Aporia

In philosophy, an aporia () is a conundrum or state of puzzlement. In rhetoric, it is a declaration of doubt, made for rhetorical purpose and often feigned.
Definitions.
Definitions of the term "aporia" have varied throughout history. "The Oxford English Dictionary" includes two forms of the word: the adjective "aporetic", which it defines as "to be at a loss", "impassable", and "inclined to doubt, or to raise objections"; and the noun form "aporia", which it defines as the "state of the aporetic" and "a perplexity or difficulty". The dictionary entry also includes two early textual uses, which both refer to the term's rhetorical (rather than philosophical) usage.
In George Puttenham's "The Arte of English Poesie" (1589), aporia is "the Doubtful, [so] called...because often we will seem to caste perils, and make doubts of things when by a plaine manner of speech we might affirm or deny [them]". In a reference from 1657, J. Smith's "Mystical Rhetoric," the term becomes "a figure whereby the speaker sheweth that he doubteth, either where to begin for the multitude of matters, or what to do or say in some strange or ambiguous thing" (OED). Herbert Weir Smyth's "Greek Grammar" (1956) also focuses on the rhetorical usage by defining aporia as "an artifice by which a speaker feigns doubts as to where he shall begin or end or what he shall do or say" (674).
More modern sources, perhaps because they come after the advent of post-structuralism, have chosen to omit the rhetorical usage of the term. In William Harmon's "A Handbook to Literature," for example, aporia is identified as "a difficulty, impasse, or point of doubt and indecision", while also noting that critics such as Jacques Derrida have employed the term to "indicate a point of undecidability, which locates the site at which the text most obviously undermines its own rhetorical structure, dismantles, or deconstructs itself" (39). Julian Wolfreys, in his essay "Trauma, Testimony, and Criticism", characterizes trauma as aporia, a wound with unending trail. Valiur Rahaman, in his book "Interpretations: Essays in Literary Theory " (2011), explained aporia as a creative force in both the artist and their art; it is, for the artist, an edgeless edge of the text or a work of art.
Etymology.
The separation of aporia into its two morphemes "a"- and "poros" ('without' and 'passage') reveals the word's rich etymological background as well as its connection to Platonic mythology. Sarah Kofman asserts that these two components are crucial to a fuller understanding of the word, which has been historically translated and understood somewhat reductively: "translators, who usually escape their perplexity by translating "poros" as 'expediency' and "aporia" as 'difficulty'...leave the reader in the dark as to all the semantic richness of "poros" and "aporia" and give no hint as to their links with other words belonging to the same 'family (9). Such links inevitably demonstrate that the terms are part of a "tradition" that Plato borrows from, a tradition which "breaks with a philosophical conception of translation, and with the logic of identity that it implies" (10). To demonstrate such a break, Kofman reviews multiple instances of the term throughout Plato's work. Her discussion of the myth of Poros, Penia, and Eros in Plato's "Symposium" especially reveals the concept's untranslatability. Penia, the "child of poverty", decides to forcefully impregnate herself with the inebriated Poros, the personification of plenty, who is always in opposition with aporia and thus defining aporia. The result of this union is Eros, who inherits the disparate characteristics of his parents (25). The perplexing aspect of the myth is revealed as one realizes that Penia is acting out of resourcefulness, a quality normally attributed to Poros, and Poros' inaction reveals his own passivity, a poverty of agency or "poros". Such a relationship intensely affects not only the context of aporia but its meaning as well: 
Ultimately, aporia cannot be separated from this etymological and cultural history. Such history provides insight into aporia's perplexing semantic qualities as well as into the historical context in which the word functions as an indicator of the limits of language in constructing knowledge.
Philosophy.
In philosophy, an aporia is a philosophical puzzle or a seemingly insoluble impasse in an inquiry, often arising as a result of equally plausible yet inconsistent premises (i.e. a paradox). It can also denote the state of being perplexed, or at a loss, at such a puzzle or impasse. The notion of an aporia is principally found in Greek philosophy, but it also plays a role in post-structuralist philosophy, as in the writings of Jacques Derrida and Luce Irigaray, and it has also served as an instrument of investigation in analytic philosophy.
Plato's early dialogues are often called his 'aporetic' (Greek: ἀπορητικός) dialogues because they typically end in aporia. In such a dialogue, Socrates questions his interlocutor about the nature or definition of a concept, for example virtue or courage. Socrates then, through elenctic testing, shows his interlocutor that his answer is unsatisfactory. After a number of such failed attempts, the interlocutor admits he is in aporia about the examined concept, concluding that he does not know what it is. In Plato's "Meno" (84a-c), Socrates describes the purgative effect of reducing someone to aporia: it shows someone who merely thought he knew something that he does not in fact know it and instills in him a desire to investigate it.
In Aristotle's "Metaphysics", aporia plays a role in his method of inquiry. In contrast to a rationalist inquiry that begins from "a priori" principles, or an empiricist inquiry that begins from a "tabula rasa", he begins the "Metaphysics" by surveying the various "aporiai" that exist, drawing in particular on what puzzled his predecessors: "with a view to the science we are seeking [i.e., metaphysics], it is necessary that we should first review the things about which we need, from the outset, to be puzzled" (995a24). Book Beta of the "Metaphysics" is a list of the "aporiai" that preoccupy the rest of the work.
In Pyrrhonism aporia is intentionally induced as a means of producing ataraxia.
Contemporary academic studies of the term further characterize its usage in philosophical discourses. In "Aporetics: Rational Deliberation in the Face of Inconsistency" (2009), Nicholas Rescher is concerned with the methods in which an aporia, or "apory", is intellectually processed and resolved. In the Preface, Rescher identifies the work as an attempt to "synthesize and systematize an aporetic procedure for dealing with information overload (of 'cognitive dissonance', as it is sometimes called)" (ix). The text is also useful in that it provides a more precise (although specialized) definition of the concept: "any cognitive situation in which the threat of inconsistency confronts us" (1). Rescher further introduces his specific study of the apory by qualifying the term as "a group of individually plausible but collectively incompatible theses", a designation he illustrates with the following syllogism or "cluster of contentions":
The aporia, or "apory" of this syllogism lies in the fact that, while each of these assertions is individually conceivable, together they are inconsistent or impossible (i.e. they constitute a paradox). Rescher's study is indicative of the continuing presence of scholarly examinations of the concept of aporia and, furthermore, of the continuing attempts of scholars to translate the word, to describe its modern meaning.
Rhetoric.
Aporia is also a rhetorical device whereby the speaker expresses a doubt—often feigned—about his position or asks the audience rhetorically how he or she should proceed. One aim of aporia may be to discredit the speaker's opponent. Aporia is also called "dubitatio". For example: