Putative examples of true contradictions in the social world have been given by dialetheists such as Graham Priest, Richard Routley, and Val Plumwood. However, we feel that it has not been decisively argued that these examples are in fact true contradictions rather than merely apparent. In this paper we adopt a new strategy to show that there are some true contradictions in the social world, and hence that dialetheism is correct. The strategy involves showing that a group of sincere dialetheists can, given an appropriately formed institution, bootstrap contradictions into existence. We discuss objections and consider the implications of this finding for debates over logic.
“The first rule of contradiction club is not the first rule of contradiction club.” – Official Contradiction Club Handbook
Perhaps the most well-known arguments for dialetheism – the view that there are some true contradictions – make use of semantic paradoxes such as the liar (“this sentence is false”) and its variants (see for example Beall (2009), Priest (2006)). Others have been presented which try to demonstrate true contradictions arising from set theoretic paradoxes (see Priest (2006)), vagueness (see for example Cobreros (2011) and Hyde and Colyvan (2008)), and motion (see Priest (1985)), to give just some examples. This article focuses on another place where we might find true contradictions: the social world.
Putative examples of true contradictions in the social world have been given by dialetheists such as Richard Routley and Val Plumwood (1989) and Graham Priest (2006). Such examples usually involve moral dilemmas and legal conflicts derived from contradictory norms, including the pacifist’s dilemma and potential conflicts over voting and property rights. However, we feel that it has not been decisively argued that these examples are in fact true contradictions rather than merely apparent. In this paper we adopt a new strategy to show that there are some true contradictions in the social world, and hence that dialetheism is true.
2 A Tale of Two Clubs
2.1 Classical Club
A group of classical logicians in our department decided to form a club. After finding a suitable clubhouse, they decided they needed a leader. One of them, Josh, volunteered, motivated by a bylaw in the club’s constitution giving the leader exclusive access to the club’s liquor cabinet. Everyone agreed and, as far as they were concerned, all was well.
2.2 Contradiction Club
When we (ourselves dialetheists – believing that there are some true contradictions) heard about Classical Club, we could not help feeling left out. So, we decided to form our own club, asking only fellow sincere dialetheists to become members. Renting a clubhouse next door, we gathered to set out Contradiction Club’s constitution. We decided that we too should have a special kind of member: the High Priest. High Priesthood is largely ceremonial, and Contradiction Club is not as stingy with its alcohol as Classical Club, but the role of High Priest is not without privilege. The High Priest alone is allowed to change the station of the clubhouse radio; no one else may touch it.
Once we had set out our constitution, a member, Val, offered up the position of High Priest to volunteers, at which point another member, Graham, raised his hand. We thus all decided that Graham was High Priest and to treat him as such. Then Val asked, “Who wants to not be High Priest?”, and everyone, including Graham, raised their hand. We thus decided that everyone is not a High Priest and to treat each other as such.
The club has been running for some time now, and everyone is aware that Graham is both a High Priest and not a High Priest, and all in the club sincerely treat him as such.
Contradiction Club is a little more esoteric than its classical counterpart, yet it seems like we can make sense both of what Classical Club has done and what we in Contradiction Club have done. The strange workings of Contradiction Club (perhaps unsurprisingly!) have strange consequences, however. Given that the members of our club intend to (and do in fact) treat Graham both as a High Priest, and non High Priest, as far as we are concerned, the sentences “Graham is a High Priest” and “Graham is allowed to mess with the radio” are both true and false.
Have those of us in Contradiction Club got it right? By way of answering this question, let us think more generally about social reality. How is someone able to become a member of the UK parliament? The exact mechanism by which this occurs is subject to debate within social ontology, but it nonetheless looks as if one can become a member of parliament, and wield the powers and responsibilities of the post, by getting voted in by one’s constituents, given that there are appropriate institutions already in place, such as there being a parliament.
Under what conditions does one fail to create a social fact, such as that one is a member of parliament? One obvious condition is when the appropriate authority is missing. Mhairi Black could not just have made herself member of the UK parliament, no matter how sincerely she intended to be, without the votes of thousands of others. And likewise, we cannot make bits of string into pounds sterling without the Bank of England’s say so. We will consider later that there could be other specific conditions in which a group of people fail to create a social fact despite the appearance that they have, but we can leave that to one side for the moment.
Returning to the case at hand, it seems as if, just as in the case of the UK Parliament, it is unproblematic that the social facts instituted by Classical Club obtain and run parallel to the parliamentary case. The social facts that Mhairi is Member of Parliament for Paisley and Renfrewshire South and that Josh is the leader of Classical Club get created in the same kind of way. Having been made leader, Josh has all of the attendant powers and responsibilities of being the leader – that is, he is allowed to access the club’s liquor cabinet – just as Mhairi has all of the responsibilities and powers that come with being a Member of Parliament. Further, the (social) fact that non-leaders of Classical Club are not allowed to access the liquor cabinet seems similarly unproblematic. The background social institutions are also already in place – Classical Club has members and a set of rules. We thus claim that the following four social facts are made the case by Classical Club unproblematically: that Josh is leader of the Classical Club, that the other members of Classical Club are not leaders of Classical Club, that Josh is allowed to access the liquor cabinet, and that the other members are not allowed to access the liquor cabinet.
Contradiction Club seems awfully similar to Classical Club in all the relevant ways. It looks like Graham gets to be High Priest of Contradiction Club by the same kind of process as the one that made Josh leader of Classical Club, and in turn this seems to confer on him the powers and responsibilities of being High Priest (namely, being allowed to change the radio in the clubhouse). Likewise, it seems that everyone in Contradiction Club gets to become non High Priest in the same way that everyone except Josh gets made non-leader of Classical Club. And likewise, Graham is not allowed to touch the radio as a result, just as the non-leaders of Classical Club are not allowed in the liquor cabinet. All this suggests that the following four social facts are made the case by Contradiction Club: that Graham is High Priest, that all of its members (including Graham) are not High Priest, that Graham is allowed to change the radio station, and that none of its members (including Graham) are allowed to change the radio station. This amounts to two contradictions, one involving Graham’s status within the club, and one involving what he’s allowed to do.
So why should you believe that these contradictions are brought into existence by Contradiction Club? Well, it looks uncontroversial that the corresponding four facts of Classical Club obtain. And we stipulated that Contradiction Club’s rules and volunteering system are virtually the same as those of Classical Club. Given that the four facts of Classical Club obtain, why would not the four facts of Contradiction Club likewise obtain? If someone wishes to deny that they do, a relevant disanalogy between the cases must be found. Yet we suggest that the cases are perfectly analogous in all relevant respects.
Where does this leave us? It seems that Contradiction Club has in fact created two contradictions in the social world: it is both a fact that Graham is High Priest, and it is a fact that he is not, and it is both a fact that he can change the radio station, and a fact that he can not. And since (we argue) we have created contradictions in the social world in this way, dialetheism is, by definition, correct with respect to the social world.
What is distinctive about this case is that it is dialetheists who form the club. It seems as if believing dialetheism to obtain allows us to show that dialetheism is true, since we can only sincerely attempt to found Contradiction Club when we believe that there could be true contradictions. We are therefore pulling ourselves up by our bootstraps in order to establish the truth of dialetheism!
This is more than a quirk of our argument – we think that it is this feature that makes our argument novel. One might suggest that, in the putative cases of true social contradictions provided by Routley and Plumwood (1989) and Priest (2006), the suggested contradictions fail to be made true, as they go unnoticed, or are at least unintended. We suspect that, for instance, there will be those who would reject such contradictions on the grounds that, because they are unintended, the purported contradictions would be somehow “ironed-out” in practice. We think that such an objection will probably be unsuccessful – as an anonymous reviewer pointed out, unintended consequences are, after all, still consequences – but in our case, we in Contradiction Club are conscious of and indeed intend the contradictions involved. In being recognised and indeed intended, the contradictions given by our argument sidestep this style of objection altogether.
3 Objections and Replies
3.1 Could Dialetheists Really Found the Club?
How could someone who was unconvinced reply to all of this? For one, they might object that it is simply psychologically impossible for us dialetheists to actually found the club in the first place. The thought might be that it is just psychologically impossible for someone, no matter how outwardly committed to dialetheism, to form the mental states (whether belief, intention or otherwise) necessary to make Graham both High Priest and non High Priest, because those mental states contain contradictory contents: that Graham is and is not allowed to touch the radio. Yet we think that this is somewhat disingenuous – in order to be charitable to dialetheists such as us, our opponents should take our claim to believe or accept some true contradictions seriously. Given that dialetheists more generally have no problem with accepting some contradictions as true, there seems to be no problem with them (perhaps in a fit of whimsy) starting a club with the aim of making some contradiction true.
Now it might be thought that whilst there is perhaps no problem with dialetheists accepting or believing that a contradiction is true, it takes something stronger than that to be in the mental states that would be needed to make one true (if it is indeed possible to make one true), such as intending or willing (see e.g. Gilbert 1989). However, here the burden of proof is upon the objector to tell us why there is a problem for having those mental states, which have conflicting contents (such as intending to treat Graham as High Priest and non High Priest), that does not also involve rejecting the claim that dialetheists can believe or accept contradictions.
3.2 The “According To” Objection
Beall (2009), p. 126–127, expanded on in 2017, p. 203–206) has responded to cases presented in e.g. Priest (2006), p. 184–185) for the existence of true contradictions within legal systems by arguing that even if some contradictions are true according to some bodies of law, that does not make them true simpliciter.
Take his example of traffic regulations: it is legal to drive on the right in the US and legal to drive on the left in Australia, and yet it is not legal (simpliciter) to drive on both the right and the left. Rather, according to US law, you should drive on the right, and according to Australian law you should drive on the left, and that is all there is to it.
Beall has also deployed this line of argument in responding to the Pinocchio paradox, originally presented by Peter and Veronique Elridge-Smith (2010) and later deployed by Peter Eldridge-Smith (2011) against dialetheism. Pinocchio, according to the story, has a nose which grows if and only if he tells a lie. What happens when he says, “My nose is growing”? If this is a lie, then his nose will grow, making his utterance true; yet if it is true, his nose will grow, meaning he told a lie. This case is supposed to be a problem for dialetheists, since it involves a contradiction which is not semantic, but physical; perhaps a sentence could be both true and false, but could a nose really grow and not grow at the same time? Beall replies to this case in much the same way as before: there is no genuine contradiction here because it is only according to the story that Pinocchio’s nose grows if and only if it does not, and so the contradiction is contained within the fiction (Beall 2011).
Should something along these lines be said about our case, that the contradictions we are claiming to show are only really true according to our club? No! It is true enough that, according to us, Graham is High Priest and non High Priest. But it is just the same with money and members of parliament – they, too, are what they are according to some group. Yet it seems entirely unproblematic to also take it as true simpliciter that Mhairi Black is an MP, and likewise that Bill Gates is worth over $80 billion. What we are claiming is as minimal as this: it is as true to say that Graham is both our High Priest and that he is not, as it is to say that between us we have got enough money for our bus home. And that is truth enough.
Beall does correctly point out that “according to body of law x, p” does not entail p (in the strictly logical sense of “entail”), and so could likewise say that a claim of the form “according to Contradiction Club, p and not−p” does not entail p and not−p. This is well and good, but to say that this rules out that bodies of law and, more importantly for our case, social institutions, could make any claims true is far too strong. Yet if Beall concedes this much, the onus is on him to explain why Classical Club can make its particular social facts true while Contradiction Club cannot.
Our argument does therefore rest on there being some claims that are true in virtue of the social world being a certain way. But to us it seems that resisting our conclusion – that there are true contradictions within social reality – by claiming that there are no truths within the social world whatsoever, and so no social facts, looks a lot like the “nuclear” option: that is, we suggest that it is a high price to pay and is perhaps ad hoc. To our minds, denying that there are social truths, such as that money can be exchanged for goods and services, just in order to rule out the possibility of dialetheism, is wrongheaded.
3.3 Constraints on Creating Social Reality
We imagine that some will be unconvinced by the case as we have presented it so far. Such people might well respond: “This is all well and good, but there just are no true contradictions! The (albeit sincere) intentions of a few deviant logicians are not enough to change that, and so Contradiction Club cannot have actually created the social reality it claims to have created, no matter what its members think.”
We sympathise with such readers. But the indicators that a club has been successfully established are there: we, as its founding members, have the right kinds of mental states, and have the right authority within the broader social world. So, it seems like Contradiction Club and Classical Club are on equal footing in these respects. No one is standing in the way of Contradiction Club. We rented the clubhouse, we have paid the electricity bill, and we have all agreed on the rules. The volunteering was binding, and no one was coerced or misled. We therefore have as much reason to think that Contradiction Club has made the relevant social facts obtain as we do to think that Classical Club has made its corresponding facts obtain.
One might suggest that there are even more constraints that wider society places on whether a club with its associated roles can be successfully formed, which might get in our way. But, looking at outlawed or secret societies, for instance, we can see that among these it cannot be a constraint that society must accept a club’s existence. Wider society might reject, or be unaware of, their existence entirely, but nonetheless they may still exist, albeit underground. But might other putative deep constraints be operative? Perhaps the powers possessed by any social group are restricted by a broader societal rule that one cannot both hold a given position and not hold that position at the same time. If so, it might look like Graham could not be High Priest and not High Priest, since that exactly violates that rule. However, it would itself be a serious task to demonstrate that there is such a deep constraint on the construction of social reality – note that this would be a constraint on what is possible within social reality, not merely what is permissible – and it would take a novel argument within social ontology, appealing to facts about how social reality is created, to show that such a constraint is operative.
While we do not think such an argument would be successful, perhaps an attempt to put forward such an argument would appeal to the fact that most people in our society are not dialetheists, and try to establish that this was sufficient for there being an underlying convention in our society that any social reality created must not contain any contradictions. But even if such an argument were successful, we could just as well imagine a situation in which all dialetheists on earth were gathered up and moved to an isolated planet, forming a new society composed entirely of dialetheists. On this planet, a small number of us, including Graham, could then form Contradiction Club. In this case, the fact that the remaining people on earth were not dialetheists would not be relevant to whether this club could be formed (in the way it intends to be), since the relevant wider society would be comprised of dialetheists. What is more, if earth-society can create a deep constraint on the construction of social reality on earth, prohibiting contradictions, by being made up of non-dialetheists, it would seem odd to claim that the new planet’s constraints regarding the construction of social reality would include that constraint, given that its population is comprised of dialetheists. If such deep constraints, dependent on the views that members of wider society have about true contradictions, exist at all, then it would seem that a planet of dialetheists would have their own, different, set of deep constraints on the construction of social reality on their planet.
Might there be worries about the intelligibility of such a practice from the perspective of the non-dialetheists left behind on earth? Perhaps they would interpret our actions as not really contradictory, or fail to be able to understand us at all, through their non-dialetheic point of view. But that is beside the point. Whether or not the old earth-bound society recognises the new society or not does not change the underlying social facts of the new dialetheic planet, where Contradiction Club is permitted to, and would in fact, exist.
4 Logical Implications
What implications does all of this have for logic? Let’s suppose that we in Contradiction Club have created a true contradiction. It seems that the correct logic for the social world must make room for this – perhaps a paraconsistent logic where contradictions do not entail everything is (one of) the correct one(s). In setting up Contradiction Club, are we therefore attempting to make a (say) paraconsistent logic correct and classical logic incorrect? No. What we are trying to do is show that such a paraconsistent logic might be correct. Let’s think about this for a moment.
We can all agree that, whatever the correct logic(s) are for the social world, that world is bounded by them, and not the other way around – we cannot defy the (correct) laws of logic. But no party to this debate should assume, prior to investigation, that they know which the correct laws are – at least, they should all be open to revising their views. Now what kind of evidence can we provide to show that contradictions do not entail everything, for example? Exactly the kind we have presented in the previous two sections – that we have made a contradiction true by forming our club, coupled with the trivial observation that some claims are false within both the social and non-social worlds: it is still not legal to drive on the right in the UK, and it’s still false that gold has atomic number 489.
Since, in classical logic, contradictions entail the truth of every statement, our argument for dialetheism can therefore be thought of as indirect evidence for the claim that the correct logic for the social world is non-classical. Indeed, it provides evidence that the laws of logic that govern the social world must at least be paraconsistent. Arguing against our conclusions ought not, therefore, merely consist in insisting on the correctness of (say) classical logic. Rather, our opponent ought to challenge the evidential basis for our rejection of explosion – the case we have presented for Contradiction Club.
Can we push this idea even further? It has been suggested to us that other esoteric clubs might be possible. Might a club be formed, for example, that suggests that some disjunctions could have no true disjunct, or that and-elimination is invalid? Such clubs might provide evidence that the correct logic(s) for the social world are even weaker (in the sense of having even fewer valid rules of inference) than the paraconsistent one we have been suggesting. Maybe – and we welcome further investigation along these lines – but we note that it is no trivial task to show that any such club could exist. We are certainly not committed to saying that there could be such clubs until we see a detailed case for their existence, like the one that we have provided for Contradiction Club.
Stepping back from the implications of our argument for logic more generally, what should we say about all of this? As creators of social reality, the members of Classical Club seem to be on equal footing with the members of Contradiction Club. It seems, therefore, that it is just as plausible that the former club could make its members leaders and non leaders as it is that the latter could make its members High Priests and non High Priests – to deny this, our opponent needs to tell us just what it is about social reality that gets in the way of us and our comrades. Failing that, the only conclusion worth entertaining is that dialetheism is correct with respect to the social world.
Funding source: Arts and Humanities Research Council
Award Identifier / Grant number: 159485529
Funding statement: Arts and Humanities Research Council, Funder Id: http://dx.doi.org/10.13039/501100000267, Grant Number: 159485529.
We would like to thank Jc Beall, Graham Priest, Brian Epstein, Rosanna Keefe, Sabina Wantoch, Michael Greer, James Lewis, Lewis Brooks, Josh Black, Graham Bex Priestley, Celia Coll, William Hornett, and Niall Connolly for their helpful comments in preparing this paper. We would additionally like to thank audiences at the University of Sheffield and the University of York, who were subjected to a theatrical version of this paper and its authors’ terrible acting.
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This paper was an entirely joint effort, written by two authors sat next to one another. We both gave it 50%. Author order was decided by random number generator.
©2020, Emma Bolton and Matthew J. Cull, published by De Gruyter, Berlin/Boston
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