The Inversion Fallacy

Posted: October 26, 2022 in Cognition, Idle Nonsense, Mental Health, Nomenclature
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A recent episode of the Dark Horse Podcast introduced what appeared initially to be a new bit of lingo: the Inversion Fallacy. I’ve discussed logical fallacies and hidden biases in the past, and this one bears directly my multipart blog series “Dissolving Reality” from 2015 where I put forward the Ironic and Post-Ironic mindsets. The Ironic is more nearly the reversal of meaning yet tracks with the Inversion Fallacy. Without getting too hung up on the pointless minutia of terminology (trying to distinguish between, say, reversal, inversion, transposition, contradiction, and opposition), inversion means to turn something upside-down or on its head. It’s also related to devil’s advocacy, topsy-turvy argumentation, and is not … is too! squabbles where a thing becomes its opposite. Several pundits and commentators have lost my readership because of frequent forays into disingenuous reverse argumentation. I simply lack patience.

As described on Dark Horse, the Inversion Fallacy occurs when a thing or idea is treated as equivalent to its inverse. One example now commonplace in Wokedom is to accuse someone of being racist and then insist denial is proof of racism. (Also heard this particular example called a Kafka Trap, also on Dark Horse). As math, the equation would be either x = 1/x or x = –x. Inversion is the former, reversal the latter. The x = –x formulation (the Ironic) suggests that an idea or thing automatically invokes (i.e., brings into being) its opposite, especially through the use of sarcasm. Here’s the old joke illustrating the point:

Professor of linguistics hold forth before a class of undergraduates, “In language as in mathematics, a double negative is a positive. But in no mathematics or language does a double positive equal a negative.”

To which a student replies dryly, “Yeah, right ….”

The modest advantage of the x = 1/x formulation is that when x = 0, the equation has no meaning because dividing by zero is … undefined. The obvious example is the oft-quoted (and misquoted) Vietnam War nonsense, “It became necessary to destroy the town to save it.” That’s dividing by zero in a nutshell.

The difference between the two formulations does not IMO prevent the fallacy from working. My suspicion is that multiple ways of observing, describing, and naming the fallacy exist. An attribute of the Post-Ironic is that the tension between thing and not thing is expanded to include a fluid spectrum of competing positions. Whether reversal or inversion, Ironic or Post-Ironic, the common element is the necessity to set aside obvious cognitive dissonance and enter a state of flux where meanings cannot be fixed. Just a few blog posts ago, I cited George Orwell’s famous formulation: “War is Peace. Freedom is Slavery. Ignorance is Strength.” Requires Orwellian Doublethink to accept those propositions.


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