I intend in the following academic paper to provide some justification for the name I've given this kind of arch:

I came up with the term 'obverted arch' to describe this architectural structure. Our website is built on its sterling reputation for never getting in the weeds, but in categorical logic the term 'obversion' refers to switching a proposition's quality (negative to affirmative or vv.), then changing the predicate to its contradictory. For example if we obvert the original proposition

Then the new, obverted proposition is

The original proposition, "All Virgos are mad" corresponds with your classic arch:

Another operation in categorical logic is called 'inversion,' and this is where the *quantity* of the original proposition is switched (from 'all'/'no' to 'some' or vv.) and the *quality* of both terms is switched:

I suppose that an 'inverted arch' should look something like this:

And I suppose this because of the symbol called the inverted cross, revered by the devotees of St. Peter but also Satan somehow:

Thus, an object put on its head is equivalent to a proposition's quantity and its terms' qualities switching.

'Conversion' is much more straightforward: we switch the subject and predicate of the original proposition and nothing more:

Note that the truth value is not necessarily preserved after conversion. This is what I suppose a 'converted arch' must look like:

The left half of your classic arch corresponds to the subject of the original proposition (Virgos) and the right half corresponds to the predicate (the mad). Thus the left and right halves are switched in a converted arch.

If only obversion, then, were sort of like inverting and converting simultaneously:

Inv.: Some non-Virgos are non-mad

Conv.: All the mad are Virgos

Obv.: No Virgos are non-mad

Just like in the inverted proposition, the obverted one switches the quality of the original statement's predicate ('mad' to 'non-mad'), thus the arch gets put on its head. However, unlike the converted proposition, the obverted one doesn't switch the subject and predicate of the original proposition, which pisses me off.

There is the operation of 'contraposition' to consider, which comprises the operations of conversion and inversion, but that doesn't feel good. It's SO COMFORTING to presume that maybe these terms just don't extend that far outside the purview of logic, but it's unbearable to wonder if maybe they do, *and I just can't figure out how--*

While we're at it, what about this: the following are the three steps in a classic wink:

But is *this* an inverted wink:

or is *this* an inverted wink?