Apophasis

Apophasis (Late Latin, from Greek apophanai, "to say no" ) refers, in general, to "mentioning by not mentioning". Apophasis covers a wide variety of figures of speech.

Apophasis
Apophasis was originally and more broadly a method of logical reasoning or argument by denial, a way of telling what something is by telling what it is not, a process-of-elimination way of talking about something by talking about what it isn't.

A useful inductive technique when given a limited universe of possibilities, the exclusion of all but the one remaining is affirmation through negation. The familiar guessing-game of "Is it bigger than a bread box?" is an example of apophatic inquiry.

This sense has generally fallen into disuse and is frequently overlooked, although it is still current in certain contexts, such as mysticism and negative theology. An apophatic theology sees God as ineffable and attempts to describe God in terms of what God is not. Apophatic statements refer to transcendence in this context, as opposed to cataphasis referring to immanence.

Paralipsis
Paralipsis, also known as praeteritio, preterition, cataphasis, antiphrasis, or parasiopesis, is a rhetorical figure of speech wherein the speaker or writer invokes a subject by denying that it should be invoked. As such, it can be seen as a rhetorical relative of irony. Paralipsis is usually employed to make a subversive ad hominem attack.

The device is typically used to distance the speaker from unfair claims, while still bringing them up. For instance, a politician might say, "I don't even want to talk about the allegations that my opponent is a drunk."

The most common English construction is the phrase "not to mention," as in "She is talented, not to mention rich." This construction is so common that it has lost much, if not all, of the device's rhetorical power. "Not to mention" no longer serves here as a device to separate the speaker from the claim of richness, but is just another way of saying "and." Another is the clause "if I don't say so myself" which is mistaken from the affirmative "if I do say so myself," meant to show the speaker's modesty.

Proslepsis is an extreme kind of paralipsis that gives the full details of the acts one is claiming to pass over; for example, "I will not stoop to mentioning the occasion last winter when our esteemed opponent was found asleep in an alleyway with an empty bottle of vodka still pressed to his lips."

Proslepsis
In logic, proslepsis, as described briefly by Aristotle and in detail by Theophrastus, is a type of proposition in which the middle term of a syllogism is implied. Such a syllogism is then described as a prosleptic syllogism, of which Theophrastus defined three kinds or figures.

Preterition
In Calvinist doctrine, preterition is one of the two manners of damnation by God, the other being reprobation. The idea being that a damned person is either actively sent to hell by God (reprobation) or simply overlooked (preterition) for salvation because they are not among the unconditionally elected. This doctrine, as part of unconditional election, is one of the five points of Calvinism.

Expeditio
A famous Christological argument, commonly referred to as the Trilemma or Lewis Triumvirate, is an example of expeditio. Premised on Jesus Christ's claim to being the God, it posits that he is thus either a liar, a lunatic, or the Lord (that is, who he claims to be). The argument then attempts to systematically eliminate all the options except for Lord.

Occultatio
Occultatio is a literary figure most often seen in plays, where a character describes a scene or object by not describing it. For example, in Shakespeare's The Taming of the Shrew, act 4, scene 1, the character Grumio describes the eventful coming of his master and new wife to a young servant by saying,
 * Hadst thou not crossed me, thou shouldst have heard how her horse fell and she under her horse; thou shouldst have heard in how miry a place, how she was bemoiled,[...]with many things of worthy memory, which now shall die in oblivion and thou return unexperienced to thy grave.

In this speech, Grumio, angry at the servant's interruptions, "refuses" to describe what happened, and in so doing, describes it fully.

H.P. Lovecraft frequently used occultatio to add an element of mystery to his stories, as his unfortunate protagonists met things too horrible to describe or too alien to describe.