# "Inverse" and "Converse" in academic writing [closed]

Do the words "inverse" and the words "converse" have the same meaning in academic writing as they do as logic terms? Or would it cause confusion?

If I write, "conversely...", will it mean that whatever I proceed to discuss involves a switching of cause-and-effect roles, different from the previous topic?

If I write, "inversely...", will it mean that an effect does not happen because the cause does not happen?

The OED gives the sense of reversed or opposite for both converse and inverse as well as defining the adverbs with "in the manner" of their associated adjectives. But the two cannot be used interchangeably. In situations in which terms are exchanged, you must use conversely:

All squares are rectangles, but conversely, not all rectangles are squares.

Inversely is the choice when you're talking about a turnabout in position:

The sculpture was an inversely situated cone.

That is, the sculpture has the base above the apex. The same is true for expressing a reversed proportionality:

The length of the sentences of the convicted were inversely related to their income.

That is, the more money you have, the less time you spend in jail.

(Obviously, the two words are also not equivalents in technical mathematical usage, e.g., in logic and algebra.)

• Thank you for clarifying those definitions. If, however, there was a situation where I wanted to use the meaning of "inverse" in logic, i.e. "This condition was NOT met, so this effect did NOT happen," what equivalent word would I use in other contexts? Literature analysis, for example. Commented Oct 24, 2015 at 20:15
• @Cameron If you're writing academic lit-crit, you may use your own private language. That said, given the proposition "If p, then q", the statement "If not p, then not q" is the inverse. The converse switches p and q: "If q, then p." Neither is logically equivalent to the original. Commented Oct 24, 2015 at 20:21
• But the contrapositive, which is the converse of the inverse (or the inverse of the converse -- they commute), is logically equivalent to the original. "If p, then q" is equivalent to "If not q, then not p". If it's raining, you get wet; if you don't get wet, it isn't raining. Commented Oct 24, 2015 at 22:24