propositional, a.
(prɒpəʊˈzɪʃənəl)
[f. proposition n. + -al1.]
a. Pertaining to or of the nature of a logical proposition; consisting of or based on propositions; spec. applied to speech and language in which statements and assertions occur.
| c 1714 Pope, etc. Mem. M. Scriblerus i. xii, When two of these propositional Channels empty themselves into a third, they form a Syllogism. 1725 Watts Logic ii. ii. §1 If a proposition..has an indefinite subject, it is generally to be esteemed universal in its propositional sense. 1847 Sir W. Hamilton Let. to De Morgan 31 The second scheme is that which logically extends the expression of quantity to both the propositional terms. 1874 J. H. Jackson in Med. Press & Circ. 14 Jan. 21/1 But if I have to say, ‘Gold is yellow’, I have to revive the words, and I have to put them in propositional order. 1879 ― in Brain I. 312 A speechless patient may retain the word ‘no’, and yet have only the interjectional or emotional, not the propositional, use of it; he utters it in various tones as signs of feeling only. 1883 H. Drummond Nat. Law in Spir. W. xi. (1884) 360 There is no worse enemy to a living Church than a propositional theology. 1892 Mind I. 10 There are five independent laws, which are necessary and sufficient for propositional synthesis. 1922 tr. Wittgenstein's Tractatus 45 The sign through which we express the thought I call the propositional sign. Ibid. 51 An expression is thus presented by a variable whose values are the propositions which contain the expression... I call such a variable a ‘propositional variable’. 1926 H. Head Aphasia i. iii. 39 Occasionally he can not only use ‘yes’ and ‘no’ correctly, but can even repeat them. Here, then, we have propositional speech and voluntary utterance. 1932 Lewis & Langford Symbolic Logic ix. 267 In elementary functions only propositional variables occur. 1935 Weisenburg & McBride Aphasia x. 277 When propositional speech is negligible, spoken expression may nevertheless be frequent. 1943 W. G. Hardy in Cornell Univ. Abstr. of Theses (1944) 57 Richards..now concerns himself with the educative values of propositional analysis. 1947 H. Reichenbach Elem. Symbolic Logic 179 The recursive definition of the term ‘propositional expression’. 1955 A. N. Prior Formal Logic i. iii. 50 We introduce the symbol ‘o’ as a propositional constant, to stand..for some arbitrarily chosen proposition. 1957 J. Eisenson in L. E. Travis Handbk. Speech Path. (1959) xii. 438 When linguistic symbols are used to communicate a specific idea or to elicit a specific response, we are dealing with propositional speech. 1968 N. Rescher Topics in Philos. Logic v. 51 The most satisfactory course is to base the logic of belief (and of assertion) upon a propositional analysis, rather than one articulated in terms of sentences, inscriptions, utterances, or the like. 1973 J. J. Zeman Modal Logic p. v, The book..contains a detailed development of non-modal propositional logic. 1976 Listener 9 Dec. 743/1 The capacity for propositional speech—the synthesis of words into statements that, by their form, give extra meaning to those words. 1977 Word 1972 XXVIII. 223 In propositional speech (both in forming constructions and in understanding them), the patient had difficulty sorting out relationships between more than two critical items. |
b. In special collocations, as
propositional attitude, an attitude which can vary expressed towards a proposition that does not vary;
propositional calculus, a calculus which formalizes the basic truth-functional operations possible in logical propositions and gives notation, indicating conjunction, disjunction, negation, etc., to their sentential connectives;
propositional connective, a connective which is used as a logical operator in propositions;
propositional function (see
quot. 1910 and
cf. predicate n. 2 a).
| [1904 B. Russell in Mind XIII. 509 Belief is a certain attitude towards propositions, which is called knowledge when they are true, error when they are false.] 1939 Mind XLVIII. 479 When we disbelieve, then doubt, and finally believe a proposition, it must be the same proposition toward which we have these different attitudes; that is, propositions must be invariant under change of propositional attitude. 1940 B. Russell Inquiry into Meaning & Truth xi. 204 A negative basic proposition thus requires a propositional attitude, in which the proposition concerned is the one which, on the basis of perception, is denied. 1966 W. V. Quine Ways of Paradox xv. 189 Striving and wishing, like believing, are propositional attitudes and referentially opaque. 1969 J. Hintikka Models for Modalities iii. 87 (heading) Semantics for propositional attitudes. |
| 1903 B. Russell Princ. Math. ii. 12 It is not with such entities that we are concerned in the propositional calculus, but with genuine propositions. 1938 Jrnl. Symbolic Logic III. 83 Chapter 2 supplements the propositional calculus, in effect, with the Boolean algebra of one-place predicates. 1959 Ibid. XXIV. 97 Gödel proves the non⁓existence of a finite matrix characteristic for the intuitionist propositional calculus IC. 1966 Mathematical Rev. XXXI. 4/1 Since the main results are existential, a really conclusive solution requires a narrow meaning of ‘propositional calculus’. 1973 J. J. Zeman Modal Logic ii. 7 Our first task will be..to set down some propositional calculi. Many systems discussed later will be presented as extensions of the propositional calculus. |
| 1938 Jrnl. Symbolic Logic III. 84 A deductive system is presented which involves..the propositional connectives, and prediction and quantification with respect to individuals. 1952 S. C. Kleene Introd. Metamath. iv. 73 In particular, ⊃, &, {logicor}, ¬ are propositional connectives, and operators of the forms {udA}x and {semE}x are quantifiers..these six are logical operators. 1974 Jrnl. Philos. Logic III. 202 The propositional connectives concern statements. |
| 1903 B. Russell Princ. Math. ii. 13 Where there are one or more real variables, and for all values of the variables the expression involved is a proposition, I shall call the expression a propositional function. 1910 Whitehead & Russell Principia Math. I. i. 15 Let ϕx be a statement containing a variable x such that it becomes a proposition when x is given any fixed determined meaning. Then ϕx is called a ‘propositional function’; it is not a proposition, since owing to the ambiguity of x it really makes no assertion at all. 1943, 1969 [see predicate n. 2 a]. 1974 Jrnl. Philos. Logic III. 196 A predicate, or propositional function, is a statement-valued function, i.e. a function that maps objects of some kind into statements (propositions). |
Hence
propoˈsitionalist, someone who is concerned with the logic of propositions;
propoˈsitionally adv.;
propoˈsitionalness, the quality of laying down propositions.
| 1864 Masson in Macm. Mag. July 216 A quality..which coining a monstrous word for my purpose, I will venture to call propositionalness. It is in the main identical with that passion for intellectual generalization which we often speak of as particularly visible in the French mind. 1879 Brain II. 215 Then propositionally ‘yes’ and ‘no’ give assent or dissent to anything whatever. 1890 Lancet 12 Apr. 787/1 note, If he only uttered them [propositions] at random, or if they were only signs of emotion, they would not serve propositionally. 1952 Mind LXI. 61 The spurious character of our propositionalist's argument becomes evident. 1970 W. V. Quine Philos. of Logic i. 3 The propositionalist by-passes differences between languages. |