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Impossibility and the Limits of Art

By Luis Rosa.

Is art as unbounded as to be able to create anything ? “Art has no limits”, one might think. Members of the society I am part of follow certain rules—and perhaps some of those rules are also followed by members of other societies—but I can easily sit in my chair and write about alternative societies where those rules are not followed at all. The objects in our environment usually fall when they are dropped. But I could shoot a movie in which objects just stay up in the air. The laws of nature, like social rules, do not put constraints in our creativity. We are pretty much free to avoid them in our imagination.

What about the laws of logic, though? Don’t we always ‘follow a logic’ when we both create and enjoy art? Consider for example the law of noncontradiction: it is not the case that A and not-A , for any proposition A . It is important to emphasize here that the same proposition
must be affirmed and denied by means of ‘ A and not- A ’. E.g. I can write a poem using the same term to express two different concepts:

As I was walking I realized
That there was a boy sitting in the bank
And yet, oh me
There wasn’t a boy sitting in the bank

Here the first use of ‘bank’ makes reference to objects that we can use to have a seat; in the second case, though, it makes reference to a certain type of financial institution. The boy was sitting in a bank in the first sense—he was not sitting in a bank in the second one. There is no contradiction here. And that is because ‘There was a boy sitting in the bank’ can be used to express two different propositions.
Likewise, no one would say that a movie is contradictory just because it contains a scene in which it is snowing in Lhasa and another one in which it is not snowing in Lhasa; the times were different, or the specific locations inside Lhasa were different. Propositions have spatio-temporal indexes: it is snowing in Lhasa on February 15 , 2017 —not snowing in Lhasa on August 21 , 2015 . What if the director intends the two scenes to be juxtaposed, meaning that they occur in parallel universes? In that case, one might say, it is raining and not raining in Lhasa at the same time . That is true, but now we just need to single out yet another index in order to individuate propositions. It is snowing in Lhasa on February 15 , 2017 at parallel universe u —not snowing in Lhasa on February 15 , 2017 at parallel universe u’ . (Presumably, ‘Lhasa’ refers to two different objects here: Lhasa-in- u in the first occurrence of the term and Lhasa-in- u ’ in the second one). So no contradiction again.

(Not snowing in Lhasa)

None of this amounts to saying that the law of noncontradiction is always true; it is only that we haven’t been shown counterexamples that stem from human creativity/imagination. Graham Priest (1987) is a dialetheist : he thinks that there are true contradictions, i.e. truths of the form P and not-P . And that is because he thinks that there are dialetheias , or sentences that are both true and false. Purported examples include paradoxical sentences, such as the liar sentence: ‘This sentence is not true’. Even if Priest is right, though, we still cannot conceive of a situation in which both P and not-P are true, assuming that it is not the case that P is both true and false . Let those paradoxical sentences be—our imagination is still constrained by a more restricted version of the law of noncontradiction (restricted to sentences that are not dialetheias). Can art lead us to consider scenarios that constitute counterexamples to that law?

Consider literature again. Of course I can write down a sentence like ‘Sam’s office was in San Francisco, and yet not in San Francisco’. That is trivial. But can my readers conceive of a situation in which that would be the case? Let us cut to the chase, then. If the possibility of contradictory literature (in the non-trivial, relevant sense) is guaranteed by the possibility of contradictory imagery plus sentences that describe the relevant scenarios, we should directly investigate into the possibility of there being contradictory images. My readers can imagine a situation in which Sam’s office is in San Francisco, and they can also imagine a situation in which Sam’s office is not in San Francisco. One might attempt to build a contradictory scenario by oscillating or transitioning between the scenario that satisfies ‘Sam’s office was in San Francisco’ and the one that satisfies ‘Sam’s office was not in San Francisco’; by increasing the frequency with which one goes from one to the other, one might expect that at some point one’s mind will ‘merge’ the two. That may be a groovy thought-experiment of sorts—but to no effect if the goal is to conceive a logically impossible scenario. The contradictory scenarios always ‘expel’ or ‘force out’ each other. Even if logical contradictions cannot be pictured, however, perhaps some non-logical yet conceptual impossibilities can. A conceptual impossibility is something that conflicts with so-called ‘conceptual’ or ‘analytic’ truths. Examples include ‘Red things are colored’, ‘A vixen is a female fox’, ‘7 + 5 = 12’ and ‘If x is bigger than y then y is smaller than x’. Denying any of these gives rise to conceptual impossibilities.

It may look like some of those conceptual truths are easy to contradict in fictional discourse. E.g. one can write a sci-fi story in which humans are brains-in-vats who are fed fake sensory experiences by a powerful supercomputer, as depicted in Hilary Putnam’s famous thought experiment (1981). Assume that the whole human history has been like that. In that case, what humans, i.e. human brains in vats, have been calling ‘vixens’ are not female foxes; they are not even animals. They are rather series of points in a digital coordinate system that is
connected to the human visual cortex. In that scenario, the word ‘vixen’ does not refer to foxes, and it does not refer to female animals. And so if ‘A vixen is a female fox’ is a conceptual truth, we would have a conceptual impossibility here. Thankfully, that much freedom was granted to human imagination—or so one might think. But that is a mistake. The appearance of a conceptual impossibility in this case is generated by the fact that one uses ‘vixen’ to make reference to whatever it is that the envatted brains make reference to, whereas one uses ‘female fox’ and ‘animal’ to make reference to what actual human beings make reference to, i.e. female foxes and animals. If in the fictional scenario everything that is called a ‘vixen’ is also called a ‘female fox’, then the target conceptual truth is also true in that scenario. And so it is not at all clear that there is a recipe for generating conceptual impossibilities through fictional discourse here.
Roy Sorensen—who has offered the not so generous amount of a hundred dollars to the first person who shows him the depiction of a logical impossibility—thinks that there are nevertheless pictures of conceptual impossibilities (see Sorensen 2002).

A purported example is the Penrose triangle.

Look at the vertices of this triangle: it looks like they need to occupy different 3D coordinates at the same time. But from the fact that this is how it looks like it does not follow that a conceptual impossibility has been depicted. This may be yet another case of optical illusion. In fact we can build an object in the real world that looks just like the Penrose triangle when seen from a certain angle (after all, some angle must be chosen to depict the object—how would the Penrose triangle look like when seen from different angles ?). The depth and thickness of different parts of that object just need to be adjusted in specific ways. So if I take a picture of that object from that angle, do I thereby generate a picture of a conceptually impossible object? Hardly so. (Relatedly, I invite the reader to check Brian McKay and Ahmad Abas’ “impossible” triangle , in Perth, Australia). It is therefore a matter of controversy whether conceptual impossibilities can be depicted. E.g. there is no guarantee that the drawing above depicts a conceptual impossibility, as opposed to a perfectly possible object as seen from a certain angle. And so there is a twilight zone between the types of impossibilities that can and those that cannot be created by human imagination. We can create scenarios that fail to abide to the laws of nature—i.e. scenarios that are nomically impossible; but we cannot create scenarios that fail to abide to certain logical principles—i.e scenarios that are logically impossible. Somewhere in between those two are the purported conceptually impossible scenarios.

There’s plenty of space for creation below the twilight zone, however. We are still fortunate enough to be able to conceive realities that differ in quite substantial ways from ours e.g. in social aspects. Some laws fail to put boundaries in our imagination, and art is the quintessential way of circumventing those.


Priest, Graham (1987). In Contradiction , Dordrecht: Martinus Nijhoff. 2nd expanded edition,
Oxford: Oxford University Press, 2006.
Putnam, Hilary (1981). Reason, Truth, and History , Cambridge: Cambridge University Press,
Chapter 1, pp. 1–21
Sorensen, Roy (2002). ‘The art of the impossible’, in J. Hawthorne & T. S. Gendler (eds.),
Conceivability and Possibility , Oxford: Oxford University Press. pp. 337–368.


Luis Rosa is a Humboldt postdoctoral fellow at the Munich Center for Mathematical Philosophy (MCMP). His area of specialization is epistemology, and his areas of competence include logic and philosophy of mind. He is mostly interested in questions about knowledge-preservation and knowledge-generation through reasoning, the epistemic role of imagination and the a priori/a posteriori distinction. He also does research on philosophical logic and the philosophy of cognitive science/AI.

First published in 3:AM Magazine: Friday, March 31st, 2017.