Inconsistent Images

The University of Adelaide Australia
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Sylvan's Box Gefunden!

The story so far. The eminent logician, Richard Sylvan, formerly Richard Routley, died in 1996, of a heart attack, after climbing a mountain. (In passing, there is a lesson here: several logicians have died or been injured on mountains, a good logician ought therefore to take heed of the obvious inductive argument and stay off mountains). Some months later, Graham Priest paid a visit to Richard’s house in Bungendore near Canberra, where his literary executor, Nick Griffin, was working on Richard’s papers. Later, Graham published a short story based on these events “Sylvan’s Box” (Notre Dame Journal of Formal Logic, 38 (1997), 573-582). You should read it to get a proper sense of the present story. To summarise, Graham’s paper relates how in going through Richard’s effects they discovered a box with the words Impossible Object on it, in Richard’s writing. On opening it, they discovered an impossible box, with contradictory properties, being both empty and yet having something in it. After getting over the shock of discovery, Graham and Nick realised that releasing this information to the world could cause widespread controversy, possible danger, and even open up the potential for exploitation by the military-industrial complex. Doubtless Richard had known this, which is why he had hidden the box. Graham and Nick decided to honour Richard’s legacy and prevent the box from falling into the wrong hands, by continuing to hide it. The story ends with the box, in true contradictory fashion, being buried on Richard’s property at the same time as being locked in Graham’s car. In his concluding comments on the story, Graham tells us that while the visit to Richard’s house and Nick in Bungendore was real, the rest of the story, including the box, is fiction, constructed in order to make the philosophical point that truth in fiction has to be inconsistency-tolerant (“paraconsistent”).

Now read on.

When I first read Graham’s story, I asked myself the obvious question. Why didn’t he give us a picture? Well, maybe he didn’t have a camera. Or maybe the camera wasn’t up to a photo of an inconsistency. But then, why didn’t he at least draw us a picture? After all, there is a rich tradition of impossible images, proving that such pictures are not beyond the capacity of humans. The question bothered me. It continued to puzzle me over the years, when I occasionally thought about it.

Over time, a suspicion began to dawn. Maybe it was deliberate that he hadn’t drawn anything. But what did that imply? If the story was fiction, there was surely no problem about a made-up picture? One day, a disturbing thought emerged: despite his claim about the box, perhaps after all it was not fiction.

Where does that lead? Clearly, he and Nick want us to believe it was a fiction. But what explains that? Why were they so keen to have us believe that it was a fiction? My head whirled. Could it really be because it was not a fiction after all? Graham and Nick claimed (in the story) to be worried that the box might fall into the hands of those who would seek personal advantage, or worse, world domination. Imagine, for example, what could be done with an impossible box, able to make impossible journeys through time, like the Tardis. But could Graham and Nick themselves have other motives, perhaps of a baser kind? And might not others, even governments, be involved too? Why else would there not be a picture, unless they thought that publishing an image would reveal some if its secrets and its potential to the enemy? Nothing could be ruled out.

I struggled to put such horrid thoughts out of my mind. I didn’t know Nick very well, but he was a friend of Richard and Graham; and, with their solid leftist views and unimpeachable integrity, they at least wouldn’t have any dealings with sinister conspiracies.

Some months later, I was visiting Graham in his apartment in Ormond College at The University of Melbourne. As we sat sipping an excellent shiraz from his extensive collection, I felt compelled to ask. “Graham, that short story you wrote about Sylvan’s box was fictional, wasn’t it?” “Don’t be silly” he replied, looking at me strangely. “Of course it was. There aren’t any boxes that are empty and not empty at the same time, that’s contradictory.”

Now I was really alarmed. Graham has argued in many published books and papers that some contradictions are true. For him to fob me off by implying that contradictory objects are ipso facto unreal was just not him. And then there was the strange look that he gave me. What could that mean? Is he going strange, or is it me? I decided to bide my time with this problem, giving it careful thought.

The next morning, Graham had an early meeting in the Philosophy Department. I remained behind in his apartment to do some reading. But my concentration wasn’t on it. What was he keeping from me? Surely the only explanation for his lack of candor was that there was something that he didn’t want me to know. But why? All my old suspicions flooded back. Because there is something important hanging on it! Something going far beyond the mere discovery of a logical oddity. The box is real and he has sold it to the military! And they are performing their hideous experiments with it! What else could it be? How else could you explain his frequent overseas trips, particularly to the United States and Russia? Not to mention his shiny new Harley Davidson, on a mere Professor’s salary?? Why else would he lie to me?

I prowled around. My disbelief that he could overturn his lifetime political views for gruesome personal profit was overwhelmed by my despair at his manifest collaboration. These contradictory beliefs were almost too much to bear. Finally I sat down next to his wine racks, full of dusty bottles of well-aged wine. I’d never bothered to look at all closely at them before, so it was some time before I noticed, almost subliminally at first, that the wine rack in the corner was a little out from the wall. I did not want to disturb the rack, but I was curious as to the origin of the failure of symmetry. I leaned over to look. At first all I could see in the gloom was what looked like old shoes. Shoes behind a wine rack? Odd. I looked closer. The shoes were sitting on something. Gingerly I lifted the shoes. They had been resting on a box, concealing it. I reached over, and picked it up.

In my hand I held a dusty box, with the lid taped down. There was writing on it. It was not Graham’s writing. It was more like Richard’s. Yes, it could be the words Impossible Object, though Richard’s handwriting was always so awful that it was hard to be sure. I was torn two ways. This is private property, I musn’t open it. But this is an opportunity which I am unable to pass up, to see a real, existing contradiction, or at least settle the issue once and for all. In the end, I gave in, promising myself to confess to Graham. I gently lifted the tape and took the top off the box. This is what I saw.

As I came to terms with the bizarre sight, several thoughts fell into place. He hadn’t sold it to the military. It was a contradiction, but it was here. He hadn’t even taken it from its hiding-place, for it was covered with the dust of years. It had obviously been hidden by him, not to be found by anyone. Yes he had lied in telling us that it was a fiction. But now, it was apparent, that could only be for the reasons that he and Nick had agreed about, to prevent it from falling into the wrong hands. The story was true, all true, and even their motives for concealment were just as the story had said. The cover-story that it was all a fiction was for reinforcement, to forestall the agents of darkness by putting it out that there was nothing to find.

I heard Graham’s key turning in the door of the apartment. I felt ashamed that I had doubted him. I had to tell him so. “Graham, I have to tell you that when I asked you last night whether Sylvan’s box is a fiction, it was because I was worried that it was real but that you had been concealing that fact for your own profit.” I blurted. “But I’ve found the box and I now know that it was not for personal gain that you hid it, but for the opposite motive, to save the world.”

“It’s true” he said. “But now you know too. What can we do?”

“Well that’s only three of us. We must do our best to see that it goes no further. As a first step, you must find a new hiding place, far from here. Then, even if they torture me, I will not be able to say where.”

“Agreed”, he said, picking up the box and walking out with it. “It will never be seen again.”

And from that day to this, I have not seen it more.*

Final comment: The above story is fictional, except for the parts where it isn’t. The part about the box is fiction, there is no such box. Trust me.

 

Postscript

Since the time of writing, an alternative reading of Sylvan’s Box has been proposed by Daniel Nolan (“A Consistent Reading of Sylvan’s Box”, The Philosophical Quarterly, 2007, 667-673). Nolan contends that both inconsistent and consistent interpretations are available. The inconsistent interpretation is as manifest to us all above. The consistent interpretation is that the fictional narrator, Priest-in-the-story, is unreliable: he simply believes wrongly that he sees an impossible box that is both empty and yet has a figurine in it. As we all know, nothing follows about whether the Priest character is correct in his beliefs. Nolan goes on to explore the conditions under which we might prefer one reading to the other, without coming down on one side rather than the other. He signals that he has sympathies with various inconsistentist positions, but offers the consistent reading as ammunition for the opposition.

But this is to assume that what we have in the Sylvan’s Box narrative really is fiction. To be fair, it is true that Priest encourages this assumption: for instance, he breaks off into his non-fiction philosophical voice in order to draw several conclusions about truth-in-fiction. But what if the narrative is not fiction but true? Then we must explain why Priest sought to mislead us into thinking it fiction. But even Nolan must acknowledge that the explanation is already apparent above: Priest wanted to divert the forces of darkness and unwisdom away from seeking out the box and exploiting it for their wicked purposes. Nolan might at this point persist with the unreliable narrator theory, but applied to non-fictional avowals: Priest and Griffin (and myself) are simply wrong in our beliefs that the box was real. But Nolan offers no reason to believe this. Is disbelief in contradictions so easy when confronted by the images above and below?

Needless to say, I must reassure readers, who may be discomfited by the thought that there are true contradictions, that I am lying. The box is unreal, and what is more the bastards will never get their hands on it.

Visit the gallery of other alleged sightings of Sylvan's Box.

Story and Image: Chris Mortensen
June 2007
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