Nonevidentialist theories in a contradictory world

C.A. Postlethwaite

Introduction

This paper investigates whether nonevidentialist theories of knowledge can adequately cope with dialetheism about the empirical world in cases where our perceptions of contradictions are consistent. The argument presented attempts to sustain that evidentialism cannot thus cope. This argument is precarious yet it can be seen as successful if one is willing to prefer certain epistemic virtues over simplicity, and if one is inclined to accept dialetheism of an empirical sort. A skeptical reflection about the nonevidentialist methodology for assessing knowledge closes the paper.  

Dialetheism is the view that there are true contradictions. This essay’s strategy for confronting nonevidentialist theories of knowledge with empirical dialetheism begins with the assumption that dialetheism of an empirical sort is correct. The assumption entails that any true contradiction of the form ‘x and not-x’ must accurately represent an obtaining contradictory state of affairs (x and not-x)[1]. The move relies on a correspondence theory of truth, where a proposition is true if and only if the proposition represents the world in the way that it is, and that a proposition is false if and only if it fails to represent the world in the way that it is.[2] The main argument thus assumes, for conditional proof, a world[3] in which at least some contradictory states of affairs obtain.

That any contradiction could obtain in the world seems a highly contentious assumption as a beginning for our query. Yet this already problematic starting point is further intensified by the intention to consider perceptions of contradictions. This perceptual requirement leads us to exclude two of the most plausible[4] types of contradictions from this particular investigation. The first type of contradiction that we must exclude is rational dialetheism’s (as opposed to empirical dialetheism) solution to paradoxes such as the liar sentence. Said solution claims that the following proposition is both true and false: ‘This proposition is false’. So according to dialetheism: it is false that ‘this proposition is false’ and it is also true that ‘this proposition is false’. The problem with said contradiction for this study is that there is no straightforward observable state of affairs that could make such a contradiction true. Recall that this essay aims to address contradictory states of affairs that may be perceived as being consistent. In the case of the solution to the liar, there is no contradiction that may be perceived at all. The second type of contradiction that we must exclude are instantiated by what are, putatively, true empirical contradictions. Concretely: contradictions that allegedly solve Sorites-style paradoxes or other situations of vagueness. Consider a proposition with the form ‘x and not-x’ as instantiated by proposition y: ‘a thirteen year-old human is a child and it is not the case that a thirteen year-old human is a child’. Proposition y would accurately represent reality if in fact a thirteen year-old human is both a child and not a child.[5] This paper is not interested in this type of example on account of there not being a straightforward explanation regarding our perception of the state of affairs represented by such contradictions. The lack of straightforwardness has to do perhaps with the suggestion that observations of vagueness are theory-laden.[6] More on this is said below on page 5, around footnote 14.

The contradictions that we will consider must have at least one of their conjuncts representing direct, minimum-theory-laden, observable content. Say contradictions of the sort: ‘there is a pen on my desk at time t and it is not the case that there is a pen on my desk at time t’.[7] It seems that we could straightforwardly observe at least one of the two states of affairs that are represented by their corresponding conjuncts. Most straightforwardly, we can observe that there is a pen on my desk at time t (which is a state of affairs represented by only one of the conjuncts). An important premise for the main argument in this essay posits that a contradictory state of affairs that is accurately represented by a conjunction must be perceived as only one of states of affairs represented by one of the conjuncts.[8]

The main argument itself does not need to argue that it is true that contradictory states of affairs in the empirical world actually obtain.[9] The premise that establishes there being contradictory states of affairs (P1 below) is an assumption for conditional proof, where the conclusion will include the assumption of contradictory states obtaining as the antecedent of a conditional. But the high risk of the conclusion being vacuously true due to a false antecedent will be addressed, since it is a situation which is important to avoid.

Once it has been argued that the assumed contradictory states of affairs (x and not-x) is perceived as consistent (as only one of the contradicting conjuncts[10], i.e., ‘x’[11] or else ‘not-x’, and not both ‘x and not-x’, of the contradicting conjuncts), we proceed to contrast this situation with the conditions for knowledge as established by nonevidentialist theories. Nonevidentialist theories, as I interpret in Feldman[12], rely precisely on some sort of appropriate type of role by part of the world on the process of belief formation. But then the contradictory states of affairs can play no such role in bringing about the formation of the true contradictory belief as would be needed since they play a role in forming consistent beliefs. This leads to the conclusion that the contradictory state of affairs (x and not-x) does not play an appropriate part in the formation of the belief that ‘x and not-x’. It only plays a role in forming the belief ‘x’ or else ‘not-x’. So for nonevidentialist theories, there are some true propositions that are the content of a belief that should be adequate for knowledge that are deemed inadequate for knowledge. It seems we can conclude that the contradictory state of affairs that makes a contradiction true plays no role in the formation of the pertinent contradictory belief. The obtaining contradictory state of affairs that is assumed plays a role in forming only a non-contradictory, or consistent, belief.    

Here’s a quick recap of the main framework of the argument: If contradictory states of affairs obtain, and our perceptions of them are nonetheless consistent, then it seems that the obtaining state of affairs in reality could never appropriately produce the contradictory belief[13] that is required by nonevidentialism for knowledge.

In the work that follows, I first offer a personally intuitive justification that motivates the assumption of contradictions obtaining in the world. This, because said assumption is reported as being theoretically repugnant.[14] Then I present a formal version of the main argument. Next, I provide explanation and defense of the argument’s premises. After that, four types of objections are identified: (1) Objections to the assumption for conditional proof. (2) Objections to the crucial premises, P2 and P11. (3) Objections to interpretations of the definition of proposition and of truth and falsity, P4 and P6. (4) Objections on contradictions not meeting the belief requirement or the justification (good reason) requirement for knowledge. They are selectively responded to. Finally, I present my conclusion.

 

The motivation behind a repugnant assumption for conditional proof

I personally do not think that it is intuitively contentious that an obtaining state of affairs in the observable world could be contradictory. Yet such a view turns out to be highly contentious philosophically. Since a world that allows contradictions is deemed impossible by prevalent philosophical standards[15], I will quickly address this matter before the main thesis is expounded. Failing to justify the assumption will produce a vacuous conclusion due it being a conditional with a false antecedent.

A specific definition of impossible world is that it “is a world that realizes explicit logical contradictions -in the simplest case: where sentences of the form A and ¬A hold.”[16] In this sense a world in which (a) there is at time t a pen on my desk, and (b) it is also not the case that there is, at time t, a pen on my desk, is taken to be an impossible world. Even a world in which a thirteen year-old human is a child and it is not the case that a thirteen year-old human is a child obtains[17] would be deemed an impossible world. This latter realization of an explicit logical contradiction seems less counterintuitive than the realization of a pen being and not being on my desk.[18] Another other less counterintuitive example of a possibly obtaining situation that for some philosophers may provide grounds for denying that true contradictions entail an impossible world is dialetheism’s solution to the liar sentence, as stated above. But contradictory propositions in response to vagueness, or to logical paradoxes such as the liar sentence, are not the paradigm for the propositions that motivate this paper.[19]

It seems to me that the world I am in right now could be one in which I am typing these words at time t and am also not typing these words at time t. If that situation obtains, then it just so happens that the only world that seems real to me is the one where I am typing these words at time t. That is, the world definitely does not seem to me to be contradictory in this sense, but I think it could well be contradictory despite the way it seems to me now. Perhaps I have reached this stance by following the persistent and skeptical intuition that my capacities fail to take in the world as it really is. This hunch has resulted in quite the rabbit hole. Perhaps there is no way the world really is.[20] Perhaps the world is in a way that is incompatible with my most basic assumptions. A great motivation for this paper is to investigate what could be said about knowledge if my basic assumption that the world is not contradictory were to be wrong. I hope that what I have said up to here is enough to justify the postulation of an obtaining contradictory state of affairs, even if in the philosophical literature it is deemed as “impossible”.

Although I need not argue for the premise that affirms said assumption (P1 below), I do hope that this ‘apologetic’ section[21] has motivated the reader to consider P1 (below) not as a necessarily false premise from which anything follows when placed as the antecedent of a conditional[22]; but as a meaningful possibility. That dialetheism has any plausibility in the philosophical landscape (however small), may serve to warrant the assumption in P1. If not, then at least curiosity about the limits of nonevidentialism might allow me the query, and the reader’s consideration.          

 

The argument, formally

P1. An obtaining state of affairs (x and not-x) in the observable world is contradictory. (Assumption for Conditional Proof)

P2. If an obtaining state of affairs (x and not-x) in the observable world is contradictory, then the obtaining state of affairs (x and not-x) is perceived to be non-contradictory (i.e., perceived either as only ‘x’ or else as only ‘not-x’). (Basic)

P3. Thus, the obtaining state of affairs (x and not-x) is perceived to be non-contradictory (i.e., perceived either as only ‘x’ or else as only ‘not-x’). (MP P1, P2)

P4. If an obtaining state of affairs (x and not-x) in the observable world is contradictory, then the proposition that accurately represents the contradictory states of affairs (x and not-x) is the contradiction which has the form of the conjunction ‘x and not-x’. (Basic)

P5. Thus, the proposition that accurately represents the contradictory states of affairs (x and not-x) is the contradiction which has the form of the conjunction ‘x and not-x’.  (MP P3, P4)

P6. If the proposition that accurately represents the contradictory states of affairs (x and not-x) is the contradiction which has the form of the conjunction ‘x and not-x’, then the contradiction ‘x and not-x’ is a true proposition about the contradictory state of affairs (x and not-x). (Basic)

P7. Thus, the contradiction ‘x and not-x’ is a true proposition about the contradictory state of affairs (x and not-x). (MP P5, P6)

P8. If the contradiction ‘x and not-x’ is a true proposition about the contradictory state of affairs (x and not-x), then, according to nonevidentialist theories, the true contradiction ‘x and not-x’ will be considered adequate for knowledge if and only if the contradictory state of affairs (x and not-x) is connected in an appropriate way to the formation of the contradictory belief that ‘x and not-x’. (Basic)

P9. Thus, according to nonevidentialist theories, the true contradiction ‘x and not-x’ will be considered adequate for knowledge if and only if the contradictory state of affairs (x and not-x) is connected in an appropriate way to the formation of the contradictory belief that ‘x and not-x’. (MP P7, P8)

P10. Thus, the proposition that accurately represents the contradictory states of affairs (x and not-x) is the contradiction which has the form of the conjunction ‘x and not-x’ but the obtaining state of affairs (x and not-x) is perceived to be non-contradictory (i.e., perceived either as only ‘x’ or else as only ‘not-x’). (&-intro P5, P3)

P11. If the proposition that accurately represents the contradictory states of affairs (x and not-x) is the contradiction which has the form of the conjunction ‘x and not-x’ but the obtaining state of affairs (x and not-x) is perceived to be non-contradictory (i.e., perceived either as only ‘x’ or else as only ‘not-x’), then it is not the case that the contradictory state of affairs (x and not-x) is connected in an appropriate way to the formation of the contradictory belief that (‘x and not-x’).  (Basic)

P12. Thus, it is not the case that the contradictory state of affairs (x and not-x) is connected in an appropriate way to the formation of the contradictory belief that (‘x and not-x’).  (MP 10, 11)

P13.  Thus, according to nonevidentialist theories, it is not the case that the true contradiction ‘x and not-x’ will be considered adequate for knowledge. (BMT MP9, MP12)

C. Thus, if an obtaining state of affairs (x and not-x) in the observable world is contradictory, then according to nonevidentialist theories, it is not the case that the true contradiction ‘x and not-x’ will be considered adequate for knowledge. (CP P1-P13)

 

The 5 Basic Premises

P2 If an obtaining state of affairs (x and not-x) in the observable world is contradictory, then the obtaining state of affairs (x and not-x) is perceived to be non-contradictory (i.e., perceived either as only ‘x’ or else as only ‘not-x’).

Kabay's argument in favor of P2 posits that a contradictory state of affairs that is represented by contradictory conjuncts necessarily acts as a single, whole, entity on the perceiver. Kabay concludes that contradictory states of affairs must appear consistent.[23] A weaker conclusion will suffice for the intentions of this paper. Support for P2 is successful if some contradictory state of affairs in the world (x and not-x) can appear consistent even if it is contradictory. It is not necessary for P2 that all contradictory states of affairs in the world (x and not-x) must appear consistent, as Kabay argues.

The particular argument that I draw upon, at its simplest, resorts initially to our consideration of ordinary cases in which there is some state of affairs that obtains and that can be represented with a conjunction, but for which only one of the conjunctsˢ can be said to be perceived. For Kabay, every case of a contradiction is a case of the type of conjunction where only one of the conjunctsˢ[24] is perceived; though of course contradicting conjuncts will have other reasons for only one being perceived other than the reason that one of the states of affairs is hidden from view (as in the ordinary cases where only one of the conjunctsˢ is perceived because the other is hidden).

Kabay’s initial resort is a strategy that appeals to our familiarity with how states of affairs that are represented by conjunctions can come apart from our propositions about perception of said state of affairs. I.e., A and B obtaining is compatible in some cases with only A being perceived (as in Saint-Exupery perceiving only the box, see footnote 24). Yet Kabay posits that it seems there are certain conditions under which said relation of only one conjunct being perceivable is compulsory. A conjunction that is a contradiction is such a compulsory case.

Kabay argues that the closeness of the states of affairs represented by contradicting conjuncts ‘x’ and ‘not-x’ should be considered to be a particular case of identity[25]. A state of affairs represented by a contradiction interacts with the perceiver as a “single, whole entity”[26], rather than each conjunct interacting with the perceiver independently, as in cases of some conjunctions where both conjuncts can be perceived[27]. Independent interaction of each of the states of affairs represented by the conjuncts with the perceiver never applies to contradictions, according to Kabay. His account includes an explanation that describes the observer of a contradictory state of affairs as being in a contradictory state (which can also be described as resulting in “the splitting of the observer into two different observers”[28]). In this way, the observer is also in an inconsistent state and so perceives ‘x’, on one hand, and ‘not-x’ on the other, but does not perceive two things at the same time ‘x and not-x’. Kabay alludes to analysis of observations of alleged superpositions in molecular physics. P2 then, has some plausibility, though I will consider some objections ahead.

P4 If an obtaining state of affairs (x and not-x) in the observable world is contradictory, then the proposition that accurately represents the contradictory states of affairs (x and not-x) is the contradiction which has the form of the conjunction ‘x and not-x’.

The main argument for P4 is Watson’s definition of ‘proposition’. P4, I think, is straightforward. By definition, “a proposition is a representation of the world which can be true or false depending upon whether or not the states of affairs corresponding to that proposition obtain.”[29] So given a state of affairs (x and not-x) that is contradictory, the proposition that accurately represents it must be a contradiction; in particular, it must be the contradictory proposition ‘x and not-x’.

I would say that in order for P4 to be false we must reject either the assumption that states of affairs obtain in reality or that they can be accurately or else inaccurately represented by propositions. But we will not object to these two very basic and intuitive assumptions in this paper. Another way to object to P4 is that I have wrongly interpreted the definition.

P6 If the proposition that accurately represents the contradictory states of affairs (x and not-x) is the contradiction which has the form of the conjunction ‘x and not-x’, then the contradiction ‘x and not-x’ is a true proposition about the contradictory state of affairs (x and not-x).

 The case in favor of this premise is Watson’s definition of ‘true and false’ in Watson (2016). P6 seems also commonsensical and straightforward. By definition, “a statement of a proposition is true if and only if it corresponds to reality as it is in itself, and false otherwise.”[30] Since we are parting from the assumption that the state of affairs (x and not-x) obtains, then -as P4 states- the proposition that accurately represents said reality is ‘x and not-x’, and by accurately representing the state of affairs (x and not-x), the proposition ‘x and not-x’ is true. Since the proposition is a contradiction, then it is a contradiction that is a true proposition. Of course, all of the derivations of the main argument are indented by the assumption for conditional proof, so we are arguing that they are true in case the assumption is true.

In order for P6 to be false we must reject either the assumption that states of affairs obtain in reality, or that they can be accurately or else inaccurately represented by propositions, or else that when said states are accurately represented by propositions we call said propositions ‘true’ and when said sates of affairs are inaccurately represented by propositions we call the propositions ‘false’. But these very basic assumptions will not be objected to in this paper. Another way to object to P4 is that I have made a mistake in applying the definition to the case at hand. 

P8 If the contradiction ‘x and not-x’ is a true proposition about the contradictory state of affairs (x and not-x) then, according to nonevidentialist theories, the true contradiction ‘x and not-x’ will be considered adequate for knowledge if and only if the contradictory state of affairs (x and not-x) is connected in an appropriate way to the formation of the contradictory belief that ‘x and not-x’.

At the heart of nonevidentialist theories of knowledge is that having the best reasons, or the strongest evidence, is not sufficient for a belief to count as knowledge. What is needed in order to have knowledge is that there be some appropriate relation between the formation of the belief and the state of affairs that makes the belief true.[31] So particularly to this case, in order for the true proposition ‘x and not-x’, to count as knowledge, the state of affairs (x and not-x) must play a role in the formation of the belief whose proposition is ‘x and not-x’. If no such role is played by the state of affairs in the formation of the belief, the belief cannot be adequate for knowledge, independent of any further reasons that a believer may have. P8 merely asserts the nonevidentialist requirement for the particular case at hand.

To reject this premise is to say that nonevidentialism does not require what nonevidentialism requires. I will not consider any objections to this premise, though a way to object is by showing that I have misunderstood the basic requirement that is common for nonevidentialist theories.

P11 If the proposition that accurately represents the contradictory states of affairs (x and not-x) is the contradiction which has the form of the conjunction ‘x and not-x’ but the obtaining state of affairs (x and not-x) is perceived to be non-contradictory (i.e., perceived either as only ‘x’ or else as only ‘not-x’), then it is not the case that the contradictory state of affairs (x and not-x) is connected in an appropriate way to the formation of the contradictory belief that (‘x and not-x’).

What has been derived from our basic premises up to before P11 is that some contradictory state of affairs (x and not-x) must be perceived as either only ‘x’ or else either only ‘not-x’ (P3) when it should be perceived as ‘x and not-x’ in order to be true (P7). Thus it seems that the role of the contradictory state of affairs that makes a contradictory belief true does not participate in the formation of the true contradictory belief. But nonevidentialist theories require some such participation. (P9)  

But sustaining that the relation between P3 and P7 results in noncompliance of P9 seems too quick. Defending P11 requires that we show that the contradictory state of affairs is not connected appropriately to the formation of the contrary belief that is needed. We must show that when P3 obtains, and a consistent perception must result from some contradictory state of affairs, said result cannot play an adequate role in the formation of the pertinent contradictory belief. So here is the move, presented a bit slower: There are states of affairs that are accurately represented by a conjunction. (For example: (i) that there is a pen and desk, (ii) that there is a sheep and a box, (iii) that there is a pen and that there is not a pen. The latter one is allowed by the assumption in P1.) Some of these states of affairs must be perceived as only one of the conjunctsˢ. (In particular: (ii) and (iii)). For all of them (i-iii), an accurate representation would include both conjuncts, since the state of affairs in reality obtains as such. Thus, the accurate representation is not appropriately produced by the obtaining state of affairs for the case of (ii-iii). It seems to be plausible that, if the conjunction in (iii) represents a single, whole, entity, then the appropriate connection cannot be established between the contradictory state of affairs and the formation of the pertinent contradictory belief, since the accurate contradictory belief requires both conjuncts to be produced. 

P11 relies on the truth of P3 (which is derived from P2) for the truth of P11’s antecedent and so to not be vacuously true. What happens, according to P2, is that given a contradictory state of affairs that obtains (x and not-x), said state of affairs must cause a consistent perception. So it (x and not-x) is not connected to the contradictory belief in the right way. Mainly, it plays no role in the production of the pertinent belief at all. The contradictory state of affairs fails to produce a contradictory perception and so fails to be adequately involved in the production a contradictory belief. The contradictory belief that ‘x and not-x’ seems never to be a result of the state of affairs (x and not-x). The contradictory true belief is arrived at through reasoning that requires the possibility of things not being as they are produced by the obtaining state of affairs; that is, forming the adequate belief requires admitting the possibility that things are not as they seem.

Perhaps the right type of seeming (the relation between the state of affairs and the belief formation) is the adequate type of connection required by nonevidentialism. If so, then said seeming will always be consistent and so will not produce the contradictory perception and arguably will not produce the contradictory belief in the right way. If Kabay is right, there is a disconnect between the contradictory state of affairs and the belief in the contradiction, since the state of affairs brings about a consistent perception.

 

Objections and Responses

I see four ways to object to this precarious argument: (1) Objections to the assumption for conditional proof. (2) Objections to the crucial premises, P2 and P11. (3) Objections to interpretations of the definition of proposition and of truth and falsity, P4 and P6. (4) Objections on contradictions not meeting the belief requirement or the justification (good reason) requirement for knowledge. There is no room to go through all the objections to this argument and then to respond. So in this section I will only briefly mention (1) and (3) and attempt to give a rough sketch of the other two.

The case of (1) constitutes the most hurtful attack, since it renders the conclusion of the main argument true but vacuous by considering the assumption for conditional proof necessarily false. In defense of P1 I refer the reader back to the section about motivation, and to the plausibility of empirical dialetheism[32]. I now briefly add a tangential comment in defense by confessing that I do not think my work has been in vain. Defending the assumption in this fashion, though, does nothing for the argument. So I’ll move on. I have mentioned in the sections for P4 and P6 that (3)’s attack consists in either revealing an incompetent interpretation or adaptation of the philosophical basic concepts of proposition and truth and falsity, or by undermining the even more fundamental assumptions to already very basic ideas. These options remain open to opponents though with very high costs.

            (2)’s attack is led by Watson’s view that logical operators such as ‘and’ do not figure in perceptual content.[33] Watson distinguishes between perceptual judgements, “which apply logically structured conceptual predicates to what is represented in perception”[34], and perceptual content. If Watson is right, Kabay’s analysis of perception is not accurate when it appeals to conjunctions as figuring in the representation of perceptual content. A response to this objection is to bite the bullet and admit that we are talking about perceptual judgements. As long as they are the element between belief formation and the obtaining state of affairs, we can still argue that the role played by state of affairs on perceptual judgements are inappropriate and produce the wrong (in this case consistent) belief formation. Another line for (2) is Beall’s call for simplicity.[35] Kabay is bending over backwards to show why the world is perceived by us as consistent when the simple answer is that we perceive it thus because it is thus. My response is that the motivation for enquiring about inconsistency in the observable world is not brought on by perceptual experiences, but rather by other intellectual yearnings and dissatisfactions. Just as Einstein’s discomfort with Newton’s gravity outrunning light entailed tweaking concepts such as space and time that didn’t seem to need tweaking, the discomfort with grounding truth on our current capacities invites revisions to our most basic assumptions and laws (like the Law on Non-Contradiction). Another strong attack for (2) could be to insist that P11 is wrong since even a consistent perception brought on by an inconsistent state of affairs could still be connected in the appropriate way to the contradictory belief. I do not know how such an explanation could be constructed, but I think there could be something to it. I have not response to an objection that is for the moment just an intuition. There might be more objections in the line of (2). But that is all that I could fathom under the time constraints.

            Finally, I will mention aspects of (4)’s attack. I left this for last because I wanted to mention that it is a pity not to give the topic the attention it deserves. I found what seem to me beautifully argued papers on the subject of inconsistent beliefs and inconsistent reality. The papers dealt with questions about our capacity to hold contradictory beliefs and of their possibility of being justifiable, rational. The strongest objections to the main argument of this essay are that it is impossible to believe a contradiction and that it is impossible to have good reasons for believing a contradiction. These attacks go outside the scope of the argument in this paper. They imply that the nonevidentialist is off the hook. Form them, a true contradiction is barred from being knowable not because the contradictory state of affairs doesn’t play the appropriate role in belief formation. On one hand, a contradictory belief could not be held in the first place; and on the second hand, even if we could hold a contradictory belief, it would necessarily be irrational to do so. Out of eight papers on related topics, seven insisted that we are able not just to hold, but to rationally hold inconsistent beliefs. A common response is that consistency is not the ‘be all and end all’ virtue for rationality. In fact, the critique for lack of simplicity in Kabay above alludes to this view. Kabay’s position could very well be consistent, as consistent as a defender of the theses that planet earth is flat.[36] For this reason, other criteria for accepting a belief might result individually or in some combination more important, or as important, than consistency. Holding beliefs that are contradictory thus can be warranted under certain conditions. Epistemic virtues may come in different types and degrees. Familiar ones are simplicity, clarity, unity, fruitfulness, explanatory power, parsimony, etc.[37] I expand this list to include something like disruptiveness. A disruptive belief that can participate dialectically without shutting out competing beliefs and which has the capacity of being incorporated into the conversation, might deserve a degree of consideration similar to the virtues noted above. My response to attack (4) is that the mere fact that a proposition is contradictory does not bar us from the possibility of believing it. Similarly the mere fact that it is contradictory does not make it necessarily irrational for us to hold.

 

Conclusion

Allowing the assumption that the world is contradictory was a fruitful exercise. My conclusion is that the main argument in this paper is extremely fragile and will result unsound for most. The hardest hits are two: (1) The conclusion is vacuous due to a false antecedent, and (2) Simplicity trumps the account that our persistently consistent perception is due to contradictions interacting as single entities with perceivers. Unless belief in contradicting reality obtains for us a higher degree of epistemic virtue, these two attacks have the upper hand. Explanatory power, unity and disruptiveness are virtues that I believe may sustain this paper’s conclusion.  

The real moral comes from analyzing the methodology that is employed when assessing knowledge form a nonevidentialist standpoint. A nonevidentialist seems to step outside a believer’s perspective and somehow possesses insight about what states of affairs obtain independent of the evidence. She must somehow know this correctly in order to evaluate whether or not a certain part of the world plays an adequate role in belief formation. In this paper, I have known the state of affairs that obtains in the world. I did so because I stipulated an assumption. But I end this essay doubting that such a perspective concerning actual states of affairs is ever attainable.   

 

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Notes

[1] References to representations such as beliefs, perceptions, and propositions are placed in quotes throughout the paper and references to states of affairs are not placed in quotes but in parentheses for ease of identification within the body of the text.

[2] The correspondence theory of truth “puts up the stiffest… resistance to the idea that there might be true contradictions”. Priest, G. (2006: 51) Priest presents an account of a correspondence theory of truth “which allows for the possibility of true contradictions”. Said account “is essentially a simple part of situation-semantics, where atomic facts are more usually called ‘states of affairs’ or ‘situation types’ and sets of facts are called ‘situations’.” This theory has to do with “a Dunn four-valued interpretation for the relevant logic of First Degree Entailment” which accommodates the existence of negative facts. Though I fail to grasp this fully, it seems that a correspondence theory of truth that allows for true contradictions is at least defendable, and actually defended in the literature.

[3] A world that may be deemed “impossible”. More is said about the motivation for such a counterintuitive assumption below on page 4, around footnote 11.

[4] If any contradiction is plausible at all.

[5] Beall, JC and Colyvan, M. (2001: 565), give the same example for a sixteen year-old being and not being a child, a 170 cm woman being tall and not, and purplish-blue objects being both blue and not blue.

[6] Although I can give no account of how to tell apart a theory-laden observation from one that is less or non-theory laden, I suggest following Beall, JC and Colvyan, M. (2001) that for more theory-laden observations of a state of affairs σ we can observe that σ; while for less theory-laden observations of a state of affairs σ, the state of affairs σ itself can be observed. I.e., perceiving that σ vs. perceiving σ may help decide the degree that an observation is theory-laden. The less theory-laden tend towards a report of perceiving the state of affairs itself (without the ‘that’).

[7] If we follow the suggestion in footnote 6, we realize that the conjunct “I perceive a pen on my desk at time t” provides a good account of the observation, and so may count as less theory-laden than states of affairs that make better due from a proposition such as: “I perceive that a thirteen year-old human is a child”.

[8] It is much easier to say, and more intuitive to get the point across,: “perceived as only one of the conjuncts”, but the conjunct is not what is being perceived, it is the state of affairs represented by one of them. I will make use of the easier way up ahead, for simplicity’s sake. 

[9] Since neither the defense nor the refutation of the claim that a contradictory state of affairs obtains matter for the argument, no attempt is made at proving or disproving said claim; though a little will be said in a tone that is proper of a self-justificatory apology. (I think.)

[10] Here I am using ‘only one of the contradicting conjuncts’ instead of ‘state of affairs represented by one of the contradicting conjuncts’. Note that ‘conjunctˢ’ (and similar use of the superscript ‘ˢ’) will be shorthand for ‘state of affairs represented by conjunct’. 

[11] In quotes for being the perception (a representation) of a state of affairs.

[12] Feldman, R. (2003: 81ff) I will lump all the nonevidentialist views together, since on my interpretation of Feldman, they share the requirement that states of affairs must have a role in belief formation. Said requirement is enough, I think, to impede any theory that sustains it from accommodating dialetheism of an empirical sort into their views concerning knowledge. This requirement is the feature under consideration for this paper. 

[13] It is important to keep in mind throughout this work that “a proposition is the content expressed by a statement, thought or belief.” (Watson, 2016)  So, although the claims in the main argument focus on propositions as truth-bearers, their content could be a belief, the talk of which parallels talk of propositions in many ways that are pertinent to this paper.

[14] Priest, G. and Berto, F. (2013).

[15] Berto, F. (2013).

[16] Berto, F. (2013).

[17] Due to the way the definition is phrased, it seems to me that if an impossible world requires the realization of an explicit logical contradiction, then the instantiation of an impossible world has to do with the state of affairs that obtain, and not directly on whether the proposition that accurately represents said ‘realization’ is true or false. Although both of these might need to go together, I am being careful to phrase cases of impossible worlds in regards to what facts obtain, not what proposition is true or false.

[18] Perhaps for it being theory-laden, see footnote 19 below.

[19] Beall, J.C. and Colvyan, M. (2001: 565) mention that claims as the one about the thirteen year-old human are theory-laden (though it “does not alter the fact that it is an observation” as opposed to non-observation claims like those concerning the liar paradox). Elsewhere, Beall, J.C. (2006: 116) suggests the success of accepting true contradictions for “non-observable domains” such as for the case of the liar sentence above. This essay must not speak to contradiction in non-observable reality and must speak to contradictions that are straightforwardly observational, perhaps non-theory laden or less heavily so. That’s not to say that dialetheist solutions to the sorites or other putative observations could not serve to make the assumption for conditional proof somewhat plausible. They are contradictions about the empirical world and so something could be said about our perception of them. Propositions as dialetheism’s solution to the liar, on the other hand, would not help the main argument in this paper.

[20] This intuition will not be pursued, since our goal is to evaluate whether certain true propositions can amount to knowledge about the observable world given a nonevidentialst theory. And since true propositions are required for this goal, I will assume that there is a way that the world is in order that there are propositions that accurately (or inaccurately) represent it.

[21] See footnote 9.

[22] I’d prefer the conclusion of the main argument to not be accepted on the same level as “If there is a square circle, then I am an ancient and eternal vaudevillian frog trapped in a concrete box below a construction site” or other such vacuous nonsense (though I’ve nothing against nonsense, and perhaps something quite in favor of it).

[23] Kabay, P. (2006: 457).

[24] Some commonsensical reports about ordinary states of affairs are of the type that can be represented by the conjunction (A and B) yet perception is accurately described by a proposition only regarding one of the two conjunctsˢ, say about A. For the state of affairs of there being a sheep and there being a box the following conjunction may accurately represent it: “there is a sheep and there is a box”. Yet the proposition about perception could be only: “S perceives a box”, in case, for example, that the sheep is inside the box and out of sight of S (although the Little Prince putatively perceives the sheep even when it is inside the box). So some states of affairs that can be represented by a conjunction are described for perception only by mentioning one of the conjuncts. A and B obtains, but only A can be perceived (in this case by S, who is perhaps Antoine de Saint-Exupery).

[25] Kabay, P. (2006: 455-456). Interestingly, in these pages, Kabay reports that Aristotle and Hegel concurred in their account of the nature of the conjuncts of a contradiction being in a type of identity relationship, though these authors differed on whether contradictions obtained in the world.

[26] Kabay, P. (2006: 455). Also: “The fact is that the conjunction αᴧ⌐α is just not like the conjunction αᴧβ. What then is a contradiction like? I suggest that it is more accurately compared to conjunctions of the form αᴧα. In other words, contradictions are like single whole entities –albeit inconsistent ones.” (Kabay, P. (2008: 160).

[27] For the state of affairs of a pen and a table, one can describe her perception being of both conjuncts “I see a pen and I see a table” due to a capacity of each conjunct interacting independently with the perceiver. Yet in case of a true contradictory state of affairs obtaining, say there is a pen and it is not the case that there is a pen, then one state of affairs cannot interact with the perceiver independent of the other state of affairs. They interact as one entity with the perceiver and so only one of the conjuncts is perceived.

[28] Kabay, P. (2006: 453).

[29] Watson, J. (2016: 12).

[30] Watson, J. (2016: 13).

[31] The causal theory requires that the state of affairs that the belief is about causally connects suitably to the belief; Nozick’s theory requires that there’s a tracking relation between acquiring the belief and the states of affairs that make the belief true; reliabilism requires the process of belief formation reliably leads to accurate representation of the state of affairs; and the proper function theory requires that the cognitive system is functioning properly and in a relation with states of affairs of an adequate environment for the system. Feldman, R. (2003: 105).

[32] Even if just to dialetheism’s solutions to sorites paradoxes in the observable, if theory-laden, world.

[33] Watson, J. (2013).

[34] Watson, J. (2013: 13).

[35] Beall, JC. (2006).

[36] Priest, G. (2006: 123).

[37] The seven papers that argue in favor of rational or belief in contradictions are: Colvyan, M. (2008).; Priest, G. (1998); Williams, J.N. (1982). Which I especially enjoyed; Klein, P. (1985).; Priest, G. (2006: Part III); Daya, K. (1957); and Foley, R. (1979). The eighth is: Piazza, T. and Piazza, F. (2010).