The simple negative particles are οὐ and μή. οὐ is the negative of fact and statement, and contradicts or denies; μή is the negative of the will and thought, and rejects or deprecates. The difference between the simple negatives holds true also of their compounds οὔτε μήτε, οὐδέ μηδέ, οὐδείς μηδείς, etc.
a. τὰ οὐκ ὄντα is that which does not exist independently of any opinion of the writer: τὰ οὐκ ὄντα λογοποιεῖν
b. The rarer οὐχί (οὐ-χί) denies with greater emphasis than οὐ. The form μηκέτι
μή as the negative of will and thought is used in various expressions involving emotion, as commands, prohibitions, wishes, hopes, prayers, petitions, promises, oaths, asseverations, and the like; in expressions marking condition, purpose, effort, apprehension, cautious assertion, surmise, and fear; in setting forth ideality, mere conceptions, abstractions as opposed to reality or to definite facts; in marking ideas as general and typical; when a person or thing is to be characterized as conceived of rather than real.—μή is used not merely when the above notions are apparent but also when they are latent. Greek often conceives of a situation as marked by feeling where English regards it as one of fact; and hence uses μή where we should expect οὐ.
a. μή corresponds to the Sanskrit prohibitive particle mā´, which in the Rig Veda is used with the independent indicative of an augmentless aorist or imper
fect which has the force of the subjunctive; rarely with the optative. In later Sanskrit mā´ was used with the subjunctive, optative, and imperative.
b. μή was originally used only in independent clauses; but later was employed in subordinate clauses, and with dependent infinitives and participles. On the origin of μή as a conjunction, see cross2222. In Homer μή is used especially with the subjunctive, optative, and imperative (i.e. in commands and wishes); rarely with the indicative (in μὴ ὤφελλον, in oaths, in questions, after
c. In later Greek (Polybius, Lucian, Dio Chrysostomus, etc.) μή has encroached on οὐ, generally by extension of usages occurring rarely in the classical language. Thus Lucian has μή after causal ὡς, ὅτι, διότι, ἐπεί; in relative clauses (sometimes οὐδέν ἐστιν ὅτι μή); with participles of cause (even ἅτε μή) or of concession; with participles without the article following an adjective; with the infinitive after
Herbert Weir Smyth [n.d.], A Greek Grammar for Colleges; Machine readable text [info] [word count] [Smyth].