1588 A. Fraunce Lawiers Logike f. 120 I haue, for examples sake, put downe a Logicall Analysis of the second Aegloge in Virgill.

1689 M. Prior Epist. to F. Shephard 39 Then he, by sequence logical, Writes best, who never thinks at all.

1814 D. Stewart Elem. Philos. Human Mind II. i. §1. 47 A process of logical reasoning has been often likened to a chain supporting a weight.

1818 S. T. Coleridge Gen. Introd. or Treat. on Method 42 in Encycl. Metrop. I These cannot be introduced into a scientific treatise, without destroying the symmetry of its parts by a suspension of the logical order.

1828 J. S. Mill in Westm. Rev. 9 144 Those who maintain, that to perform the logical analysis of an argument, in the manner pointed out by the syllogism, is not the best means of discovering whether it contain a flaw.

1900 R. J. Drummond Apost. Teaching i. 25 He wants a logical explanation of the Christian faith.

1958 G. J. Warnock Eng. Philos. since 1900 ix. 120 The narrowly logical, context-neglecting manner adopted by the practitioners of ‘logical analysis’.

1860 J. L. Motley Hist. Netherlands (1868) I. i. 11 Having the sovereignty to dispose of, it seemed logical that the Estates might keep it, if so inclined.

1874 W. Stubbs Constit. Hist. I. i. 3 In France accordingly feudal government runs its logical career.

1883 P. L. Lavroff tr. ‘Stepniak’ Underground Russia 121 It may be called the sign of a lofty mind to which heroism is natural and logical.

a1652 J. Smith Select Disc. (1660) i. iii. 20 We may..be too apt to rest in a meer Logical life (it's Simplicius his expression) without any true participation of the Divine life.

a1774 A. Tucker Light of Nature Pursued (1831) IV. xxii. 220 The logical worship is rendered reasonable service in Rom. xii. 1.

1551 R. Robinson tr. T. More Vtopia ii. sig. Liii^v Those rules of restryctyons, amplyfycatyons and supposytyons, very wittelye inuented in the small Logycalles, whyche heare oure chyldren in euerye place do learne.

1569 J. Sanford tr. H. C. Agrippa Of Vanitie Artes & Sci. 22 b Other intollerable, and vaine wordes which are writen in the little Logicals.

1691 A. Wood Athenæ Oxonienses I. 10 John Colet..after he had spent seven years in Logicals and Philosophicals, was licensed to proceed in Arts.

1716 M. Davies Athenæ Britannicæ II. 328 He was educated in Grammaticals in Wikeham-School..in Logicals and Philosophicals in New College Oxon.

1868 C. S. Peirce in Proc. Amer. Acad. Arts & Sci. 1865–8 7 250 Let a + b denote all the individuals contained under a and b together. The operation here performed will differ from arithmetical addition in two respects: 1st, that it has reference to identity, not to equality; and 2d, that what is common to a and b is not taken into account twice over... The process denoted by +..I shall call the process of logical addition.

1903 B. Russell Princ. Math. ii. 18 From this point we can prove the laws of contradiction and excluded middle and double negation, and establish all the formal properties of logical multiplication and addition—the associative, commutative and distributive laws.

1970 O. Dopping Computers & Data Processing i. 23 In Boolean algebra..instead of the usual mathematical operations, there are certain logical operations; the most common ones of these are logical addition, logical multiplication, and negation.

1873 C. S. Peirce in Mem. Amer. Acad. Arts & Sci. New Ser. 9 ii. 343 The logical atom, or term not capable of logical division, must be one of which every predicate may be universally affirmed or denied... A logical atom, then, like a point in space, would involve for its precise determination an endless process.

1918 B. Russell in Monist 28 497 The reason that I call my doctrine logical atomism is because the atoms that I wish to arrive at as the..last residue in analysis are logical atoms and not physical atoms.

1958 G. J. Warnock Eng. Philos. since 1900 v. 54 Russell's world of indefinitely numerous, independent logical atoms is the metaphysical opposite of Bradley's Absolute.

1996 L. Holzman & F. Newman Unscientific Psychol. (ed. 2) iii. 43 The logical positivists..interpreted Wittgenstein's Tractatus as a directive to transform philosophy (now without the metaphysics, but not without the particular, which had become a logical atom!) into a servant of science.

1914 B. Russell Sci. Method in Philos. 16 The philosophy which I wish to advocate may be called logical atomism or absolute pluralism, because while maintaining that there are many things, it denies that there is a whole composed of those things.

1918 B. Russell in Monist 28 497 The reason that I call my doctrine logical atomism is because the atoms that I wish to arrive at as the..last residue in analysis are logical atoms and not physical atoms.

1973 E. Gellner in Horton & Finnegan Modes of Thought 179 The..formal fact of the existence and nature of the mosaic's framework itself. This vision is shared by classical empiricism and by doctrines such as ‘logical atomism’.

1997 Noûs 31 (Philos. Perspectives Suppl.) 351 Russell's logical atomism militated in favor of the reification of precision. This became manifest in Ludwig Wittgenstein's Tractatus-Logico-Philosophus.

1919 C. A. Richardson Spiritual Pluralism & Recent Philos. p. vii I refer to that school which is represented in America by the neo-realists, and in this country by logical atomists of the type of Mr Bertrand Russell.

1941 Mind 50 166 They may themselves choose to be called Logical Atomists or Logical Positivists, or may repudiate all such titles.

2000 A. J. Cortens Global Anti-realism ii. 39 A rather different account (somewhat more congenial to phenomenalism) was offered by the logical atomists: the perspicuous representation ‘shows’ or ‘pictures’ the form or structure of the fact it conveys, while the unperspicuous representation obscures its form or structure.

1903 B. Russell Princ. Math. i. 3 Pure Mathematics is the class of all propositions of the form ‘p implies q’, where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member, the notion of such that, the notion of relation, and such further notions as may be involved in the general notion of propositions of the above form.

1914 B. Russell Our Knowl. External World vii. 208 Such words as or, not, if, there is, identity, greater, plus, nothing, everything, function, and so on, are not names of definite objects, like ‘John’..but are words which require a context in order to have meaning... ‘Logical constants’, in short, are not entities.

1922 C. K. Ogden et al. tr. L. Wittgenstein Tractatus 69 My fundamental thought is that the ‘logical constants’ do not represent. That the logic of the facts cannot be represented.

1958 G. J. Warnock Eng. Philos. since 1900 x. 125 We thus get a distinction between so-called ‘logical constants’, the irreplaceable words on which the validity of general patterns of inference depends, and items of non-logical vocabulary.

1965 B. Mates Elem. Logic iv. 49 The logical constants occurring in ϕ are understood in the way usual among logicians (i.e., ‘∨’ as standing for ‘or’, ‘—’ for ‘not’, the universal quantifier for ‘all’, etc.).

1883 F. H. Bradley Princ. Logic 236 To show a new relation of elements in a logical construction is demonstration in the sense of reasoning.

1914 B. Russell Our Knowl. External World iv. 101 The only justification possible must be one which exhibits matter as a logical construction from sense-data.

1936 A. J. Ayer Lang., Truth & Logic iii. 73 The English State..is a logical construction out of individual people.

1956 J. O. Urmson Philos. Anal. iii. 36 If ‘X’ is an incomplete symbol then Xs are logical constructions. Thus if the expression ‘the average man’ is an incomplete symbol we may say that the average man is a logical construction.

1936 A. J. Ayer Lang., Truth & Logic 10 Our own logical empiricism to be distinguished from positivism.

1937 Mind 46 345 Logical Empiricists are not attempting to be metaphysical, when they distinguish between language and reality. On the contrary, the distinction refers only to certain rules of usage for statements and modes of speech. Since we have investigated the rules of speech in empirical sciences, we are justified in calling our viewpoint ‘Logical Empiricism’.

1966 J. J. Katz Philos. Lang. iii. 16 The chief reason for this failure on the part of logical empiricism..and ordinary language philosophy..was that both were governed in their inferences..by an assumption about the nature of language.

1936 Mind 45 545 J. Somerville [in] ‘The Social Ideas of the Wiener Kreis's International Congress’ reflects on the Paris Congress 1935, [and] announces that the ‘logical positivists’ desire to repudiate Comte and to be henceforth known as ‘scientific’ or ‘logical’ empiricists.

1967 Philosophy 42 293 A failure to work out in detail the consequences of logical empiricist principles for ethics.

1843 J. S. Mill Syst. Logic I. iii. v. 404 This tendency shows itself very visibly in the different logical fictions which are resorted to even by philosophers... Thus, rather than say that the earth causes the fall of bodies, they ascribe it to a force exerted by the earth, or an attraction by the earth.

1918 B. Russell in Monist 28 512 I believe that series and classes are of the nature of logical fictions.

1933 L. S. Stebbing Mod. Introd. Logic (ed. 2) 502 To say that the table is a logical fiction (or construction) is not to say that the table is fictitious..it is rather to deny that, in any ordinary sense, it is an object at all.

1933 L. S. Stebbing Mod. Introd. Logic (ed. 2) 502 ‘Logical fiction’ may be taken to be an unfortunate synonym for ‘logical construction’.

1840 J. S. Mill in London & Westm. Rev. 33 266 A truth..to be believed in opposition to all that appears proof to the mere understanding; nay, the more to be believed, because it cannot be put into words and into the logical form of a proposition without a contradiction in terms.

1967 A. E. Blumberg in Encycl. Philos. V. 13/2 Logic confines itself to those arguments whose validity rests exclusively on the logical form of the statements composing them... There is still no fully satisfactory account of logical form.

1922 C. K. Ogden et al. tr. L. Wittgenstein Tractatus 55 A symbolism..which obeys the rules of logical grammar—of logical syntax.

1962 L. J. Cohen Diversity of Meaning iii. 81 The most obvious fault in the doctrine of logical grammar is that it suggests the conceptual study of meanings to be concerned with something that is timeless and unchanging.

1937 Atlantic CLIX. 49/2 The logical-grammatical construction involved is so commonly mishandled in current American speech and print.

1887 A. Seth Hegelianism & Personality v. 172 In the first sense..development means simply logical implication.

1904 B. Russell in Mind 13 209 It would seem that..logical implication is a simple notion, into whose composition the notion of terms does not enter.

1934 M. R. Cohen & E. Nagel Introd. Logic i. 9 (heading) Logical implication does not depend on the truth of our premises.

1870 W. S. Jevons in Proc. Royal Soc. 18 167 To explain the nature of the logical machine alluded to, it may be pointed out that the third of the fundamental Laws of Thought allows us to affirm of any object one or the other of two contradictory attributes.

1883 F. H. Bradley Princ. Logic 344 We shall discuss the Indirect Method, and with it the claims of the Logical Machine.

1943 Mind 52 319 He is thus stymied at the outset, and being neither a logical machine nor an esthetic idiot he is likely to feel uncomfortable about it.

1868 C. S. Peirce in Proc. Amer. Acad. Arts & Sci. 1865–8 7 251 Let a, b denote the individuals contained at once under the classes a and b... If a and b were independent events, a, b would denote the event whose probability is the product of the probabilities of each. On the strength of this analogy..the operation indicated by the comma may be called logical multiplication.

1903 B. Russell Princ. Math. ii. 18 From this point we can prove the laws of contradiction and excluded middle and double negation, and establish all the formal properties of logical multiplication and addition—the associative, commutative and distributive laws.

1970 O. Dopping Computers & Data Processing i. 23 In Boolean algebra..instead of the usual mathematical operations, there are certain logical operations; the most common ones of these are logical addition, logical multiplication, and negation.

1885 C. S. Peirce in Amer. Jrnl. Math. 7 186 I prefer not to assign determinate values to f and v, nor to identify the logical operations with any special arithmetical ones.

1932 C. I. Lewis & C. H. Langford Symbolic Logic i. 7 It would have coincided with what we now know as symbolic logic. That is, it would have been an organon of reasoning in general, developed in ideographic symbols and enabling the logical operations to be performed according to precise rules.

1960 M. G. Say et al. Analogue & Digital Computers vii. 165 A zero input digit to this unit gives a one-digit output and a one-digit input gives a zero output. This is the logical operation ‘ not’.

1904 W. James Ess. Radical Empiricism (1912) i. 11 ‘Representative’ theories of perception avoid the logical paradox, but on the other hand they violate the reader's sense of life, which knows no intervening mental image.

1954 I. M. Copi Symbolic Logic 332 These two kinds of paradoxes were first explicitly distinguished by F. P. Ramsey in 1926. Since then those of the first kind have been known as ‘logical paradoxes’.

1967 J. van Heijenoort in Encycl. Philos. V. 45/2 In logic the word [sc. paradox] has taken on a more precise meaning. A logical paradox consists of two contrary, or even contradictory, propositions to which we are led by apparently sound arguments.

1931 A. E. Blumberg & H. Feigl in Jrnl. Philos. 28 281 To facilitate criticism and forestall even more unfortunate attempts at labelling this aspect of contemporary European philosophy, we shall employ the term ‘logical positivism’.

1934 Philos. Rev. 43 125 The logical positivism of the Vienna Circle..is based..upon this consideration of empirical meaning.

1968 M. Black Labyrinth of Lang. vi. 147 Logical Positivism has seen its best days.

1931 Jrnl. Philos. 28 291 The principle of causality is for the logical positivist not a categorical necessity of thought.

1967 J. Passmore in Encycl. Philos. V. 55/1 The logical positivists ordinarily took for granted the substantial truth of contemporary Science. Thus, it was a matter of vital concern to them when it became apparent that the verifiability principle would rule out as meaningless all scientific laws.

1868 C. S. Peirce in Proc. Amer. Acad. Arts & Sci. 1865–8 7 411 The numerical rank of a logical product depends on the identity or diversity..of parts of the factors.

1903 B. Russell Princ. Math. ii. 21 Most of the propositions of the class-calculus are easily deduced from those of the propositional calculus. The logical product or common part of two classes a and b is the class of x's such that the logical product of ‘x is an a’ and ‘x is a b’ is true. Similarly we can define the logical sum of two classes (a or b).

1941 R. Courant & H. E. Robbins What is Math.? ii. 110 By the ‘intersection’ or ‘logical product’ of A and B we mean the set consisting only of those elements which are in both A and B.

1955 A. N. Prior Formal Logic i. i. 7 We may also have a conjunction or logical product of more than two propositions, the analogy with arithmetical multiplication still holding.

1871 A. C. Fraser Life & Lett. G. Berkeley ii. 39 I have tried elsewhere..to explain the logical structure of the Essay on Vision.

1918 B. Russell in Monist 28 510 The first thing to do would be to discover the kinds of atoms out of which logical structures are composed.

1943 Mind 52 26 Linguistic structure, though at times it conceals or distorts, has to be taken as capable of revealing logical structure, otherwise the study of logic would be impossible.

1970 L. J. Cohen Implications of Induction i. 6 Many propositions are never hypothesised at all, even if alike in logical structure to those that are.

1898 Mind VII. 34 (heading) On the logical subject of the proposition.

1903 B. Russell Princ. Math. iv. 44 Every term..is a logical subject.

1933 L. S. Stebbing Mod. Introd. Logic (ed. 2) ix. 153 The point that is of importance is to distinguish the grammatical subject of a sentence from the logical subject of the proposition expressed by the sentence.

1965 N. Chomsky Aspects Theory Syntax i. 23 In (8i) [sc. ‘I persuaded a specialist to examine John’] the phrase ‘a specialist’ is the Direct-Object of the Verb Phrase and the logical Subject of the embedded sentence.

1965 N. Chomsky Aspects Theory Syntax iv. 163 It seems that beyond the notions of surface structure..and deep structure (such as ‘logical subject’), there is some still more abstract notion of ‘semantic function’ still unexplained.

1868 C. S. Peirce in Proc. Amer. Acad. Arts & Sci. 1865–8 7 411 The numerical rank of a logical sum depends on the identity or diversity..of the integrant parts.

1959 C. V. L. Smith Electronic Digital Computers ii. 32 Given two binary words..it is possible to generate a third word each bit of which is the logical sum or the logical product or, indeed, any Boolean function of the bits in the corresponding position of the given words. Operations of this sort may be called ‘logical operations’.

1963 G. T. Kneebone Math. Logic ii. 53 In older accounts of symbolic logic, the terms ‘logical sum’ and ‘logical product’ are often used where ‘disjunction’ and ‘conjunction’ would now be preferred. There is indeed an analogy between the arithmetical operations of addition and multiplication.

1818–19 S. T. Coleridge Philos. Lect. (1949) ix. 276 This necessarily led men..to doubt whether a logical truth was necessarily an existential one, i.e. whether because a truth was logically consistent it must be necessarily existent.

1877 W. S. Jevons Princ. Sci. (ed. 2) viii. 153 Nothing is more certain than logical truth.

1943 Mind 52 272 An exhaustive formulation of logical truth remains a worthy undertaking.

1940 B. Russell Inq. into Meaning & Truth 20 We pass from the primary to the secondary language by adding what I shall call ‘logical words’, such as ‘or’, ‘not’, ‘some’, and ‘all’, together with the words ‘true’ and ‘false’ as applied to sentences in the object-language.

1958 S. E. Toulmin Uses Argument iv. 149 The validity of syllogisms being closely bound up with the proper distribution of logical words within the statements composing them.

1972 Sci. Amer. Sept. 82/3 Language performs this miraculous function largely through such little particles as ‘if’, ‘when’, ‘not’, ‘therefore’, ‘all’ and ‘some’, which have been called logical words because they account for the ability of language to formulate logical inferences (also known as syllogisms).