Word of the day — terribly perspicuous edition
March 14, 2007
Among notwithabang…’s less prurient interests is a casual pursuit of philosophy, particularly logic, as it keeps him occupied whilst he waits for the third coming of the sacred Command and Conquer (more in an upcoming post).
Thumbing through one of my logic textbooks this evening, I came across the word “converse.” My immediate mental associations consisted of:
1. The opposite of something. Can be used as an adverb. E.g. I hated “300.” Conversely, my friend liked it so much that he threatened me in order to change my opinion.
As one might have guessed, my logic book had a technical definition for “converse” that only kind of jived with my own. Namely, the converse of a categorical statement (a statement that either affirms or denies the predicate of a subject) reverses the subject and predicate.
Some word-of-the-day columns (subject) are written by notwithabang… (predicate).
Some S are P.
Some of notwithabang…’s writings (subject) are word-of-the-day columns (predicate).
Some P are S.
That’s when things got weird.
Checking with Merriam-Webster’s, converse is defined as
Something reversed in order, relation, or action, as:
a. a theorem formed by interchanging the hypothesis and conclusion of a given theorem
b. a proposition obtained by interchange of the subject and predicate of a given proposition <“no P is S ” is the converse of “no S is P ”>
So, with the thought of Chuck Taylors’ aside, is the original example I gave a legitimate use of the term? Before I jumped to the defense of the vernacular, I decided to look a little farther in the text. The result was the introduction of the term obverse, handily defined by MW as
1: the side of a coin or currency note bearing the chief device and lettering; broadly : a front or principal surface
2: a counterpart having the opposite orientation or force <their rise was merely the obverse of the Empire’s fall — A. J. Toynbee>; also : opposite 1 <joy and its obverse, sorrow>
3: a proposition inferred immediately from another by denying the opposite of what the given proposition affirms <the obverse of “all A is B” is “no A is not B” >
Were our opinions of 300 actually the obverses of one another? Although this might be a loophole in the vernacular, perhaps it is appropriately suppressed; the phrase “obversely, I thought the film was awful,” is at best an invitation to misunderstanding, and more likely an invitation to a well-earned slap in the face. Before going further in the book and trying to see if our opinions were in fact contrapositives, I got lazy and decided that it was just a linguistic problem. Then I got some paper and actually discovered that it was a linguistic problem… just not of the sort that I had originally guessed.
To use the formal (logical) definitions of converse and obverse, it is first necessary to make them into categorical statements. Thus,
Notwithabang…: 300 was awful. (300 is a member of the set of awful movies).
Friend: 300 was not awful. (300 is not a member of the set of awful movies).
and the converses become
Notwithabang…: One of the members of the set of awful movies is 300.
Friend: One of the members of the set of awful movies is not 300.
So, we can see that they aren’t converses of one another.
As for obverses,
Notwithabang…: 300 was not non-awful, or 300 was not good. (Some S is P -> Some S is not non-P)
Friend: 300 was not awful, or 300 was good. (Some S is not P -> Some S is non-P)
Our opinions *are* obverses of one another, or in another light, subcontraries (sadly, they are not subalterns). But again, that depends on how they are cast. If we think of them as predicate statements, with P equivalent to “300 was awful,” we get
Friend: not P
No converse or obverse here. Just opposites. Ergo, for non-technical discussions, any synonym of “opposite” should suffice. So while MW snobs (if they exist) may insist on calling them obverses in one sense of the word, I’m going to continue using converses simply so people know what the hell I’m talking about.