Tolerating Trivialism

C.A. Postlethwaite

Abstract

Engaging with trivialism –the claim that every proposition is true– might eventually be as productive for philosophy as confronting skepticism[1]. Yet trivialism is largely ignored in the current literature. For trivialism to join the contemporary philosophical conversation, grounds for engaging with the trivialist must override trivialism’s absurdity. If, like skepticism, trivialism can be rejected and still be seen to present our consensus view with a plausible analogous challenge, then philosophy should engage with trivialism. In his doctoral thesis ‘A Defense of Trivialism,’ Paul Kabay (2008) proposes that the world appearing consistent is not good reason for concluding that reality is consistent. The possibility of a contradictory world putatively serves as an analogous challenge to our current metaphysical consensus view. In this essay, I present an extraction of the argument and evaluate the argument’s success in providing motivation for tolerating trivialism. Then I give an argument of my own supporting trivialism’s acceptance into contemporary philosophical discussion.

 

Introduction

Absurd claims should be rejected, but rejecting an absurd claim does not necessarily entail that the position that supports said claim should be ignored. An example of a position that is almost universally rejected and has considerable presence in the philosophical literature is skepticism. I propose that the reason for engaging with skepticism has a parallel in trivialism –the claim that every proposition is true–. A reason for engaging with skepticism is that skepticism proposes what C.J. Hookway (2005: 838) calls an ‘analogous challenge’ to a commonly held view about knowledge. Trivialism proposes an analogous challenge to a commonly held view about reality, since every proposition being true entails that the world is inconsistent. Paul Kabay (2008) offers an argument that reality could be contradictory and still appear consistent. If the argument holds, it offers support to an analogous challenge that threatens our consensus view of reality, which denies that the world is contradictory. If the parallel between skepticism’s challenge and the challenge offered by trivialism is appropriate, then trivialism should acquire a more prominent role in current philosophical discussion, since trivialism currently enjoys little, if any, treatment in the contemporary literature.

In continuation, this introduction exposes the absurdity of trivialism and provides motivation for engaging with trivialism in the face of very strong objections to do so. After the introduction, I offer a charitable extraction of an argument put forth by Paul Kabay (2008) in his doctoral thesis ‘A Defense of Trivialism’. Kabay’s argument attempts to prove that reality might be inconsistent, even if it appears otherwise. I provide an analysis of the argument and conclude that Kabay’s argument is easily defeasible under the most widely accepted logical system. Still, the argument may be successful under alternative logical systems that have some support in the current philosophical landscape. Readings from both logical perspectives will be provided. Finally, I will consider the significance of Kabay’s argument towards the purpose of attracting interest in trivialism and offer reasons for current philosophers to engage with trivialism.        

Trivialism’s absurdity can be quickly placed into sharp relief. From the consensus view[2], a trivialist must be either wrong or right about trivialism. But from the trivialist’s point of view, a trivialist is both wrong and right about trivialism. The trivialist agrees with all propositions, regardless of whether those propositions support or reject her position. For the trivialist, it is true that she is wrong and that she is right about trivialism. The trivialist holds that there is no alternative position to trivialism, since the trivialist embraces every opposing view to her stance as well as every supporting view. The trivialist agrees with anything that we assert against her position. She agrees that trivialism is false, but she also agrees that trivialism is true. The trivialist thinks that trivialism is consistent and she thinks that trivialism is inconsistent. The trivialist holds that inconsistency is grounds for accepting trivialism, and also that inconsistency is grounds for rejecting trivialism. Not only does the trivialist agree to any proposition made in regards to trivialism, she agrees with absolutely everything that is uttered and that can be uttered about anything. The trivialist believes water is H₂O and she believes it is not the case that water is H₂O. She believes that a bachelor is a married under-aged wombat and that the King of America is bald and also has long curly locks. The trivialist believes that shouting gives rational justification to a belief and that false beliefs are true beliefs. But the trivialist also believes all our commonsensical and logical assertions. In short, the trivialist asserts every proposition (including every proposition’s opposite). Two lessons can be reached from this paragraph: trivialism should be rejected on grounds that it entails contradictions, and arguing with the trivialist is futile.

But the enounced lessons of the previous sentence could well have been about skepticism. Supporting skepticism may imply that we know that we cannot know: which is a contradiction. Also, the skeptic will claim that we are not certain about anything. Any reason given will have no purchase with the skeptic, rendering her stance unmovable. Philosophers are inclined to reject skepticism and recognize skepticism’s unbeatable status.[3] Yet skepticism’s challenges are abundantly confronted in the literature. Rejecting skepticism and recognizing the futility of arguing against the skeptic doesn’t stop philosophers from answering the skeptic’s challenges. Trivialism is similar to skepticism in being almost universally rejected and a position that is very hard to argue against. To summarize, it is possible to reject trivialism and admit the trivialist’s intractable status, and still think that engaging with trivialism can be fruitful for philosophical enquiry. I hope that it is clear that it is possible to engage with a position we reject. The question is whether there are reasons for bringing trivialism into the current literature, even if we reject trivialism and admit the ineffectiveness of our arguments against the trivialist. The next paragraph will try to show that it is not just possible, but also reasonable to engage with trivialism.    

There is an abundance of philosophical writings that engage with skepticism, while the number of papers on trivialism in the Philosopher’s Index is in the realm of the single digits.[4] An example of a skeptical position addressed in the literature is that our experience might not be what we take it to be, but rather that our experience is the result of a computer stimulating our brains. Following C.J. Hookway (2005: 838), I consider artificial brain stimulation to be an “analogous challenge” to the consensus view that our experiences are caused by the external world. An analogous challenge is an alternative explanation to a commonly held view. For many years, the work of philosophers in response to skeptical analogous challenges has led to fruitful investigations about beliefs, justification, interpretation and method of inquiry, among others.[5] I suggest that trivialism offers an analogous challenge to our consensus view of reality, a challenge similar to skepticism’s analogous challenge of our experience. In particular, trivialism posits that reality is such that everything that we can ever say about reality is true. Trivialism seems to entail that even if we utilize all of our currently available recourses for accessing reality (perception, reason, intuition, memory, testimony, consciousness, science, you name it…) we still arrive at only a partial view of reality. If trivialism is correct, then all currently held views about reality are true, yet incomplete. As Paul Kabay (2008: 19) states: “If trivialism is true, then reality consists of the greatest possible totality –a totality so inclusive that it includes everything, even its opposite.” This presents an analogous challenge to our view of reality which -like skepticism’s challenge- is difficult to defeat. For reasons we saw above, once the trivialist is in position, we cannot convince her to only deny trivialism, as the consensus view demands. Much like we can never get the skeptic to admit that she at least knows that she cannot know. Philosophers that engage with skepticism presumably do so because they think it would be irresponsible to ignore skepticism’s challenges, however untenable the analogous challenges may be. The question is whether ignoring trivialism is prudent for philosophers, who “seek an overall assessment of [their] cognitive position”[6].

A reason to consider accepting trivialism into the philosophical conversation is that trivialism entails an analogous view of reality which is hard to defeat, much like skepticism’s analogous view of experience. If skepticism’s analogous challenge is answered in the literature, trivialism’s challenge could be accepted on the same grounds, even if both trivialism and skepticism are rejected, and their respective advocates are admittedly impossible to defeat. An important difference between the analogous challenge of skepticism and the analogous challenge of trivialism, is that skepticism’s postulate is pertinent to epistemology, while trivialism’s challenge pertains to metaphysics. With this paragraph, I nominate the metaphysical view derived from trivialism as a candidate for overriding trivialism’s absurdity, and as an incentive for encouraging philosophers to admit trivialism into the philosophical conversation. Paul Kabay (2008: 134-167) sets forth an argument that, in case the argument is successful, may provide support for the analogous view of reality. Kabay’s point[7] is that reality can be perceived as fully consistent, even if the world is contradictory, as trivialism entails. An extraction of this argument[8] is presented further ahead.  

Even after all that has been said in the preceding text, denying trivialism a place in the philosophical discussion may still be the most viable option. Justification for shutting out trivialism should not even be necessary. As opponents of trivialism, we could simply ignore trivialism. Our silence provides proper justification, since it would be irrational to provide reasons for refusing to engage with a position that asserts that we are scrambled eggs (amongst other even more intolerable assertions). Not engaging with trivialism is the quickest and most effective way to keep trivialism out of the philosophical discussion. Of course there are philosophical reasons to justify our silence, but we should not provide those reasons. If we explain why we ignore trivialism, then we are engaging the conversation that we aim to avoid. If we give our reasons to evade trivialism, then anyone that is interested in trivialism could evaluate our motives, and so trivialism will have found its way into the discussion despite our goal to keep trivialism out.

I am at an impasse concerning the position to not engage with trivialism. I cannot bring myself to reproach the position to ignore trivialism. The silent objector to trivialism finds the position abhorrent and, if she will not speak, then I must guess her reasons for not engaging with the trivialist. Presumably, her grounds for rejecting trivialism are so strong, that even attending to the trivialist is out of the question. Reasons this strong could be located in what were traditionally called the laws of thought and the logical laws, of which I will talk in the vocabulary section below. The strongest reason for not letting trivialism passed the gate can be found in trivialism’s violation of the Law of Noncontradiction (LNC). It may seem that we confronted this issue above, when we traced trivialism’s absurdity to the contradictions that trivialism entails. But a distinction should be drawn between violating the LNC (which is as an underlying rule of reality and of logic)[9] and violating common sense intuitions that we get from our ordinary sense of the world. We previously spoke of contradictions as grounds for trivialism’s absurdity, but this was based on common sense observations that ridiculous states of affairs do not obtain in reality. Rejecting trivialism on these grounds is similar to rejecting the fact that space curves and contracts. In modern physics, relativity theory has proven that the physical space that a mile occupies actually gets longer the slower the observer travels. Such a violation of common sense could be seen as absurd, but it can still be true. A trivialist could argue that violating common sense in this degree is not a good reason for rejecting trivialism. An opponent to the trivialist could posit that the impossibility of contradictions holding is a priori, unlike the truth about space. But I leave arguments about rejecting or supporting trivialism for another occasion. Today we aim to argue that even if rejecting trivialism is the right option, engaging with trivialism is still rational. Furthermore, our evaluation of trivialism no longer contemplates contradictions as violations of ordinary appearances, but as violations of the LNC, which Aristotle proposed as the firmest of all principles. Graham Priest (1998: 91) states concerning the LNC, that “nearly every Western philosopher and logician has deferred to the authority of Aristotle on this matter”. There are two suggestions that I offer the silent objector, whose grounds for maintaining silence is that trivialism violates the firmest law of reality and logic. The first suggestion merely repeats what has already been said about not confusing grounds for rejecting trivialism with grounds for not engaging with trivialism. I posit that this suggestion still holds, no matter how strong the rejection, though I am inclined to think that the trivialist’s challenge to our consensus view of reality will not be strong enough to override the degree of absurdity entailed by the violation of the LNC.

The second suggestion for the silent objector to trivialism is to consider, as many philosophers do these days, the truth of some (but not all) contradictions. It is very odd that, even with all the certainty the LNC exerts, “there is hardly a defense of the Law [LNC] since Aristotle, worth mentioning”[10]. Indeed, Aristotle himself says that the LNC is so evident that it is “not susceptible to demonstration”[11]. Even J.C. Beall (2000: 16), in his article opposing the existence of contradictions in the observable world states that “there seem to be very few good arguments to back the thesis that no contradiction could be true”[12]. The lack of arguments defending the impossibility of contradictions, coupled with obvious candidates for true contradictions, has led to the development of Dialetheism. Dialetheism is the position that some contradictions are true. An example of a true contradiction, for a dialetheist could be something like the proposition: “I can say with words that it is not the case that I can say with words”, which is a rather stiff version of several common expressions that we use when an experience seems to be beyond the capacity of our words. We often use words to express that something is not expressible in words, which is a contradiction. The dialetheist holds that this contradiction should be taken to be true by our logical system. There are other heftier motivations for being a dialetheist. I just wished to provide a quick and accessible example. Logicians have developed alternative logical systems in order for the dialetheist to support her view that there are true contradictions. A paraconsistent logic is a logical system whose inference rules are such that they allow contradictions to be true without resulting in trivialism.

A philosopher who refuses to engage with trivialism, presumably will not be a dialetheist or subscribe to paraconsistent logic. It’s rational to assume that trivialism’s silent objectors are committed to orthodox logic. Modern, orthodox logic asserts that the only correct stance concerning a proposition’s truth value is that every proposition must be either true or false. The trivialist agrees, of course, though not in the way that the consensus view would ratify. For the logical orthodoxy, the trivialist is necessarily wrong when asserting that a conjunction made up of a proposition and the denial of that proposition is true. According to orthodox logic, a conjunction of contradictory propositions must always necessarily be false, a priori. But one does not need to be a trivialist to oppose the consensus view; as one does not need to support the consensus view to oppose trivialism.

Dialetheism, in this sense, provides a middle ground. A dialetheist will deny trivialism, as will a supporter of the consensus view. A dialetheist believes that not all contradictions are true. For a dialetheist, the consensus view that no contradictions are true is wrong, but so is the view that all contradictions are true. A dialetheist is more inclined to engage with the trivialist since the dialetheist cannot shut out the trivialist by stating that a contradiction is impossible. Inviting trivialism’s objector to consider dialetheism could assuage a philosopher who believes that engaging with the trivialist is plain wrong.  

This introduction has attempted to define and situate trivialism and has offered the view that trivialism may be accepted into the philosophical conversation even if one rejects trivialism, and even when one considers the trivialist to be an unbeatable foe. The grounds for engaging with trivialism can be compared with the grounds for engaging with skepticism. Skepticism presents the consensus view about knowledge with a plausible analogous view of knowledge which is not easily defeated, much in the way that trivialism presents our consensus view of reality with an analogous view of reality which is not easily defeated. One reason for thinking that the analogous view supplied by trivialism is plausible is that the analogous view supplied by trivialism is not easily defeated. (I can think of other reasons for the plausibility of trivialism’s analogous challenge. But it is beyond the scope of this essay to develop those reasons. The plausibility of trivialism’s view of reality is topic for another essay. Such an essay would be the best proof that trivialism deserves a place in philosophical discussion.) Lastly, for the philosopher who is not motivated to engage with trivialism at all, two reasons for motivation have been offered. Both reasons respond directly to the specific reason of strongly rejecting trivialism; i.e., trivialism’s violation of the LNC. The first suggestion simply restates the idea to not confuse rejecting trivialism with engaging with trivialism. The second suggestion presents the position afforded by dialetheism and by systems of paraconsistent logic. There are logical stances and systems that might relax the LNC’s constraint on contradictions while still salvaging inference rules and resisting explosion. [13] Openness to either of these suggestions will still allow the philosopher to reject trivialism but will motivate her to engage in fruitful argument with the trivialist’s stance. It is questionable whether the strength of these motivations may override the absurdity of violating the LNC, as interpreted by the uninterested party.

 

Extraction

Vocabulary and Key Concepts

The following section includes basic vocabulary for the topic at hand and for this essay in particular.

• Contradiction: A conjunction that includes both a conjunct and also the denial of that conjunct. Examples: ( and ~) where  is a proposition; (It is raining and it is not the case that it is raining.)
• Inconsistent: A supposed inconsistent state of affairs is one where contradictory states obtain. “It is raining and not raining at the same time in the same place in the same sense”, is a blatantly inconsistent proposition. If the actual state of affairs obtained, then that state of affairs would be an inconsistent state of affairs.
• Consistent: A consistent state of affairs is one where no contradictions obtain. Consider the proposition: “It is true that it is raining and it is false that it is not the case that it is raining” and compare to example above.
• Law of Non-Contradiction (LNC): Aristotle calls it the firmest of principles. “It is impossible for the same thing to belong and not to belong at the same time to the same thing and in the same respect.” IV 3 1005b19–20.[14] Note that in this form the LNC is stated as a metaphysical claim. Purportedly, reality cannot violate the LNC. Metaphysical reality must abide by the LNC. “The opinion that opposite assertions are not simultaneously true is the firmest of all.” Met. 1011b13–14.[15] This second quote is concerning assertions. Its area of influence is what we can and cannot reasonably say about the world.
• Logical laws: Example: LNC, Law of Excluded Middle (LEM), Law of Identity (LI). “If we are persuaded… that Zeno has found contradictions in the concept of motion… we retain the view that things move and look for a consistent theory of motion.”[16] This proposition may well represent today’s consensus philosophical attitude, a very commonsensical disposition.
• Laws of thought:LI, LNC, LEM Thety are “…not often disputed… not descriptive laws, telling how people think, but rather prescriptive, telling people how to think, or more precisely, how to reason.”[17]
• LNC Aristotle: “Nearly every Western philosopher and logician has deferred to the authority of Aristotle on this matter. There is hardly a defense of the Law since Aristotle, worth mentioning.”[18]
• Dialetheism: “A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true.”[19] Motivations to be a dialetheist: Paradox (Russell’s, Liar, Cantor, Infinity, Transition states, Vagueness…)
• Paraconsistent logic: Any system of logic that blocks the principle of explosion. Inconsistency will not spill over into triviality in a paraconsistent logic. For explosion, see below.
• Ex falso quodlibet, Ex contradictione quodlibet, Explosion: Principle of inference that asserts that from a contradiction anything follows. According to orthodox modern logic, if any contradiction were to obtain, then anything (and everything) would follow. One true contradiction is all it takes for everything to be true. So trivialism would be true if one contradiction were true, according to this principle.
  
  

(1)    & ~                          (assumption for CP)

(2)                                      (conj elim., 1)

(3)   ~                                  (conj elim., 1)

(4)    v  y                            (disj. Intro 3)

(5)   y                                    (DS 3,4)

(6)   ( & ~ ) > y               (completes CP)

3 Précis

1^st Précis: Priest (2000) ‘Could Everything Be True?’:
The Case of the Non-Existent Trivialist

Graham Priest (2000: 190) suggests that the only point in arguing directly with the trivialist is to better understand one’s own views. Every position is contained in the trivialist’s beliefs, so there is no way to change the trivialist’s mind about anything. To pit our view against trivialism we assume that our view is correct and present our arguments to an arbitrator. An independent, impartial arbitrator will evaluate between trivialism and nontrivialism and conclude who is right. The rules of engagement are to not beg the question. We cannot resort to pointing to inconsistency or to a contradiction, since it begs the question of the trivialist’s argument. The trivialist will not do well with the arbitrator if she simply states her position that everything is true. So the trivialist will do some independent arguing as well.

The nontrivialist can inflict three weighty consequences to the trivialist’s position. Priest estimates that the most effective of these is to prove that certain features of consciousness entail the “impossibility of being a trivialist”[20]. Hence, there is no such thing as a trivialist and the arbitrator should rule in our favor. Human conscious existence must include that we act (or at least that we believe that we act) to bring things about. But the belief to act to bring something about cannot occur in the trivialist, since whatever will be brought about already obtains for the trivialist. A trivialist would have to be void of the belief that any of her actions will bring something about, and there can be no one that is conscious without the belief that her actions bring something about.

The two lesser inflictions in this paper state that 1) that the trivialist must hold that all physical objects have every tolerant physical property, and 2) that the trivialist must hold that all speech is meaningless babble. It is strange to think that someone would be willing to pay such lofty prices.

2^nd Précis: Priest (1999) ‘Perceiving Contradictions’:
Nearly Provable Real World Consistency

The question whether a contradictory state of affairs can obtain should be an empirical one. One must go out into the world and investigate whether there are such things as contradictions. At the end of the day, we don’t identify any of our perceptions to be of contradictory states of affairs. So there must not be any contradictions.

We know what it is to perceive that it is raining and we know what it is to perceive that it is not raining, but we do not know what it is to perceive that it is both raining and not raining. We know what it is like to “have perceptual experiences the contents of which are contradictory” [21]. Visual illusions serve as examples for the experience of perceiving contradictory situations, so we should recognize a contradictory state of affairs when we see one. The illusions that give the impression of being contradictory are consistent, so it is not clear whether an inconsistent situation will yield the perceptual experience of an illusion. But there is “no cogent evidence that our perception ever does deceive us by making an inconsistent situation appear consistent”[22]. We can also perceive when something is not the case. Since we know what it is to see an inconsistency in some visual illusions, and we don´t see inconsistencies in the actual world, then the actual world is consistent.

3^rd Précis: Beall (2000) ‘Is the Observable World Consistent?’:
Simply Consistent

We can safely conclude that we have not seem any contradictions on grounds of this being the most simple explanation for what we report to observe. Adding a conjunct to our description of an observable situation complicates without adding explanatory power.

Graham Priest (1999) is right in his conclusion that the actual world is consistent, but Priest’s argument is wrong. Priest relies on two premises:

            “(P) If α ^ ⌐ α were ever the case, then it would be seen.”[23] And

            “(O) We have not seen any contradictions (apart from visual illusions, which don´t matter).”[24]

Beall does not grant the truth of O because we might have been exposed to a contradictory state of affairs without seeing the contradictory state of affairs as such. Sometimes a conjunction representing a state of affairs will look like only one of the conjuncts. The following example is offered: Take the obtaining state of affairs that Greg is at the piano and there is an opaque shield surrounding the piano. We are outside the shield, so the state of affairs is seen in a manner that it is described by only one of the conjuncts. In this case: ‘there is an opaque shield surrounding the piano’ is what we see when exposed to the state of affairs ‘Greg is at the piano and there is an opaque shield surrounding the piano’. We are exposed to the obtaining state of affairs described by a conjunction of two conjuncts, but we perceive only one of the two states of affairs. Perhaps when we are exposed to a contradictory state of affairs, each state of affairs interacts with the other in a way that we describe the state of affairs with only one of the conjuncts. It could be raining and not raining, yet it is possible that we perceive only that it is raining, much like the example concerning Greg and the shield.

We don’t know what an inconsistent state of affairs would look like. But explaining that an observable situation which appears consistent is actually an inconsistent situation constituted by that which we observe plus the opposite of what we observe is more complicated than taking the observable state of affairs as consistent. Adding a conjunction complicates our description of a state of affairs without providing any explanatory benefit. The reason for a philosopher to posit the existence of contradictions in the first place was a yearning for simplicity in the non-observable domain. Dialetheism, the claim that there are some true contradictions, “seems to afford a beautifully simple account of natural language”[25]. We must conclude that the observable world is consistent, not based on observation, but because, ceteris paribus, the simpler explanation is superior to the more complicated one.     

 

Extraction

Paul Kabay (2008):
‘A Defense of Trivialism,’ Doctoral Thesis for The University of Melbourne

Key Terms:

• Contradictory state of affairs: A situation expressed with a conjunction of a consistent conjunct and the opposite of that conjunct.
• Causal relationship: A situation that holds between two entities where the changes that occur in one entity are brought about by the other entity.
• Specific content: The type of thing an entity is, together with the particular features that constitute the entity.
• Perceptual state: The situation that holds in an observer pertaining to an observation.
• Observable state of affairs: A situation which we can pass judgment on by means of physical evidence. When Sherlock Holmes infers from looking at Dr Watson’s muddy shoes that Watson went to the post office, the state of affairs (that Watson was at the post office) is an observable state, even if indirectly observed.
• Observable contradiction: Other things being equal, an observable state of affairs that could be described by a contradiction.
• Contradiction: A conjunction that includes both a consistent conjunct and the denial of that conjunct. Examples: ( and ~) where  is a proposition; it is raining and it is not the case that it is raining.

 

Developed extraction

(1) We are exposed to an obtaining contradictory state of affairs (C). (Assp for CP)

• C could be directly observable or indirectly observable, as long as C is successfully described by a contradiction and C exists in the physical world.
• Candidates for C are states of affairs that could be described by a contradiction.
  Here’s one example:
  (1A) A particular benzene molecule (B) sometimes reacts as if its structure were (X) and other times as if its structure were not-X (~X).  (Basic)(1B) If B sometimes reacts as if its structure were X and other times as if it structure were ~X, then the physical state of affairs of B -i.e. the physical structure of B- before measurement could be described as being: X and ~X. (Basic).
  David Lewis (2004: 4) comments: “We do not think that a population of molecules is a mixture of the two structures. Neither… that each molecule oscillates rapidly between one structure and the other. Neither… that each molecule has a betwixt-and-between structure… Rather, we think that each molecule is in a superposition: a state objectively indeterminate between two structures.”

(1C) Thus, the physical state of affairs of B -i.e. the physical structure of B before measurement- could be described as being: X and ~X. (MP 1A, 1B)

• Although the physical state of affairs of B is described as contradictory (i.e., indeterminate between two states of affairs X & ~X) and the measurements of that state of affairs are determinate (i.e., sometimes only X, other times only ~X) we can say that we are exposed to the state of affairs (X & ~X), no matter the outcome of our observation (X in one instance, ~X in another). What we are exposed to and what we observe may differ. In this case we are presumably exposed to (X & ~X) but observe sometimes only X, others only ~X.
• Another candidate for C is the state of affairs that obtains when a person expresses that she cannot put a feature of the world into words. In “saying what those features are, one is liable to say the unsayable.” Graham Priest (2002: 11)
• If concerning a certain experience that we are asked to describe, we are right in saying: “I can´t say with words”, then it is true that “We can say with words and we can´t say with words” because we have just used words to say that we can´t use words. This is a candidate for a true contradiction. It is arguably observable. If we speak in such a manner, we are able to describe an obtaining situation where words are and aren’t describing it.
• Other paradoxes may also provide contradictory state of affairs. Though it is not sure that they would be observable. For example, consider that the set of all natural numbers is larger and not larger than the set of all even numbers. Perhaps we can visualize the example, but it’s arguable whether the state of affairs is observable or not.

 (2) If we are exposed to C, then we are in a causal relationship with C. (Basic)

• This premise is proposed to hold for any state of affairs, not just contradictory states of affairs.
• “Take a concrete example… the pen on my desk, for instance. To perceive it is to be in a causal relationship with this state of affairs. The pen on the desk causes some effect in me the observer, or more accurately a series and cluster of effects, such as photons colliding with my eye, electrical transmissions through my nervous system to the brain, and so on.” Paul Kabay (2008: 152)
• “These considerations apply equally to the negation of any state of affairs –in the case at hand, my pen not being on the desk. This also is a straightforwardly consistent state of affairs. Moreover, to perceive this state of affairs is to be in a complex causal relationship with the absence of my pen on the desk. This results in my seeing that my pen is not on the desk. As an observer I am effected (sic) in an intimate manner by the state of affairs in question.” Paul Kabay (2008: 153)
• Since a contradictory state of affairs is expressed by a conjunction of opposites, and there is a causal relationship between an observer and each of the state of affairs expressed with the conjuncts, then we have reason to believe that the relationship with the state of affairs expressed with the conjunction will also be causal.
• The causal relationship can be noticed and identified, as in the case above, or not noticed nor identified. For example: UV-rays are observable with a sensor. Imagine I lack a sensor. The rays are still observable in the sense we mean. I am in a causal relationship with the UV rays. They produce an effect in my skin, my eyes, etc…, even if I can’t for the moment identify or notice the effect.

(3) Thus, we are in a causal relationship with C. (MP 1,2)

(4) If we are in a causal relationship with C, then we are changed by C. (Basic)

• “The perception of the state of affairs in question causes certain changes in me.” Paul Kabay (2008: 153)
• In the example given, the point is that the observer goes from being in a state of not perceiving the pen, to being in a state of perceiving the pen. Hence, a change in the observer.
• Again, the change could be unnoticed or noticed in the wrong way. Example: Take the observable state of affairs that oxygen is running out for an observer O. O is changed, but she doesn’t notice that oxygen is running out. Rather, she thinks that some problem in her lungs is producing breathing difficulties. Noticed or not, identified or not, the observer is changed.

(5) Thus, we are changed by C. (MP 3,4)

(6) If we are changed by C, then we acquire the specific content of C. (Basic)

• “All this results in my having a perceptual experience with a specific content – I actually see my pen on the desk.” Paul Kabay (2008: 153)
• The specific contents of C, reach out to the observer and materialize that specific content.
• The particularities of C are acquired by the observer, when C causes an effect in the observer.

(7) Thus, we acquire the specific content of C. (MP 5,6)

(8) If we acquire the specific content of C, then our perceptual state (P) is in a contradictory state. (Basic)

• Whatever the observer acquires, it can only be C-like. If C is inconsistent, the change brought about in the observer is to put her into an inconsistent state.
• Again, the effect can be noticed or unnoticed, correctly or incorrectly identified. See 5^th bullet in (2) and 3^rd bullet number in (4).

(9) Thus, P is in a contradictory state. (MP 7,8)

(10) The specific content of C is contradictory. (Basic, implicit in (1))

• By definition of (1).

(11) Thus, P is in a contradictory state and the content of C is contradictory. (&-intro 9, 10)

(12) If P is in a contradictory state and the content of C is contradictory, then our observation of C will be consistent. (Basic)

• Since P is on the same footing as C.
• “[One] way to ensure that a cross-eyed person will see the world as if it were in perfect focus would be to change the physical properties of the world itself such that the world actually exists in a cross-eyed state i.e. the world naturally appears as out of focus to someone with normal eye sight. Such a person would see a perfectly focused world.” Paul Kabay (2008: 149)
• Recall the 5^th bullet from (1). Here is an explanation of why measurements of benzene’s reaction is not inconsistent for each reading, even under a presumably inconsistent state of affairs:
• “Why don’t we observe… states of superposition? According to one interpretation… it is because the observer also goes into a state of superposition as a result of interacting with the superposition of, say, the device measuring the benzene superposition.” Paul Kabay (2008: 151)

The following five bullets is a sequence of explanations that Kabay uses to justify (12).[26]

• A state of affairs (S) is such that it can be described with a conjunction. But when observing S, S looks exactly like only one of the conjuncts[27]. This is because each situation described by the conjuncts interacts with the other. Consider S: Greg is at the piano (G) and there is an opaque shield surrounding the piano (O). We observe only the opaque shield.[28] The description of the state of affairs (S) is: (G & O). Yet, due to the way that G interacts with O, we only perceive O.
• Other states of affairs (A) are such that they can be described as a conjunction, and when observing A, A looks like a combination of the conjuncts. This is also because each situation described by the conjuncts interacts with the other. Consider the following state of affairs: There is a desk (D) in sight and there is a book (B) on the desk. The description of the state of affairs (A) is: (D & B). And, due to the way D interacts with B, we perceive both: (D & B).
• For S: G is different than O. That is why they can interact. G can interact with O because G is not the same thing as O.
• For A: D is different than B. D That is why they can interact. D can interact with B because D is not B.
• But the conjuncts of a contradiction are not distinct parts. Each situation described by opposing conjuncts (R & ~R, for example) is the same entity as the other. There is a relation of identity between the two conjuncts. There is no interaction between R and ~R like there is between D and B or between G and O. Hence, the states of affairs described by opposing conjuncts do not interact with each other. They are not available to the observer as an interaction (as G and O are). So the appearance of a contradictory state of affairs must be consistent.

(13)Thus, our observation of C will be consistent. (MP 11,12)

(14) If we are exposed to an obtaining contradictory state of affairs (C), then our observation of that contradictory state of affairs (C) will be consistent. (Complete CP 1-13)

 

Analysis of extraction

I see five ways to stop this argument from being sound. The first is by siding with the LNC and denying a priori the possibility of contradictions. Hence, (1) is made false. The second is by taking the dialetheist stance that denies contradictions obtaining in the observable world. Hence, (1) is made false. The third is by offering an obtaining situation where the specific content of what is observed is not necessarily acquired by the observer. Hence, (6) is made false. The fourth is by demonstrating that the perceptual state is not necessarily placed into a state that is compatible with what is observed. Hence, (8) is made false. And the last way that I see to stop this argument from being sound is by positing a situation where there is compatibility between the observer and the observed, yet the perception is out of sync. Hence, (12) is made false. A quick comment on the validity of the argument ensues, followed by an exploration of whether any of the five mentioned objections to soundness hold.

Paul Kabay’s argument[29] is presented above in the format of an extraction. The argument is valid, since the conclusion cannot be false while the premises are true. In fact, (1) is seen as necessarily false under the logical orthodoxy, which is by far the most prevalent of logical systems in philosophy today. If (1) must be false, then the argument is vacuously valid. That is, anything can be inferred from (1), when (1) is necessarily false. Think of the example: If green is red, then X. Any proposition can take the place of X, and the conditional will still be true, since it has a false antecedent. It is thus true that “if green is red, then I am the King of America”. Similarly, in the extraction offered above, (1) is offered as an assumption for Conditional Proof. So (1) will be the antecedent of a conditional statement, once the Conditional Proof is discharged. This allows us to place anything in the last line of the extraction and the conditional will still be true. The extraction, thus, cannot possibly be invalid. But it is meaninglessly valid. Since (1) must be false, then it is impossible for the argument to be sound. A sound argument must have only true premises.

To test for the soundness of the argument, I will limit my commentary to the underived premises that I consider most controversial: (1), (6), (8) and (12).

Let’s start with (1). Even under dialetheism we still have an uphill battle for (1) to be true. Our defense of the soundness of the argument is vulnerable. A dialetheist believes there are true contradictions, yet she is not convinced that contradictions exist in the observable world. Dialetheism posits that any contradiction could be true, but dialetheism favors the view that contradictions exist in the non-observable realm (like in mathematics or in language). Still, under the protection of dialetheism we can at least argue for (1) being true, which is precisely what Kabay tries to do.

A counterexample for (1) obtains if it is not the case that there are some contradictory states of affairs. But I believe there are some contradictory states of affairs, so from my standpoint the counterexample doesn’t hold. Here’s the basis for my opinion: If all contradictions were propositions that do not describe any state of affairs, then (1) must be false. In order to defeat the counterexample, there has to be at least one obtaining contradictory state of affairs that we can be exposed to in the physical world. Some candidates are described in the bullet points below premise (1). I am inclined to believe that at least one of these obtains in the physical world. I believe, for example, that the proposition ‘I don’t have words to describe the love I have for my children’ is a true proposition that describes an observable state of affairs that obtains. And as far as I can tell, the proposition is a contradiction and the state of affairs is contradictory because the words that I have is that I don’t have words. I also think that the following explanation of quantum superpositions is feasible (whether it is accepted or not in modern physics): A quantum particle in this world is located in one point in space and is also not located in that point in space, but our observation differs from what we know about the particle’s location. The particle is actually in two places at the same time, we just can’t observe it thus.

The exercise below serves only as an analogy to what I am driving at:

As an analogy only, the image to the right can be described as being a duck and also not a duck. I can actually perceive it as a duck and as not a duck (as a rabbit). But I can never perceive it as both at the same time even though I am quite comfortable saying that it is both duck and not duck (i.e., rabbit) at the same time. The image can be understood to be the two things at once, even if I cannot perceive the two things at once. I am exposed to a figure that is duck and not duck, but I never visually experience duck-and-not-duck together. This experience is analogous to being exposed to a contradictory state of affairs. If I didn´t have the concept of rabbit, or if I didn´t have the memory of an image of a rabbit, perhaps I would see only duck all the time. Perhaps this is analogous to what I see in the world. Since I don´t have the adequate concept of a contradiction, I only see consistency. (As a further exercise: What does a baby with no concept or recollected visual image of rabbit or duck see when it sees the image above? The image I report to see is not produced only by the physiological structure of my visual apparatus. If it were, how do I explain the change from duck to rabbit? Presumably, it’s a conceptual change. Could we see this differently if we acquire the contradictory concept of a duck-not-duck? How would the world appear if we acquired such a concept?) Of course we have not the (developed) capacities to see a contradictory state of affairs as a contradictory state of affairs, but if a contradictory state of events exists, then we could be exposed to it (even if we see it otherwise).

The next premise to place under attack is (6). I’ll try to imagine a counterexample of a state of affairs that changes an observer (B) but whose specific content B does not acquire. Let B be exposed to the sun’s UV rays the instance of (1) would be: B is in causal relationship with the rays (2): B is changed by the rays since the relationship is causal (4): but B doesn’t acquire the specific content. B could be not conscious of acquiring the content. But I’m obliged to side with Kabay. The fact that B does not notice that B has acquired the content of that state of affairs does not mean that B’s skin is not placed in the specific manner that UV rays place skin. B acquires the specific content of the UV rays, regardless of whether B is aware of acquiring that state. Up to the moment, I can’t see how it would be otherwise.

Next I´ll place (8) under scrutiny. I´ll look for an analogy. Say B is exposed to a banana. The instances of premises (2)-(7) are analogously straightforward: The banana has causal effects in B, the causal effects change B, the changes are banana-like… can B’s perceptual state resist the banana’s specific content? But what is the specific content? Perhaps that the banana is a fruit, that the banana is yellow. The categories that I can place this banana under are perhaps what the specific content is. But my perceptual state does not become fruity, or yellowy. I’m confused about what B’s perceptual state being fruity or yellowy could mean.

Lastly, let’s consider (12). A counterexample could be that an observer’s (B’s) perceptual state is in focus and the world B looks at is assembled in a compatible focused state, but the world looks out of focus. It seems to me that compatibility between the state of perception and the state of the perceived will ensure a perception that will be described as consistent by the observer.             

This last part needs more pondering. The limits constraining my capacity to further develop this last section have been exceeded due to the time that I dispose of and the deadline for the polished draft.

 

Conclusion

Paul Kabay’s argument[30] merely states that our perception of an inconsistent world could be a consistent perception. If this is true, then the fact that our perception of the world is consistent is not enough to prove that the world is consistent. But the world could still be consistent. Other arguments might be available for someone wanting to assert that it is so. Even if Kabay’s argument is successful, all that the argument purchases is that we not reject the possibility of an inconsistent world based on our perception. Other reasons to deny that the world could be inconsistent would be still available.

 

My contribution

My position is that success for trivialism in today’s philosophical landscape must rely on motivating philosophers to engage with the trivialist’s stance. Kabay’s argument[31] may motivate the view that the gap between our perception of the world and what we can rationally imagine the world to be is far wider than we commonly think. A reality that is beyond our current means could motivate us to further develop our means and not just work within their constraints. In particular, I think that it would be healthy to remove all the metaphysical constraints that we are tempted to place on the world. There should at least be a methodology available where even our strongest conclusions about the world speak more about our epistemic capacities than what is metaphysically (and physically possible).

That our thought or language cannot fathom a contradiction obtaining in the world (or an inconsistent world) is no reason to conclude that it is not obtaining beyond our faculties. It is almost certain that all our capacities have evolved over time, perceptual or rational. Reading causality into the world was perhaps not available to our ancestors 200,000 years back. Our capacity of representing the world in images and language may be different now than at the time of the first cave paintings (40,000 years ago). If we could go back far enough, we’ll get to a point where the differences are more patent.

Perhaps there was a time when we weren’t capable of switching the image in our minds from duck to rabbit in the illusion presented above. (Even as individuals, there is most probably a time in our infancy when we were not able to switch the image.) Perhaps in the future there will be a time when we can see duck, rabbit or duck-and-rabbit because we will be able to perceive contradictions that obtain. Perhaps, there will be a time when can see things as William Blake suggested they are: infinite[32]. All I have said in this section is speculative and non-philosophical. But the ideas in this section are my motivation for studying philosophy. And they got me through this project concerning trivialism, which proposes the possibility of an all-inclusive reality. A possibility I think should have a place, as I said, at least in our methodology.        

     

References

Beall, J.C. (2000) ‘Is the Observable World Consistent?’ Australasian Journal of Philosophy 78(1), 113-118.

Blake, William (2009) Antología bilingüe (Alianza Editorial).

Gottlieb, Paula (2013) ‘Aristotle on Non-contradiction’ The Stanford Encyclopedia of Philosophy.

Hodges, Wilfred (2005) ‘Modern Logic’ in Ted Honderich 533-536.

Honderich, Ted (2005) Oxford Companion to Philosophy (Oxford University Press).

Hookway, C.J. (2005) ‘Scepticism,’ in Ted Honderich (2005: 838-840).

Horn, Laurence R. (2014) ‘Contradiction’ The Stanford Encyclopedia of Philosophy (Online).

Kabay, Paul (2008) ‘A Defense of Trivialism’ Doctoral thesis for the University of Melbourne.

Kirwan, Christopher (2005) ‘Laws of thought’ in Ted Honderich 507.

Lewis, David (2004) ‘How Many Lives has Schrödinger’s Cat? The Jack Smart Lecture, Canberra, 27 June 2001’ Australasian Journal of Philosophy 82(1) 3-22.

Priest, Graham (1998) ‘To be and not to be: That is the Answer. On Aristotle on the Law of Non-Contradiction’ Philosophiegeschichte Und Logische Analyse 1, 91-130.

Priest, Graham (1999) ‘Perceiving Contradictions’ Australasian Journal of Philosophy 77 (4) 439-446.

Priest, Graham (2000) ‘Could Everything Be True?’ Australasian Journal of Philosophy 78(2) 189-195.

Priest, Graham (2002) Beyond the Limits of Thought (Oxford University Press).

Priest, Graham and Francesco Berto (2013) ‘Dialetheism’ The Stanford Encyclopedia of Philosophy (Online).

Priest, Stephen (2005) ‘Logical laws’ in Ted Honderich 540.

Tahko, Tuomas E. (2009) ‘The Law of Non-Contradiction as a Metaphysical Principle’ The Australasian Journal of Logic 7 32-47.

 

Notes

[1] Skepticism will refer to global skepticism in this essay, unless otherwise noted.

[2] Nontrivialism is taken to be the consensus view about truth values for propositions; i.e., the stance that it is not the case that all propositions are true, and that every proposition must be either true or false.

[3] C.J. Hookway (2005: 838).

[4] The Philosopher’s Index database was consulted. A search for the keyword trivialism produces 9 results on April 27, 2015, compared to 7,182 results for skepticism.

[5] C.J. Hookway (2005: 839).

[6] C.J. Hookway (2005: 838).

[7] Paul Kabay (2008: 134-167).

[8] Paul Kabay (2008: 134-167).

[9] Tuomas E. Tahko (2009: 32).

[10] Graham Priest (1998: 91).

[11] Paula Gottlieb (2013).

[12] J.C. Beall (2000: 116).

[13] Explosion is briefly explained in the vocabulary section ahead.

[14] Laurence Horn (2014).

[15] Laurence Horn (2014).

[16] Stephen Priest (2005: 540).

[17] Christopher Kirwan (2005: 507).

[18] Graham Priest (1998: 91).

[19] Graham Priest and Berto, Francesco (2013).

[20] Graham Priest (2000: 195).

[21] Graham Priest (1999: 443).

[22] Graham Priest (1999: 443).

[23] J.C. Beall (2000: 114).

[24] J.C. Beall (2000: 114).

[25]J.C. Beall (2000: 116).

[26] This argument is presented in Paul Kabay (2008: 156 -164).

[27] For brevity and to avoid convoluting even more, I repeatedly refer to the state of affairs described by a conjunct as “the conjunct”. Of course, the state of affairs does not look like one of the conjuncts, since the conjunct is a sentence. What I mean is that the state of affairs described by a conjunction looks like the state of affairs described by only one of the conjuncts. The economic phrasing described in this footnote occurs elsewhere, though I avoid it for the explicit and correct phrasing when possible.

[28] J.C. Beall (2000: 115).

[29] Paul Kabay (2008: 156 -164).

[30] Paul Kabay (2008: 156 -164).

[31] Paul Kabay (2008: 156 -164).

[32] William Blake (2009:148).