PROPOSITION. — From Latin *pro-ponere*, “to set forth.” The corresponding Greek is *πρότασις* (*pro-tásis*), usually referring to the *p.* as the premise of a syllogism (v.). Alongside “proposizione,” Latin often uses “enunciatio” (from *ex-nunciare*, “to say, manifest, set forth”; cf. Greek *ἀπόφασις*).
A *p.* is the verbal (or possibly symbolic, algebraic: V. LOGICA SIMBOLICA) expression of a judgment, that is, of affirmation and negation: *πρότασις... λόγος καταφατικός ἢ ἀποφατικός τινός κατὰ τινός* (Aristotle, *Anal. pr.*, I, 24 a 16). A *p.* is therefore a statement, an “enunciative” phrase (*λόγος ἀποφατικός*) and is distinguished from the simple *φάσις* or *λέξις σημαντική*, which may express only feelings or states of mind (the “oratio affectiva” in its various forms: interrogative, imperative, hortatory, etc.). Since it is a property of affirmation to be either true or false, Aristotle characterizes the enunciative phrase as “that in which truth or falsity inheres”: *ἐν ᾧ τὸ ἀληθεύειν ἢ ψευδὲς ἀπάρχει* (*Perih.*, ch. 4). In logic, however, parts of a conditional sentence are also called *p.* even when the “hypothesis” is neither true nor false in itself. Grammatically, every expressive sentence is a *p.*
As the expression of a judgment (v.), the *p.* follows its structure and modalities. It may therefore assume various forms. Essential in it is merely the expression of a predicate, that is, any affirmation: *“Omnis oratio qua aliquid affirmatur vel negatur propositio est”* (Quintilian, 7, 1, 9); and in this lies the logical-formal unity to which the structural-material multiplicity of *p.*—vast in scope—may be reduced. Alongside the nominal *p.*, which usually indicates the ontological or at least logical belonging of an attribute to a subject and is, morphologically, in inflected languages, binary (e.g., *l’uomo è ragionevole*), there is the verbal *p.*, which may consist of a single term (*leggo, piove*) and thus, possibly, be monosyllabic. The *p.* may be simple, as in the examples given, or linked with other *p.* in more or less organically complex periods, according to the syntactic nature of the idiom. The closest coordination occurs when one *p.* functions as another, without which it is not semantically complete (e.g., the “hypothesis” in a conditional: *“se la virtù è un bene va desiderata”*; or, in general, the dependent *p.*: *“avendo paura, fuggi”*). In the fullness of discourse, the *p.* is further inflected by accidental determinations according to the various complemental and relational specifications that particularize and individuate the predicates.
From the logical point of view, the *p.* is, with respect to the extension of the subject (quantity), universal if the predicate is affirmed or denied of all subjects of a given class (e.g., *ogni corpo è pesante*), particular if only of some (e.g., *alcuni corpi sono radioattivi*), indefinite if the extension of the subject is unspecified (e.g., *si dissero cose importanti*). With respect to the predicate-subject relation (matter), the *p.* may be necessary (e.g., *in ogni triangolo la somma degli angoli equivale a due retti*) or contingent (e.g., *l’albero non ha frutti*). Considering together the predicate-subject relation and the gnoseological meaning of the *p.*, it is analytico-rational if the predicate is contained in the notion of the a priori (v.), synthetico-empirical if the predicate is added to the subject through experience.
Aristotelian logic has chiefly developed the nominal *p.* and, in particular, the relations of opposition among nominal *p.* in terms of quantity and quality or “form” (affirmation and negation). Important is the law on the extension of the predicate, according to which in an affirmative *p.* the predicate is, in itself, particular, and in a negative *p.* universal (*A è B = A è alcuno, non tutti i B; A non è B = A è nessuno dei B*). As for opposition (*oppositio* consists in affirming and denying the same univocal predicate of the same subject: *τοῦ αὐτοῦ καὶ τὰ τοῦ αὐτοῦ, μὴ ὁμωνύμως*: *Perih.*, ch. 6, 17 a 34), fundamental is the division of *p.* into contradictory and contrary. Two *p.* with the same subject and predicate are contradictory if they oppose each other in quantity and quality, that is, if one is universal and the other particular, one affirmative and the other negative (e.g., *ogni frutto è dolce – qualche frutto non è dolce*); they are contrary if, both universal, they oppose each other in quality, that is, one negates and the other affirms (e.g., *ogni frutto è nutritivo – nessun frutto è nutritivo*). While between two contradictories there is absolute incompatibility in truth and falsity (never both true, never both false, and therefore always dialectical toward each other, that is, one derivable from the removal of the other, since it is simply its negation), two contraries may, in the case of a non-essential predicate, both be false (cf. *op. cit.*, chs. 7 and 14; St. Thomas *ad loc.*).
Regarding further divisions of the *p.*, apart from those predominantly morphological (conditional, copulative, disjunctive, causal, exclamatory, exclusive, reduplicative—note that the truth-value in these *p.* is not measured by their individual elements but by their formal structure: e.g., the *p.* *“se Dio non esiste, non si dà bene morale assoluto”* is true), mention should be made of the division of the *p.* into assertoric, a simple affirmation of a predicate; modal, expressing the logical mode of the predicate’s belonging (e.g., *l’uomo è necessariamente imperfetto*); and problematic, expressing the possibility of the predicate (e.g., *può guarire*; cf. *Perih.*, chs. 12–13). Among the properties of *p.* is the convertibility or transposition of the predicate into the place of the subject, according to the laws of the extension of the predicate (e.g., *nessuna virtù è odiosa – nessuna cosa odiosa è virtù; tutte le virtù sono desiderabili – alcune cose desiderabili sono virtù*).