is biological impossibility. Thus, we can posit that it is biologically impossible for the Non-S Humans to possess sentience, meaning by this that their possessing sentience is not consistent with the facts of human biology.

Now, we might have a hard time conceiving of how this could apply to a extreme severe and profoundly disabled person, so let us just focus on the case of the comatose person. In other words, what we are dealing with is a human that is irreversibly comatose.

So now that we have that in focus, the real question we must consider is: would it be wrong for someone to mistreat this human in anyway they please? For instance, to rape them?

To avoid some possible objections, we will say that the irreversibly comatose human has no friends or family members and that there is no way that anyone could find out that they had been raped.

Now to me, at least on a first approximation, it appears that it would be a profound moral injustice for someone to rape an irreversibly comatose human. But, and here is the catch, it seems to me that doing so would be to directly wrong the comatose human.


This seems to be the central issue on which the entire argument rests. Now of course, someone very well might respond to my intuition by pointing out that raping an irreversibly comatose human cannot be a direct wrong, because there is no center of experience that can be the object of the wrong. In other words, there is no 'person' as such that can be wronged.

Taking this response into consideration, I think that the ultimate conclusion that we draw from this argument will depend on our answer to a further question, namely: Does the existence of value as such necessarily depend upon the existence of a valuer?

The way I would like to approach this question is by an analogy. Let us suppose for the sake of argument that there is an afterlife. Let us also suppose that you had undergone a terrible accident that left you irreversibly comatose. After some time, you pass away and you enter the afterlife state. Upon entering this state, you are informed that some time after you had become comatose, a person had sexually assaulted your body. How would you react to this shocking information? Would you say that you yourself had been morally wronged? Or would you react with indifference, since you were not subjectively harmed in anyway by this event?

From my point of view, I am sure that I would very definitely find that I myself had been morally wronged, and it is my strong suspicion that many other people would agree with me on this. However, I should say though that it is not at all clear to me that non-sentient living beings should be given the same moral consideration as sentient living beings. Perhaps the sentiocentrist is definitely gesturing at an ultimate truth, namely that sentience, though not the only determiner for moral status, definitely places one higher on the totem pole than a merely living item.

Or perhaps the argument presented above is just mistaken and sentience is in fact the sole determiner. If that is the case, I would love to hear your objections to the argument.

A Critique of Ecological Animalism

In this post, I would like to offer a critique of Val Plumwood's philosophical theory called ecological animalism, which she formulated in an attempt to address the human relationship to other animals and to the environment. The theory can in many ways be best understood by contrasting it to what Plumwood calls ontological veganism, so we will start our discussion there.

The term 'ontological veganism' really just denotes the common variants of animal rights philosophy. The idea here is that we find some property the possession of which would accord moral standing to any item that possesses that property. In this context, the property in question is usually something like 'sentience' or 'being a subject-of-a-life'. Once we establish this, and once we recognize that all (or nearly all) animals possess this property, we then conclude that animals are not food and are not to be exploited by humans.

But, so Plumwood argues, taking this notion on board actually serves to reproduce the human/animal duality that vegans are trying to avoid. For if animals are not food, and if we condemn humans for consuming them, then why do we not also condemn carnivorous animals for doing the same thing? If we answer this question by saying that such animals are a part of 'nature', and humans are a part of 'culture', then we have quite seemingly just erected another duality between the two.

This is where Plumwood's theory comes into play. ecological animalism, she claims, avoids such dualities by placing humanity right back into the fold of nature. For her, all natural items are deeply interdependent upon one another and must of necessity make use of one another. Just one among many of these uses in that of consumption. In some situations, humans have no choice but to do this. Conversely, other animals must sometimes consume humans. Thus humans are at the same level of importance as the other animals, and like the other animals, they can also be food.

My critique of this view will take the form of a reductio ad absurdum. To begin, let us consider a widespread behavior within the animal kingdom; namely that of sexual coercion. This is a behavior that has been observed in numerous animal species (those who doubt this should check the wikipedia article here for the references). But the interesting thing to note here is that if a human commits an act that would qualify as sexual coercion, then we would say that the human has committed rape, and thus they have committed a moral transgression. The reason we say this is because we consider all sentient beings or all subjects-of-a-life to be not the kind of items that can be sexually assaulted.

But if sentient being/subjects-of-a-life are not the kinds of objects that can be sexually assaulted, and if we condemn humans for committing this act, then why do we not condemn the other animals for doing the same thing? If we answer this question by saying that such animals are a part of 'nature', and humans are a part of 'culture', then we have just erected another duality between them.

Therefore, if we are beholden to ecological animalism, we should just get rid of this otiose duality and place humans right back into the fold of nature. Indeed, we must recognize that there are certain times when species must make use of one another for the purpose of procreation, and this might require them to commit sexual coercion. Thus, we should discontinue punishing rapists and other assorted sex offenders.

If it is not clear at this point, ecological animalism has one key flaw that very well might be fatal: namely, it does not give due consideration to moral agency. Indeed, to say that the Vegan's response to the question concerning why we do not condemn carnivorous animals is merely that they are not a part of culture, the ecological animalist has committed a strawman fallacy. For this is not anywhere near the strongest reply we can give, as any requisite analysis will demonstrate.

In fact, the appropriate response that the vegan should give is to point out that most human beings are moral agents, while all nonhuman animals (so far as we can tell) are not. This is the key difference at issue. For if a being lacks any understanding of right and wrong, and thus is incapable of making moral judgments, then it is analytically true that they cannot be held accountable for their actions. This is precisely why vegans do not condemn carnivorous animals, because to do so would be entirely nonsensical.

But we should also note that this is not a human/animal duality, for some actual humans lack moral agency, and just like the other animals, these humans also cannot be held accountable for their actions. There might be a worry about the harmful effects of a potential moral agent/non moral agent duality, but I think we can avoid this altogether by carefully avoiding any assertions that would entail the superiority of moral agents over nonmoral agents.

Meinongianism and Platonism

I have recently been reflecting on an objection to Meinongianism that I have encountered on occasion (cf. David Lewis 'Noneism or Allism?' for just one example), and that is the notion that the Meinongian is trying to have his cake and eat it too. In effect, the objection here states that the Meinongian is quantifying over and making theoretical use of a plenitude of objects, but avoids the requisite ontological commitment to these objects by holding that they do not exist. In effect, the Meinongian is doing nothing more than playing a word game.

If we wholeheartedly accept the current Quinean dogma in contemporary Meta-Ontology, then this would certainly be a natural objection. But what I would like to do is to turn this objection on its head and demonstrate how we can raise the very same sort of worry with regard to the Platonist.

The Platonist, for those who don't know, believes that, in addition to the singular concrete objects of the everyday world, there exist untold infinities of 'abstract objects' (such objects might include Numbers, Universals, Propositions, States of Affairs, etc.). What distinguishes these abstract objects from the aforementioned concrete objects is that, while concrete objects are always spatio-temporally locatable, abstract objects exist beyond space and time. 

This view is certainly well-established within the history of Philosophy, but it does appear rather strange sounding at first glance. For if someone were to inform us that an object such as Bigfoot exists, we might very sensibly want to ask 'Where does Bigfoot exist?' If we were told that Bigfoot does not exist anywhere in the universe, we might feel that our interlocutor was using the word 'exist' to mean 'timeless existence.' Realizing this, we might then ask him 'Well then, at what time does Bigfoot exist?' If he responds by saying that 'Bigfoot does not exist at any point in time, for he is an abstract object!' we would most likely feel that the wool has been pulled over our eyes.  Surely to claim that an object exists nowhere and never is the same thing as to say that it does not exist at all. And since the Platonist makes the exact same claim regarding all the endless abstracta, should we not then conclude that the abstracta also do not exist in any way?

(For clarification's sake, let us call the Platonist view of Ontological Commitment the Quantificational View, and let us call the view we have just adumbrated the Spatio-Temporal View, for obvious reasons).

Of course, a standard reply that the Platonist might make at this point is to say that "While abstract objects surely do not exist in our physical universe, they nevertheless do exist in the Realm of the Forms." But this can't be right, for to say that these objects exist 'in' the Realm of the Forms is already to imply that they are spatially located somewhere.

So is it not already apparent how we can apply the same sort of reasoning to attack the Platonist? For at least according to one plausible way of looking at things, the Platonist is doing nothing more than playing a word game. The Platonist has denied both of the factors that are used in determining existence (at least according to the Spatio-Temporal View). So we can very easily say that he has actually denied the existence of abstract objects, but in order to hold on to his pristine Platonic Heaven, he has inexplicably claimed that these abstract objects still somehow exist. Quite literally (to adapt a phrase from David Lewis) he has 'affirmed existence without affirming existence.'

In closing, what I would like to get across with my observations is that the objection that the Meinongian is playing a word game holds no water as of yet, because as has just been demonstrated, the same sort of remark can be made towards the Platonist. What is actually needed is a solid argument in favor of the Quantificational View and also a demonstration that something like the Spatio-Temporal View is incorrect. Modern classics like 'On What There Is' and 'Noneism and Allism' contain only dogmatic assertions, and thus are not fruitful places to look for the requisite arguments.

Finishing the Fifth Corner of Four

I have now finished reading the Fifth Corner of Four. The final three chapters of the work are particularly interesting because Graham Priest uses the Plurivalent Logical tools he has already adumbrated to provide a formal analysis of the Jinzang Hierarchy, the Net of Indra, and the notion of Enlightenment (especially how it relates to the work of Dogen).

Now these sections of the work started to drift away from my areas of specialization, but it was clear from my reading that Buddhist metaphysical issues can be given a rigorous logical grounding. Take the Jinzang Hierarchy for instance. This concerns the notion of transcending dualities in order to reach Ultimate Reality. Say we have some true description P of Conventional Reality. Since we know that Ultimate Reality is ineffable, we must conclude that ~P is true of Ultimate Reality. But we have already concluded earlier that Ultimate Reality is ineffable, and ~P is just as conceptual as P. Therefore, we must conclude that we are actually also describing conventional reality with the sentence ~P. Thus, the compound proposition P & ~P is true of Conventional Reality.

So to throw off this additional conceptual fetter, it is only natural to conclude that neither conjunct is true of Ultimate Reality, in other words ~(P & ~P) is true of Ultimate Reality. But this is still just another concept, so it too must also describe Conventional Reality. Thus (P & ~P) & ~(P & ~P) is true of Conventional Reality. But then we must negate this new compound proposition in order to reach Ultimate Reality, and so on, ad infinitum.

What Graham Priest concludes from all of this is that the transcendence of all dualities is not a final state that must be reached, but an ever continuing process up the hierarchy. Priest connects this result to the view of enlightenment broached by the Japanese philosopher Dogen. For Dogen, enlightenment is not some ultimate state that must be reached after a long and arduous regime of disciplinary practice, rather, enlightenment is already here, right before our eyes. Indeed, while the notions of samsara and nirvana are useful notions for the practitioner, we can only be enlightened once we see that they are actually one and the same. To borrow a metaphor from Wittgenstein, they are like a ladder which once climbed, must be thrown away.


So to conclude, I would highly recommend this book to anyone interested in Logic or Metaphysics. I would recommend it in particular to 2 classes of people: Firstly, I would recommend it to those who might not be familiar with Buddhist Metaphysics. Secondly, I would recommend it to those who might be curious regarding the applicative capabilities of Non-Classical Logics.

But one thing that especially shines through in my opinion is the perennial usefulness of First Degree Entailment, which Priest makes quite patent throughout the course of the book. Anyone familiar with Non-Classical Logics is certainly aware that FDE can be a base system for a wide variety of other systems of logic. These systems can be reached either by tweaking the truth values (a la K3, LP, Classical Logic, and FDEe) or by adding on a suitable conditional (a la N4 or the Affixing Relevant Logics). This being the case, I think we might be justified in concluding that FDE provides the true 'basement level' consequence relation (to use a term of JC Beall).

I certainly plan on continuing my study of Buddhist Philosophy, and I am now confident that FDE and FDEe are the perfect tools for logical analysis in this endeavor.

Continuing on in my reading of the Fifth Corner of Four

I have now gone deeper into my reading of The Fifth Corner of Four. Graham Priest has now touched upon the Paradox of Ineffability. For those who don't know, this arises when we attempt to say that some part of reality cannot be talked about and we give reasons why it cannot be talked about, but in the course of giving those reasons we inevitably talk about that which cannot be talked about. In other words, the ineffable is indeed effable.

Anyone familiar with the history of Philosophy should recognize this dilemma from the works of such gigantic figures like Kant, Heidegger, and Wittgenstein. Now the Paradox of Ineffability cannot be adequately dealt with using the system FDEe that I alluded to in the last post. For if a state of affairs is both effable and ineffable, we cannot just give that state of affairs the value e, because even though that does describe one facet of the situation at hand (namely its ineffability), we have to remember that the paradoxical state of affairs is also effable. So perhaps we should just give the state of affairs the value b? That won't work either, for while a state of affairs with such a value is certainly effable, it is not ineffable. Similar reasoning applies to all of the other cotis.

So a natural thought might be to just add a sixth coti, called 'P', that means something like 'both effable and ineffable.' But this solution is inadequate. For suppose that a certain Philosopher was to say something like the following: 'Ultimate Reality is ineffable because it is beyond all conceptual understanding and dualistic thinking.' This obviously leads to the Paradox of Ineffability, and thus it would be correct to say that Ultimate Reality under this picture is both effable and ineffable. But this isn't the end of the story. For what would be the value of the state of affairs described by the following sentence: 'Ultimate Reality is beyond all conceptual understanding?' Obviously, it has the value e (since all states of affairs that include Ultimate Reality are ineffable), but some thought into the matter makes it clear that it also has the value 'b'. The reason for this is that the sentence in question must describe a true state of affairs (since being beyond conceptual understanding is one of the reasons that Ultimate Reality is ineffable), but the state of affairs it describes is also False since we can conceptually understand that Ultimate Reality is beyond all conceptual understanding. So it would appear that the state of affairs in question has both the value e and the value b.

In order to accommodate this insight, Priest makes use of Plurivalent Logic. Plurivalent Logic is unique among Non-Classical Logics because instead of forcing wffs to be assigned only one truth-value, it allows wffs to be assigned more than one truth-value. The main technical trick that allows one to achieve this is making use of a relation between wffs and truth values, rather than the standard functional assignment of wffs to truth values.

When we do this, we can very easily accommodate the fact that sentences describing states of affairs can have more than one truth value, and thus we can solve the Paradox of Ineffability.

As a side note, one quite surprising feature of Plurivalent FDE is that it has exactly the same theorems as the Many-Valued FDE. So this means we can simply bring over all the deductive apparatus of FDE when applying our new semantical modeling.

Meinongianism, Noneism, Radical Noneism

In this post, I would like to describe three closely related Philosophical theories, viz. Meinongianism, Noneism, and Radical Noneism. Collectively, we might refer to all of these schools of thought as belonging to the Philosophical field known as object theory, or item theory. I should also like to lay out the features of these theories that I find attractive and the reasons why I personally am a Radical Noneist.

Meinongianism is a wide ranging theory encompassing every subdiscipline of philosophy. Its comes out of the work of the severely underappreciated Austrian philosopher Alexius Meinong. It is based on several important theses. Firstly, it holds that everything whatever is an object. This feature distinguishes Meinongianism from other schools of thought that either do not include objects at all, or do not take everything to be an object. Secondly, it holds that many objects do not exist, and among those objects that don't have existence, some have a lower form of being called subsistence (like numbers, universals, properties etc.) and others have a 'being-like' property called absistence (like fictional characters and impossible objects). Last but not least, it holds that nonexistent objects possess properties and true statements can be made about them.

We should quickly note that since nonexistent objects are given standing in Meinongian theory, the traditional philosophical subfield of Ontology is extended into Sistology. Sistology is the field of enquiry that investigates all objects, whether existent, or nonexistent; Ontology, as the field concerned with the study of all existent objects, is included within Sistology.


Noneism is a closely related theory that builds off of Meinongianism in 2 different ways. It agrees with Meinongianism in holding that everything whatever is an object. It also agrees that very many objects do not exist, but Noneism does not recognize the notions of subsistence and absistence. For the Noneist, if an object does not exist, then it does not have any kind of being at all (This idea goes back to the work of Thomas Reid). Noneism also holds that nonexistent objects can have properties and that true statements can be made about them. The other change that Noneism brings to bear upon Meinongianism is that it situates nonexistent objects within different worlds, both possible worlds and impossible worlds. So for example, Gandalf is a nonexistent object that is a part of the world that realizes the Lord of the Rings stories. Crucially for the Noneist, inconsistent objects, like the round square, are part of impossible worlds where the laws of logic are different.

Radical Noneism has exactly the same principles as Noneism, but with only one difference: namely, for the Radical Noneist, the actual world is inconsistent. This being the case, the Radical Noneist locates some inconsistent objects within the actual world.


Now to the benefits and drawbacks of the theories. Meinongianism has numerous theoretical virtues to it's credit, including scope, explanatory power, and adherence to the data. But more importantly, Meinongianism resolves a number of long-standing problems in Philosophy. The first of these problems does not have a name in the literature (as far as I am aware), but it concerns the paradox of describing something as not being an object. Gottlob Frege and Alfred North Whitehead are 2 notable Philosophers that ran into this problem. For Frege, the world is split up into 3 different kinds of things: objects, concepts, and names. Consequently for Frege, concepts and names are not objects. But this leads us straight into a paradox, as Frege himself recognized. For if we say that 'A concept is not an object', we are treating a concept as if it were an object. Frege was never able to get around this problem and was eventually forced to say that natural language does not allow him to properly express what he means in this case.

Whitehead ran into a similar problem. For Whitehead, there really are no such things as objects at all, only what he called 'processes'. But again, just as with Frege, if we say that 'A process is not an object', we are treating a process as if it were an object. There seems to be no way around this paradox for Whitehead.

However, Meinongianism is able to avoid this paradox entirely. Since Meinongianism takes everything whatever as an object, it simply does not run across the problems of Frege and Whitehead. Indeed, even things that are not objects are still considered objects by the Meinongian. So the Meinongian could perfectly well say that 'A concept is not an object', and he could perhaps speak truly by saying this, but he does not run into the paradox because he still takes concepts to be objects (even though they might not be objects).

The second longstanding problem that Meinongianism resolves is the so-called 'Paradox of Non-Being'. This is one of the oldest problems of Philosophy, going all the way back to the days of Parmenides and Plato. The basic idea behind the paradox is that, in order to say of an object that it does not exist, it would allegedly seem to be the case that the object must exist in order for us to say this. Or to put in a more memorable way: "Non-being must in some sense be." This problem has absolutely befuddled many of the greatest philosophers since the earliest days of the subject. But this problem does not even arise for the Meinongian, since he allows non-existent objects to have standing in his theory. Thus, the Meinongian can perfectly well say that a certain object does not exist, without thereby committing himself to the existence of that object.

Meinongianism also has another benefit. As we noted earlier, Meinongianism holds that true statements can me made about nonexistent objects. Thus, if we say 'Unicorns have one horn', we speak truly by saying this. This is quite natural, since if someone were to say 'Unicorns have 17 horns', we would most likely dispute that statement. But mainstream Philosophical theories do not believe that true statements can me made about nonexistent objects. For Parmenides and Plato, all statements about nonexistent objects are meaningless. For Frege and P.F. Strawson, all such statements are neither true nor false. For Bertrand Russell and contemporary Classical Logic, all such statements are false. But these theories are all incorrect. For we can perfectly well understand what is meant by saying 'Unicorns have one horn', to wit, it is ascribing the property of having one horn to every Unicorn. In addition, there have been times throughout history where people have thought that something exists, only to later find out that it doesn't. For instance, luminferous aether. This object was a standard feature of cutting edge scientific theory in the late 19th century. Many scientists did in fact think that such an object existed, only to eventually discover that it does not exist. Should we then say that when those 19th century scientists had made statements regarding the luminferous aether they were thereby talking nonsense? But they perfectly well understood the statements they were making about the aether, and surely it is incoherent to speak of understanding a meaningless statement, since there is quite literally no meaning there to be understood. So it is incorrect to say that such statements are meaningless. It is also incorrect to say that it is either false or neither true nor false; because we can actually provide evidence that Unicorns do have one horn, for example by consulting the relevant folk and mythological traditions and the relevant texts. Thus, Meinongianism admirably fits perfectly with the data on this point. Some people might respond to this by saying that merely consulting folk traditions and textual sources is not sufficient evidence to determine the truth-value of statements concerning nonexistent objects. However, if this were true, then all historical investigation of ancient people and cultures is thereby illegitimate, since in many cases these disciplines must rely on folk traditions and textual sources.

But Meinongianism has 2 major difficulties. The first difficult concerns how to make sense of subsistence and absistence. What does it mean to possess a 'lower level of being' than ordinary existence? What is meant by saying that absistence is 'being-like'? Also, quite apart from the interpretational difficulties involved with these notions, they complicate our logical theory by introducing two new primitives. We would do well to simplify the theory if at all possible. The second difficulty is in my opinion more damaging. Meinongianism locates every nonexistent object within the actual world (along with all the existent objects). But this leads to numerous problems, for take a nonexistent object such as Bigfoot. Even though this object does not exist, we can truly describe it as being located in the Pacific Northwest. But, and here is the kicker, if we were to conduct an exhaustive search of the Pacific Northwest, we would not find any such creature. The situation is similar with many fictional stories that take place in real locations in the actual world.

But there is also a more troubling facet of this problem, and that concerns impossible objects. Since impossible objects are given standing according to Meinongianism, and since impossible objects are located in the actual world, it follows that the actual world contains both incomplete and inconsistent objects. Whether this is considered to be a problem will of course depend on one's view of logic, but for many this implication would count against the theory. Thus it would seem that many nonexistent objects cannot be located in the actual world if they are to properly perform the needed work in logical theorizing.


Noneism does not run into the 2 aforementioned problems. Firstly, the Noneist does away with the notions of subsistence and absistence entirely. For the Noneist, an object either exists or it does not, full stop. This greatly simplifies our logical theory. Secondly, Noneism duly locates every object within either a possible or an impossible world (Note: This does not mean that every object is located in a unique world. Some nonexistent objects can be a part of the same world) Worlds, both possible and impossible, are another sort of nonexistent object for the Noneist. The role they play is in smoothing out the logical geography of Sistology. Since the Noneist locates Bigfoot within a possible world we can coherently say that 'Bigfoot is located in the Pacific Northwest', because what we mean by this is that if the possible world that contains Bigfoot existed, we would find Bigfoot in the Pacific Northwest region of that world. Noneism also allows us to avoid the problem of impossible objects populating the actual world by placing those objects in the appropriate impossible worlds.

Noneism does have one glaring weakness though, and that is that it does not have anything to say about the logical paradoxes of self-reference. There are a large number of these paradoxes, but perhaps the most famous example of that of the Liar Sentence. Put quite simply, the Liar Sentence says the following: "This sentence is false". This immediately leads us into a paradox, for if the sentence is false, then the sentence is actually true (because it says that it is false). But if the sentence is true, then it is actually false (because it says that it is false). So the sentence seems to be both true and false.


One might think that the Noneist can accompany the Liar Sentence by locating it in the appropriate Impossible World, but this does not help matters because the Liar Sentence is surely a part of the Actual World, and the Noneist (like the Meinongian) does not allow for contradictions to inhabit the Actual World.

This where Radical Noneism comes in. As I mentioned earlier, Radical Noneism is exactly like Noneism, except that it holds that the Actual World is inconsistent. By doing this, it is able to accept that the Liar Sentence is both true and false in the Actual World. This means that Radical Noneism provides a uniform solution to the paradoxes of self reference, since they all have essentially the same logical structure as the Liar Sentence

Now Radical Noneism has one big limitation, namely, it does not provide a solution to the Paradoxes of Implication. However, dealing with these paradoxes takes us outside of the realm of object theory. In particular what is needed is a Relevant Logic, and in particular a Deep Relevant Logic (since the main systems of Relevant Logic do not solve Curry's Paradox).


So to conclude, we can see the appeal of all 3 of these theories. They are all very powerful and work very effectively in areas where mainstream philosophical theories have considerable difficulties. However, it is my opinion that Radical Noneism is the best of the 3. Radical Noneism, duly combined with a Deep Relevant Logic, promises to be a universal paradox solver and that cherished goal of many Philosophers, a true theory of everything.

Beginning the Fifth Corner of Four

I have begun reading the new book by Graham Priest called The Fifth Corner of Four. This book covers both Buddhist Logic and Metaphysics, and particularly the philosophical import of the Catuskoti. The Catuskoti, for those who don't know, is a principle within Buddhist logic that allows for any proposition to have one of four values: True only, False only, Both True and False, and Neither True nor False.

Of course, in all the Aristotle-related systems of Logic (such as Classical Logic) only the first two cotis would be considered live options. This means that any attempt to interpret the Catuskoti from such a framework will be doomed to failure. However, we can very easily capture the logical structure of the Catuskoti by appealing to the simple Relevant Logic called FDE ('First Degree Entailment').


Now, where the title of the book comes in is to explain certain rather odd passages in the Buddhist literature which seem to indicate that the Catuskoti is not applicable to certain questions concerning the nature of ultimate reality. These passages can obviously not be captured by using FDE, but as Graham Priest has alluded to in previous work, we can adequately capture them by adding a fifth, 'Bochvar-style' truth-value to our system. The main effect that this has on the deductive capacity of the apparatus is to invalidate the rule of Addition (although there is a way that we can regain a variant of this rule with some suitable refinements).

I am very interested to see how this work will turn out. However, what I am particularly interested to know is what is the correct system of Relevant Logic to capture the higher-degree inferences of Buddhist philosophy. We can see on the Stanford Encyclopedia of Philosophy article for Logic in Classical Indian Philosophy that:

"Many of the arguments formulated in these texts correspond to such well recognized rules of inference as modus ponens (i.e., from α and α→β, one infers β), modus tollens (i.e., from ¬β and α→β, one infers ¬α), disjunctive syllogism (i.e., from ¬α and α∨β, one infers β), constructive dilemma (i.e., from α∨β, α→γ and β→γ, one infers γ), categorical syllogism (i.e., from α→β and β→γ, one infers α→γ) and reductio ad absurdum (i.e., if something false follows from an assumption, then the assumption is false)."

Of course, the minimal system needed to capture these rules of inference is N* coupled both with a Reflexive accessibility relation on at least the actual world, and with an Intensional Disjunction to accommodate Disjunctive Syllogism. I am particularly interested to know whether the Buddhist logicians would have accepted the principles of Prefixing and Suffixing, and thus the Relevant Logic B.

However, it really remains to be seen whether they would have accepted the Exported form of Categorical Syllogism. One would hope not, since that would lead to the problem of incompleteness in the Routley-Meyer semantics.