Proposition

PROPOSITION. - From Lat. pro-ponere, "to place before." The Greek πρότασις (προκτίθημι) corresponds to it, referring, for the most part, to the proposition as the premise of the syllogism (v.). Alongside "propositio" Latin often has "enunciatio" (from ex-nunciare, "to say, manifest, set forth"; cf. Gk. ἀπόφανσις).

A proposition is the verbal expression (possibly symbolic, algebraic: v. SYMBOLIC LOGIC) of the judgment, that is, of affirmation and negation: πρότασις... λόγος καταφατικὸς ἢ ἀποφαντικὸς τινὸς κατὰ τινος (Aristotle, Anal. pr., I, 1, 24 a 16). A proposition is therefore a sentence, an "enunciative" phrase (λόγος ἀποφαντικὸς), and is distinguished from the simple φάσις or λέξις σημαντικὴ which can be expressive of feelings and states of mind alone (the "affective oratio" in its various forms: interrogative, imperative, exhortative, etc.). Since it is the property of affirmation to be true or false, Aristotle characterizes the enunciative phrase as "that in which the true or the false is contained": ἐν ᾧ τὸ ἀληθεύειν ἢ ψεύδεσθαι ὑπάρχει (Perih., ch. 4). In logic, however, the parts of a conditional are also called propositions, of which at least the "hypothesis" is not in itself either true or false. Grammatically every expressive phrase is a proposition.

As the expression of the judgment (v.), the proposition follows its structure and modalities. It can therefore assume various forms. Essential in it is only the expression of a predicate, that is, any affirmation whatsoever: "Omnis oratio qua aliquid affirmatur vel negatur propositio est" (Quintilian, 7, 1, 9); and in this lies the logico-formal unity to which the extremely broad structural-material multiplicity of propositions can be reduced. Alongside the nominal proposition, which for the most part indicates the ontological or at least logical belonging of an attribute to a subject, and is, morphologically, in inflected languages, binary (man is rational), there is the verbal proposition, which can also have a single term (I read, it rains) and therefore, possibly, be monosyllabic. The proposition is then either simple, as in the examples proposed, or linked with other propositions in periods more or less organically complex according to the syntactic character of the idioms. The tightest coordination occurs when one proposition functions as part of another, without which it is not semantically complete (e.g., the "hypothesis" in the conditional: "if virtue is a good" it is to be desired; or generally the dependent proposition: "being afraid," he fled). In the fullness of discourse the proposition is then inflected into further accidentals according to the various determinations of complement and relation that specify and individuate the predicates.

From the logical point of view, the proposition is, as regards the extension of the subject (quantity), universal, if the predicate is affirmed or denied of all the subjects of a determinate class (e.g., every body is heavy), particular, if only of some among them (e.g., some bodies are radioactive), indefinite if the extension of the subject is unspecified (e.g., important things were said). As regards the predicate-subject relation (matter), the proposition can be necessary (e.g., in every triangle the sum of the angles equals two right angles), or contingent (e.g., the tree has no fruit). Considering together the predicate-subject relation and the gnoseological meaning of the proposition, it is analytic-rational if the predicate is contained in the notion of the subject and therefore derivable from it a priori (v.), synthetic-empirical if instead the predicate is added to the subject through experience.

Aristotelian logic has developed principally the nominal proposition and in particular the relations of opposition among nominal propositions, as a function of the quantity and quality or "form" (affirmation and negation) of the proposition. Important is the law on the extension of the predicate, according to which in the affirmative proposition the predicate is, in itself, particular, in the negative universal (A is B = A is some, not all, B; A is not B = A is none of the B). As regards opposition (opposition consists in affirming and denying one and the same univocal predicate of one and the same subject: τοῦ αὐτοῦ κατὰ τοῦ αὐτοῦ, μὴ ὁμωνύμως; Perih., ch. 6, 17 a 34), fundamental is the division of propositions into contradictory and contrary. Two propositions, with the same subject and predicate, are contradictory if they are opposed in quantity and quality, that is, one is universal, the other particular, one affirmative, the other negative (every fruit is sweet - some fruit is not sweet); contrary if, both universal, they are opposed in quality, that is, one denies, the other affirms (every fruit is nutritious - no fruit is nutritious). While between two contradictories there is absolute incompatibility in truth and falsity (never both true, never both false, and therefore always dialectical with respect to each other, that is, one derivable from the removal of the other, because it is its simple negation), two contraries can, in the case of a non-essential predicate, both be false (cf. op. cit., ch. 7 and 14; St. Thomas on this passage).

Regarding the further divisions of propositions, apart from those that are predominantly morphological: conditional, copulative, disjunctive, causal, exceptive, exclusive, reduplicative (it should be noted that the truth value in these propositions is not measured by their individual elements but by their formal structure: true, for example, is the proposition if God does not exist, there are no absolute moral values), mention should be made of the division of the proposition into assertoric, a simple affirmation of a predicate, modal, expressing the logical mode of belonging of the predicate (e.g., man is necessarily imperfect), and problematic, expressing the possibility of the predicate (e.g., he may recover; cf. Perih., ch. 12-13). Among the properties of propositions, note should be taken of the "convertibility" or "transposability" of the predicate in place of the subject, according to the laws of the extension of the predicate (no virtue is hateful - no hateful thing is a virtue; all virtues are desirable - some desirable things are virtues).