I've previously used "conversely" to mean "on the other hand". For example.
I always thought this the correct usage. Conversely, I might be wrong.
However, the OED defines it as:
In the converse manner or order; as the converse; by conversion.
This appears to be more restricted, as it implies the opposite direction. For example, if A then B; conversely, if B then A. (Wiktionary has a similar definition.)
Other dictionaries include both definitions. From The Free Dictionary,
In a contrary or opposite way; on the other hand.
Is the more general usage that does not necessarily imply the opposite direction a relatively new development? Also, is it considered colloquial?
Best Answer
Reference-book definitions of 'conversely'
Merriam-Webster's Eleventh Collegiate Dictionary (2003) defines the noun converse and the adjective converse as follows:
The definitions seem reasonable enough, but the extent to which they accurately reflect how people actually use the noun and adjective converse and (more especially) the adverb conversely depends on how broadly we interpret the meaning of the phrase "reversed in order, relation, or action."
Bryan Garner, Garner's Modern American Usage, third edition (2009) outlines the traditional logical senses of various members of the -verse family of words quite clearly:
But in everyday situations—as opposed to in discussions of mathematical relationships or in analyses of logical forms—English speakers rarely say obversely when they mean "as an equivalent statement made by negative inference," or reversely when they mean "to the contrary." Instead, the most common way to say these things in a single word is to use contrarily or conversely.
Real-world, nonspecialist usage of 'conversely' in the 1800s (and before)
An Ngram chart for the years 1800–2000 strongly suggests that the frequency of occurrence of conversely (blue line), obversely (red line), and reversely (green line) doesn't reflect the relative commonness in human thought of the underlying logical relationships "proposition with transposed terms," "proposition based on negation of a prior proposition's terms," and "proposition expressed generally as the reverse of a prior proposition":
In geometry, converse relationships are undoubtedly of much greater interest than obverse relationships; and reverse relationships (which, as Garner says, encompass both converse and inverse relationships) form too broad a designation to be especially useful in mathematical contexts. So conversely (along with inversely and directly) was much more common than obversely or reversely in the nineteenth century, a period when (to judge from Google Books search results) the terms appeared primarily in the context of mathematics or formal logic. A typical example, from Thomas Duncan, Elements of Plane Geometry (1848):
But when people began looking to the -versely family of words for a way to describe everyday, nonmathematical relationships involving a reversal of terms, or of actions, or of viewpoint, conversely appears to have appealed to them more than inversely did. One striking (and quite early) example of this preference is in David Hartley, Observations on Man, His Frame, His Duty, and His Expectations (1749):
Here, it seems clear that Hartley is using conversely to mean "looked at from the opposite extreme or point of view"—which is essentially the meaning that the Free Dictionary (cited in the OP's question) reports with its definition "In a contrary or opposite way; on the other hand."
Alexander Bain, English Composition and Rhetoric: A Manual (1867) criticizes the use of conversely to indicate negation:
Modern real-world, nonspecialist usage of 'conversely'
But a century later, it was not at all uncommon to see conversely used to indicate negation (in the sense of "to the contrary") or an alternative (in the sense of "on the other hand"), or simply to provide a transition word of no clear meaning. Here are recent examples of each.
From Paul Ellefson, Calder Hibbard, and Michael Kilgore, Federal and State Agencies and Programs Focused on Nonfederal Forests in the United States: An Assessment of Intergovernmental Roles and Responsibilities (2003) [combined snippets], where conversely seems to mean "nevertheless" or "to the contrary":
From Robert Mainfort, Indian Social Dynamics in the Period of European Contact: Fletcher Site Cemetery, Bay County, Michigan (1979) [combined snippets], where Conversely appears to be standing in for "In contrast" or "On the other hand":
And from Charles Herdendorf, C. Nicholas Raphael, and Eugene Jaworski, The Ecology of Lake St. Clair Wetlands: A Community Profile (1986):
It's hard to say what Conversely is doing in the middle of this long paragraph, other than perhaps signifying "Moving on to another point..."
Conclusions
In everyday English, conversely has a wide range of meanings—including "on the other hand," "in contrast," "nevertheless," "from a very different point of view," and "to the contrary"—in addition to its narrow traditional meaning of "with the terms transposed," in mathematics and formal logic.
The reluctance of some dictionaries to admit the legitimacy of such everyday usage, despite evidence that the usage has persisted over many decades, is baffling. In any case, the real-world usage shows no sign of abating, with or without dictionary approval.