An Ironic Paradox
Oct. 14th, 2011 08:26 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
cheekbones3This is a piece by Simon Varey, University of Melbourne, reproduced from "The Reasoner", vol.5, issue 10.
I was amused, so I thought I'd give you the pleasure too.
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In 1995, Alanis Morissette released the song “Ironic”. Little did she suspect she would be walking into a semantic minefield. The song proved to be a lightning rod for those pedants who had long been railing against what they saw as rampant misuse of the term ‘ironic’ in popular discourse. For comedians, possessed as they are with a heightened sense of irony, it proved a potent source of humour. What could be more ironic, they asked, than a song called “Ironic” being completely devoid of irony.
But is “Ironic” ironic, or isn’t it? The joke, that “Ironic” is ironic because it isn’t, seems to be arguing
that it is ironic, but that this irony is conditional on it being non-ironic. Yet, if “Ironic” is ironic, then it fails to fulfil the condition of being non-ironic, so it isn’t ironic. Under the principles of irony that seem to underlie the joke, “Ironic” is ironic if and only if it isn’t ironic, clearly leading to paradox. How did this paradox arise? At the risk of o_ending the same pedants who first attacked Morissette, I will
attempt the following definition of (at least one kind of) irony.
An entity E is ironic if and only if there exists some property P such that E would be expected to possess P and E in fact possesses the opposite of P
This definition will cover concrete objects, abstract objects (like songs) and events, but not situations, which I believe will require a di_erent definition. We can present this definition formally by defining a function opposite which will take a property and return its opposite (if it has one) or some arbitrary impossible property (if it doesn’t have an opposite). In other words, for every pair of opposite properties P and Q, opposite(P) = Q (and opposite(Q) = P).We will also need the relation expect such that expect(E,P) will hold only where entity E is expected to possess property P. The definition above will then be equivalent to the following:
ironic(E) <-> ƎP(expect(E; P) & opposite(P)E) (1)
This seems to be the definition that the joke above is using. A song named “Ironic” may reasonably be expected to be highly ironic, so for it to possess the property of being completely non-ironic would seem to make it very ironic. Let us, for the sake of argument, say that the only property P such that expect(“Ironic”,P) is the property ironic. As such, we can substitute “Ironic” for E and ironic for P into (1), giving us:
ironic(“Ironic”) <-> (expect(“Ironic”; ironic) & opposite(ironic)(“Ironic”)) (2)
Now, assuming that anything called ‘ironic’ will be expected to be ironic, expect(“Ironic”,ironic) will hold necessarily, so we can treat this conjunct as satisfied in every model. Let us take, as a first approximation for opposite(ironic), the property :ironic. So, from (2), we get the following thesis:
ironic(“Ironic”) <-> ¬ironic(“Ironic”) (3)
As such,“Ironic” is ironic if and only if it isn’t ironic. Parallels with the liar paradox should be clear. Irony can be understood as a form of negation—the (absolute) negation of expectation. Hence irony, like any form of negation, when applied to itself, will lead to paradox. We can generalise this result as the following, which may be called the Morissette Paradox:
An entity expected to be ironic (and only expected to be ironic) will be ironic if and only if it is not ironic
Now, of course, this discussion is highly simplified. For one, opposite(ironic) would be better understood as contrary, rather than contradictory, to ironic. More importantly, the assumption that we made that the only property expected of “Ironic” was that it was ironic is almost certainly wrong. Indeed, the point that the joke is making could, perhaps, not be that “Ironic” is ironic because it isn’t ironic, but rather that it is ironic because it doesn’t contain any irony in its lyrics.
If a formal system of irony had as an axiom that no entity could only be expected to be ironic then the Morissette Paradox would not arise. Yet, even if “Ironic” is not such an entity, it isn’t clear that such an entity could not exist. If such entities could exist, then an axiom ruling them out would seem unjustified. Without such an axiom, a formal system of irony would need to resolve the paradox in some other fashion to avoid triviality.
In conclusion, a song by someone who didn’t know what irony was has actually told us a great deal about irony. And isn’t that ironic, don’t you think?
I was amused, so I thought I'd give you the pleasure too.
~~~~~~~~~~~~~~~~~~~~~~~~
In 1995, Alanis Morissette released the song “Ironic”. Little did she suspect she would be walking into a semantic minefield. The song proved to be a lightning rod for those pedants who had long been railing against what they saw as rampant misuse of the term ‘ironic’ in popular discourse. For comedians, possessed as they are with a heightened sense of irony, it proved a potent source of humour. What could be more ironic, they asked, than a song called “Ironic” being completely devoid of irony.
But is “Ironic” ironic, or isn’t it? The joke, that “Ironic” is ironic because it isn’t, seems to be arguing
that it is ironic, but that this irony is conditional on it being non-ironic. Yet, if “Ironic” is ironic, then it fails to fulfil the condition of being non-ironic, so it isn’t ironic. Under the principles of irony that seem to underlie the joke, “Ironic” is ironic if and only if it isn’t ironic, clearly leading to paradox. How did this paradox arise? At the risk of o_ending the same pedants who first attacked Morissette, I will
attempt the following definition of (at least one kind of) irony.
An entity E is ironic if and only if there exists some property P such that E would be expected to possess P and E in fact possesses the opposite of P
This definition will cover concrete objects, abstract objects (like songs) and events, but not situations, which I believe will require a di_erent definition. We can present this definition formally by defining a function opposite which will take a property and return its opposite (if it has one) or some arbitrary impossible property (if it doesn’t have an opposite). In other words, for every pair of opposite properties P and Q, opposite(P) = Q (and opposite(Q) = P).We will also need the relation expect such that expect(E,P) will hold only where entity E is expected to possess property P. The definition above will then be equivalent to the following:
ironic(E) <-> ƎP(expect(E; P) & opposite(P)E) (1)
This seems to be the definition that the joke above is using. A song named “Ironic” may reasonably be expected to be highly ironic, so for it to possess the property of being completely non-ironic would seem to make it very ironic. Let us, for the sake of argument, say that the only property P such that expect(“Ironic”,P) is the property ironic. As such, we can substitute “Ironic” for E and ironic for P into (1), giving us:
ironic(“Ironic”) <-> (expect(“Ironic”; ironic) & opposite(ironic)(“Ironic”)) (2)
Now, assuming that anything called ‘ironic’ will be expected to be ironic, expect(“Ironic”,ironic) will hold necessarily, so we can treat this conjunct as satisfied in every model. Let us take, as a first approximation for opposite(ironic), the property :ironic. So, from (2), we get the following thesis:
ironic(“Ironic”) <-> ¬ironic(“Ironic”) (3)
As such,“Ironic” is ironic if and only if it isn’t ironic. Parallels with the liar paradox should be clear. Irony can be understood as a form of negation—the (absolute) negation of expectation. Hence irony, like any form of negation, when applied to itself, will lead to paradox. We can generalise this result as the following, which may be called the Morissette Paradox:
An entity expected to be ironic (and only expected to be ironic) will be ironic if and only if it is not ironic
Now, of course, this discussion is highly simplified. For one, opposite(ironic) would be better understood as contrary, rather than contradictory, to ironic. More importantly, the assumption that we made that the only property expected of “Ironic” was that it was ironic is almost certainly wrong. Indeed, the point that the joke is making could, perhaps, not be that “Ironic” is ironic because it isn’t ironic, but rather that it is ironic because it doesn’t contain any irony in its lyrics.
If a formal system of irony had as an axiom that no entity could only be expected to be ironic then the Morissette Paradox would not arise. Yet, even if “Ironic” is not such an entity, it isn’t clear that such an entity could not exist. If such entities could exist, then an axiom ruling them out would seem unjustified. Without such an axiom, a formal system of irony would need to resolve the paradox in some other fashion to avoid triviality.
In conclusion, a song by someone who didn’t know what irony was has actually told us a great deal about irony. And isn’t that ironic, don’t you think?
