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Logic[Gr. ]:Ger.Logik; Fr.logique; Ital.logica. Logic is ascience which has not yet completed the stage of disputes concerning itsfirst principles, although it is probably about to do so. Nearly a hundreddefinitions of it have been given. It will, however, generally be concededthat its central problem is the classification of arguments, so that allthose that are bad are thrown into one division, and those which are goodinto another, these divisions being defined by marks recognizable evenif it be not known whether the arguments are good or bad. Furthermore,logic has to divide good arguments by recognizable marks into those whichhave different orders of validity, and has to afford means for measuringthe strength of arguments.

An approach to such a classification is made by every man whenever hereasons, in the proper sense of that term. It is true that the contemplationof a state of things believed to be real may cause the contemplator tobelieve something additional, without making any classification of suchsequences. But in that case he does not criticize the procedure, nor somuch as distinctly reflect that it is just. He can, consequently, not exerciseany control over it. Now, that which is uncontrollable is not subject toany normative laws at all; that is, it is neither good nor bad; it neithersubserves an end nor fails to do so. But it is only the deliberate adoptionof a belief in consequence of the admitted truth of some other propositionwhich is, properly speaking, reasoning. In that case the belief is adoptedbecause the reasoner conceives that the method by which it has been determinedwould either in no analogous case lead to a false conclusion from truepremises, or, if steadily adhered to, would at length lead to an indefiniteapproximation to the truth, or, at least, would assure the reasoner ofultimately attaining as close an approach to the truth as he can, in anyway, be assured of attaining. In all reasoning, therefore, there is a moreor less conscious reference to a general method, implying some commencementof such a classification of arguments as the logician attempts. Such aclassification of arguments, antecedent to any systematic study of thesubject, is called the reasoner'slogica utens, in contradistinctionto the result of the scientific study, which is calledlogica docens.See REASONING.

That part of logic, that is, oflogica docens, which, setting out with such assumptions as that every assertion is either true or false, and not both, and that some propositions may be recognized to be true, studies the constituent parts of arguments and produces a classification of arguments such as is above described, is often considered to embrace the whole of logic; but a more correct designation is Critic (Gr. . According to Diogenes Laertius, Aristotle divided logic into three parts, of which one was ). This word, used by Plato (who divides all knowledge intoepitactic andcritic), was adopted into Latin by the Ramists, and into English by Hobbes and Locke. >From the last it was taken into German by Kant, who always writes it Critik, the initialc being possibly a reminiscence of its English origin. At present it is written Kritik in German. Kant is emphatic in the expression of the wish that the word may not be confounded with critique, a critical essay (Ger. Kritik). [The forms Critique and Critic are used interchangeably in this work. (Cf. CRITICISM.) (J.M.B.)]

It is generally admitted that there is a doctrine which properly antecedeswhat we have called critic. It considers, for example, in what sense andhow there can be any true proposition and false proposition, and what arethe general conditions to which thought or signs of any kind must conformin order to assert anything. Kant, who first raised these questions toprominence, called this doctrine transcendentale Elementarlehre, and madeit a large part of hisCritic of the Pure Reason. But theGrammaticaSpeculativa of Scotus is an earlier and interesting attempt. The commonGerman word is Erkenntnisstheorie, sometimes translated EPISTEMOLOGY (q.v.).

It is further generally recognized that another doctrine follows aftercritic, and which belongs to, or is closely connected with, logic. Preciselywhat this should contain is not agreed; but it must contain the generalconditions requisite for the attainment of truth. Since it may be heldto contain more, one hesitates to call it heuristic. It is often calledMethod; but as this word is also used in the concrete, methodic or methodeuticwould be better.

For deciding what is good logic and what is bad, appeal is made by differentwriters to one or more, generally several, of these eight sources: to directdicta of consciousness, to psychology, to the usages of language, to metaphysicalphilosophy, to history, to everyday observation, to mathematics, and tosome process of dialectic. In the middle ages appeal was frequently madeto authority.

The appeal to direct consciousness consists in pronouncing certain reasoningto be good or bad because it is felt to be so. This is a very common method.Sigwart, for example, bases all logic upon our invincible mental repulsionagainst contradiction, or, as he calls it, 'the immediate feeling of necessity'(Logic§ 3, 2). Those who think it worth while to make anydefence at all of this proceeding urge, in effect, that, however far thelogician may push his criticisms of reasoning, still in doing so, he mustreason, and so must ultimately rely upon his instinctive recognition ofgood and bad reasoning. Whence it follows that, in Sigwart's words, 'everysystem of logic must rest upon this principle.' It is, however, to be notedthat among the dicta of direct consciousness, many pronounce certain reasoningsto be bad. If, therefore, such dicta are to be relied upon, man not onlyusually has a tendency to reason right, but also sometimes has a tendencyto reason wrong; and if that be so, the validity of a reasoning cannotconsistin a man's having a tendency to reason in that way. Some say that the validityof reasoning consists in the 'definitive dictum' of consciousness; butit has been replied that certain propositions in Euclid were studied fortwo thousand years by countless keen minds, all of whom had an immediatefeeling of evidence concerning their proofs, until at last flaws were detectedin those proofs, and are now admitted by all competent persons; and itis claimed that this illustrates how far from possible it is to make directappeal to a definitive pronouncement. Besides, say those who object tothis method, all reasoning and inquiry expects that there is such a thingas the truth concerning whatever question may be under examination. Now,it is of the very essence of this 'truth,' the meaning of the expectation,that the 'truth' in no wise depends upon what any man to whom direct appealcan be made may opine about that question.A fortiori it does notdepend upon whether I am satisfied with it or not. It is further insistedthat there can be no genuine criticism of a reasoning until that reasoningis actually doubted; and no sooner is it actually doubted than we findthat consciousness has revoked herdictum in its favour, if sheever made any. It is, indeed, maintained that so far from true is it thatevery system of logic must be based upon any instinctive recognition ofgood and bad reasoning, that it is quite impossible for any reasoning tobe based upon such recognition in respect to that same reasoning. In reasoning,a man may feel sure he is right; but to 'rest' that confidence on nothingbut itself is to rest it on nothing at all. If the fact that we must useour reasoning instinct in criticizing reasoning proves that we must appealto nothing else in such criticism, it equally proves that we ought to followthe lead of that instinct without any logical control at all, which wouldbe as much as to say that we ought not to reason at all. A man cannot criticizeevery part of his reasoning, since he cannot criticize the act of reasoninghe is performing in the criticism, it is true. But he can criticize stepswhose validity he doubts; and in doing so, ought to consider in what charactersthe validity of reasoning consists, and whether the reasoning in questionpossesses those characters.

Under an appeal to psychology is not meant every appeal to any factrelating to the mind. For it is, for logical purposes, important to discriminatebetween facts of that description which are supposed to be ascertainedby the systematic study of the mind, and facts the knowledge of which altogetherantecedes such study, and is not in the least affected by it; such as thefact that there is such a state of mind as doubt, and the fact that themind struggles to escape from doubt. Even facts like these require to becarefully examined by the logician before he uses them as the basis ofhis doctrine. But many logicians have gone much further, and have avowedlybased their systems upon one or another theory of psychology. Another classof logicians have professed to base logic upon a psychological theory ofcognition. Of course, if this is done, such psychological doctrine is placedabove logical criticism, or, at any rate, above logical support. For ifthe truth of a conclusion is known only from certain premises, it cannotbe used to support those premises. Now, it may be doubted whether psychologyis not, of all the special sciences, the one which stands most in needof appeal to a scientific logic.

Appeals to the usages of language are extremely common. They are madeeven by those who use algebraical notation in logic 'in order to free themind from the trammels of speech' (Schröder,Logik, i. p. iii).It is difficult to see what can be hoped for from such a proceeding, unlessit be to establish a psychological proposition valid for all minds. Butto do this, it would be necessary to look beyond the small and very peculiarclass of Aryan languages, to which the linguistic knowledge of most ofthose writers is confined. The Semitic languages, with which some of themare acquainted, are too similar to the Aryan greatly to enlarge their horizon.Moreover, even if other languages are examined, the value of any logicalinferences from them is much diminished by the custom of our grammariansof violently fitting them to the Procrustean bed of Aryan grammar.

The objection which has been suggested to appeals to psychological resultsapplies with far greater force to appeals to metaphysical philosophy, which,it will generally be conceded, can hardly take a step with security unlessit rests upon the science of logic. Nevertheless, a great many logicaltreatises of various colours make it their boast that they are built uponphilosophical principles.

Logicians occasionally appeal to the history of science. Such and sucha mode of reasoning, it is said, for example, was characteristic of mediaevalismor of ancient science; such another produced the successes of modern science.If logic is to be based upon probable reasonings, as some logicians maintainthat it must be, such arguments, if critically examined, must be admittedto have great weight. They will naturally be out of place in a system oflogic which professes to demonstrate from certain initial assumptions thatthe kinds of reasoning it recommends must be accepted.

There is probably room for dispute as to whether logic need assert anythingat all as an absolute matter of fact. If it does not, any appeal to experiencewould seem to be irrelevant. If it does, still the opinion may be thatsuch assertions of logic are of so exceedingly broad and slight a naturethat the universal experience of every man's every day and hour puts thembeyond all doubt -- such experiences as that the world presents appearancesof variety, of law, and of the real action of one thing upon another. Asappearances, these things do not seem likely ever to be doubted. If logichas need of any facts, and if such facts will suffice, no objection canwell be made to an appeal to them.

The boundary between some parts of logic and pure mathematics in itsmodern treatment is almost evanescent, as may be seen in Dedekind'sWassind und was sollen die Zahlen(1888, Eng. trans. 1901). There are,however, departments of logic, such as the logic of probable inference(if that be regarded a part of logic), in which appeal is sometimes madeto mathematical results, such as Bernoulli's law of high numbers. It seemsto be the general opinion that nothing so difficult as mathematics canbe admitted into, or be appealed to by, the science of logic, which hasthe peculiarity of consisting chiefly of truisms.

In mathematical reasoning there is a sort of observation. For a geometricaldiagram or array of algebraical symbols is constructed according to anabstractly stated precept, and between the parts of such diagram or arraycertain relations are observed to obtain, other than those which were expressedin the precept. These being abstractly stated, and being generalized, soas to apply to every diagram constructed according to the same precept,give the conclusion. Some logicians hold that an equally satisfactory methoddepends upon a kind of inward observation, which is not mathematical, sinceit is not diagrammatic, the development of a conception and its inevitabletransformation being observed and generalized somewhat as in mathematics;and those logicians base their science upon such a method, which may convenientlybe termed, and is sometimes termed, a Dialectic. Other logicians regardsuch a method as either extremely insecure or as altogether illusory.

The generally received opinion among professors of logic is that allthe above methods may properly be used on occasion, the appeal to mathematics,however, being less generally recognized.

Literature: the history of logic in Western Europe, down to the revival of learning, is given by PRANTL, Gesch. d. Logik im Abendlande. Upon the points upon which this author touches, he always affords valuable information, though his judgments are peremptory and slashing. Unfortunately, he omits much which was regarded by the authors of whom he treats as most important, because he does not himself so regard it. He also omits much which would be interesting to a reader taking a broader conception of logic. It is hardly necessary to say that upon some large subjects his views are controverted. Of the modern development of logic there is no satisfactory history; but there are notices good as far as they go in UEBERWEG, Syst. d. Logik (Eng. trans.); in the much earlier work of BACHMANN, Syst. d. Logik (1828); in HAMILTON, Lects. on Logic; and for later work in B. ERDMANN, Logik. CH. SIGWART, Logic (Eng. trans.), and WUNDT, Logik, may also be profitably consulted. See under the logical topics generally (e.g. EMPIRICAL LOGIC, FORMAL LOGIC, JUDGMENT, and PROPOSITION); and also BIBLIOG. C. (C.S.P.,C.L.F.)

Logic (Hegel'sLogik): seeHEGEL'S TERMINOLOGY, II.b.

Logic (exact): Ger.exakte Logik;Fr.logique exacte; Ital.logica esatta. The doctrine thatthe theory of validity and strength of reasoning ought to be made one ofthe 'exact sciences,' that is, that generalizations from ordinary experienceought, at an early point in its exposition, to be stated in a form fromwhich by mathematical, or expository, REASONING (q.v.), the rest of thetheory can be strictly deduced; together with the attempt to carry thisdoctrine into practice.

This method was pursued, in the past, by Pascal (1623-62), Nicolas Bernoulli(1687-1759), Euler (1708-83), Ploucquet (1716-90), Lambert (1728-77), LaPlace (1749-1827), De Morgan (1806-71), Boole (1815-64), and many others;and a few men in different countries continue the study of the problemsopened by the last two named logicians, as well as those of the properfoundations of the doctrine and of its application to inductive reasoning.The results of this method, thus far, have comprised the development ofthe theory of probabilities, the logic of relatives, advances in the theoryof inductive reasoning (as it is claimed), the syllogism of transposedquantity, the theory of the Fermatian inference, considerable steps towardsan analysis of the logic of continuity and towards a method of reasoningin topical geometry, contributions towards several branches of mathematicsby applications of 'exact' logic, the logical graphs called after Eulerand other systems for representing in intuitional form the relations ofpremises to conclusions, and other things of the same general nature.

There are those, not merely outside the ranks of exact logic, but evenwithin it, who seem to suppose that the aim is to produce a calculus, orsemi-mechanical method, for performing all reasoning, or all deductiveinquiry; but there is no reason to suppose that such a project, which ismuch more consonant with the ideas of the opponents of exact logic thanwith those of its serious students, can ever be realized. The real aimis to find an indisputable theory of reasoning by the aid of mathematics.The first step in the order of logic towards this end (though not necessarilythe first in the order of inquiry) is to formulate with mathematical precision,definiteness, and simplicity, the general facts of experience which logichas to take into account.

The employment of algebra in the investigation of logic is open to thedanger of degenerating into idle trifling of too rudimentary a characterto be of mathematical interest, and too superficial to be of logical interest.It is further open to the danger that the rules of the symbols employedmay be mistaken for first principles of logic. An algebra which bringsalong with it hundreds of purely formal theorems of no logical import whatevermust be admitted, even by the inventor of it, to be extremely defectivein that respect, however convenient it may be for certain purposes. Onthe other hand, it is indisputable that algebra has an advantage over speechin forcing us to reason explicitly and definitely, if at all. In that wayit may afford very considerable aid to analysis. It has been employed withgreat advantage in the analysis of mathematical reasonings.

Algebraic reasoning involves intuition just as much as, though moreinsidiously than, does geometrical reasoning; and for the investigationof logic it is questionable whether the method of graphs is not superior.Graphs cannot, it is true, readily be applied to cases of great complexity;but for that very reason they are less liable to serve the purposes ofthe logical trifler. In the opinion of some exact logicians, they leadmore directly to the ultimate analysis of logical problems than any algebrayet devised. See LOGICAL DIAGRAM (or GRAPH).

It is logical algebra, however, which has chiefly been pursued. De Morganinvented a system of symbols, which had the signal advantage of being entirelynew and free from all associations, misleading or otherwise. Although heemployed them for synthetical purposes almost exclusively, yet the greatgenerality of some of the conceptions to which they led him is sufficientto show that they might have been applied with great advantage in analysis.Boole was led, no doubt from the consideration of the principles of thecalculus of probabilities, to a wonderful application of ordinary algebrato the treatment of all deductive reasoning not turning upon any relationsother than the logical relations between non-relative terms. By means ofthis simple calculus, he took some great steps towards the elucidationof probable reasoning; and had it not been that, in his pre-Darwinian day,the notion that certain subjects were profoundly mysterious, so that itwas hopeless, if not impious, to seek to penetrate them, was still prevalentin Great Britain, his instrument and his intellectual force were adequateto carrying him further than he actually went. Most of the exact logiciansof to-day are, from the nature of the case, followers of Boole. They havemodified his algebra by disusing his addition, subtraction, and division,and by introducing a sign of logical aggregation. This was first done byJevons; and he proposed^.|^. , a sign of divisionturned up, to signify this operation. Inasmuch as this might easily beread as three signs, it would, perhaps, be better to join the two dotsby a light curve, thus . Some use the sign+ for logical aggregation. The algebra of Boole has also been amplifiedso as to fit it for the logic of relatives. The system is, however, farfrom being perfect. See RELATIVES (logic of).

Certain terms of exact logic may be defined as follows: --

Aggregation. The operation of uniting two or more terms or propositions,calledaggregants, to produce anaggregate term or propositionwhich is true of everything of which any aggregant is true, and false ofeverything of which all the aggregants are false. It is opposed tocomposition,which is the operation of producing from two or more terms or propositions,called thecomponents, a new term or proposition, called theircompound,which is true of all of which all the components are true, and false ofall of which any are false.

Absorption,law of(Ger.Absorptionsgesetz). Theproposition that if of two aggregants one contains the other as a component,the aggregate is identical with the latter.

Alternative proposition. A term preferred by some logicians to'disjunctive,' because the latter term is often, as by Cicero and AulusGellius, understood to imply that one, and one only, of the alternativesis true. At the same time, the standard traditional example of a disjunctivewas 'Socrates currit vel Plato disputat,' and the rule was 'Ad veritatemdisiunctivae sufficit alteram partem esse veram.' Nevertheless, the narrowersense was also recognized, and the term alternative is perhaps preferable.

Associative. An operation combining two elements isassociativeif, and only if, in combining the result with a third element, it makesno difference whether the middle element be first combined with the lastand the result with the first, or the other way, so long as the order ofsequence is preserved. Addition and multiplication are associative, whileinvolution is not so; for ten to the three-square power is a milliard,while ten cube squared is only a million. An associative algebra is analgebra in which multiplication is associative.

Commutative. An operation by which two elements are united issaid to becommutative if, and only if, it makes no difference whichis taken first. Thus, because twice three is thrice two, numerical multiplicationis commutative.

Composition: seeAggregation, above.

Compound: seeAggregation, above.

Copula is often defined as that which expresses the relationbetween the subject-term and the predicate-term of a proposition. But thisis not sufficiently accurate for the purposes of exact logic. Passing overthe objection that it applies only to categorical propositions, as if conditionaland copulative propositions had no copula, contrary to logical tradition,it may be admitted that a copula often does fulfil the function mentioned;but it is only an accidental one, and its essential function is quite different.Thus, the proposition 'Some favoured patriarch is translated' is essentiallythe same as 'A translated favoured patriarch is'; and 'Every mother isa lover of that of which she is a mother' is the same as 'A mother of somethingnot loved by her is not.' In the second and fourth forms, the copula connectsno terms; but if it is dropped, we have a mere term instead of a proposition.Thus the essential office of the copula is to express a relation of a generalterm or terms to the universe. The universe must be well known and mutuallyknown to be known and agreed to exist, in some sense, between speaker andhearer, between the mind as appealing to its own further considerationand the mind as so appealed to, or there can be no communication, or 'commonground,' at all. The universe is, thus, not a mere concept, but is themost real of experiences. Hence, to put a concept into relation to it,and into the relation of describing it, is to use a most peculiar sortof sign or thought; for such a relation must, if it subsist,existquite otherwise than a relation between mere concepts. This, then, is whatthe copula essentially does. This it may do in three ways: first, by avague reference to the universe collectively; second, by a reference toall the individuals existent in the universe distributively; third, bya vague reference to an individual of the universe selectively. 'It isbroad daylight,' I exclaim, as I awake. My universe is the momentary experienceas a whole. It is that which I connect as object of the composite photographof daylight produced in my mind by all my similar experiences. Secondly,'Every woman loves something' is a description of every existing individualin the universe. Every such individual is said to be coexistent only withwhat, so far as it is a woman at all, is sure to be a lover of some existingindividual. Thirdly, 'Some favoured patriarch is translated' means thata certain description applies to a select individual. A hypothetical proposition,whether it be conditional (of which the alternative, or disjunctive, propositionis a mere species, orvice versa, as we choose to take it) or copulative,is either general orut nunc. A general conditional is preciselyequivalent to a universal categorical. 'If you really want to be good,you can be,' means 'Whatever determinate state of things may be admissiblysupposed in which you want to be good is a state of things in which youcan be good.' The universe is that of determinate states of things thatare admissable hypothetically. It is true that some logicians appear todispute this; but it is manifestly indisputable. Those logicians belongto two classes: those who think that logic ought to take account of thedifference between one kind of universe and another (in which case, severalothersubstantiae of propositions must be admitted); and those whohold that logic should distinguish between propositions which are necessarilytrue or false together, but which regard the fact from different aspects.The exact logician holds it to be, in itself, a defect in a logical systemof expression, to afford different ways of expressing the same state offacts; although this defect may be less important than a definite advantagegained by it. The copulative proposition is in a similar way equivalentto a particular categorical. Thus, to say 'The man might not be able voluntarilyto act otherwise than physical causes make him act, whether he try or not,'is the same as to say that there is a state of things hypothetically admissiblein which a man tries to act one way and voluntarily acts another way inconsequence of physical causes. As to hypotheticalsut nunc, theyrefer to no range of possibility, but simply to what is true, vaguely takencollectively.

Although it is thus plain that the action of the copula in relatingthe subject-term to the predicate-term is a secondary one, it is neverthelessnecessary to distinguish between copulas which establish different relationsbetween these terms. Whatever the relation is, it must remain the samein all propositional forms, because its nature is not expressed in theproposition, but is a matter of established convention. With that proviso,the copula may imply any relation whatsoever. So understood, it is theabstractcopula of De Morgan (Camb.Philos.Trans., x.339). Atransitive copula is one for which the mood Barbara is valid.Schröder has demonstrated the remarkable theorem that if we use insmall capitals to represent any one such copula, of which 'greater than'is an example, then there is some relative termr, such that theproposition 'SP' is precisely equivalentto 'S isr toP and isr to whateverPisr to.' Acopula of correlative inclusion of one for whichboth Barbara and the formula of identity hold good. Representing any onesuch copula byis in italics, there is a relative termr,such that the proposition 'Sis P' is precisely equivalentto 'S isr to whateverP isr to.' If the lastproposition follows from the last but one, no matter what relativermay be, the copula is called thecopula of inclusion, used by C.S. Peirce, Schröder, and others. De Morgan uses a copula defined asstanding for any relation both transitive and convertible. The latter characterconsists in this, that whatever termsI andJ may be, ifwe represent this copula by is in black = letter, then from 'I isJ'it follows that 'J isI.' From these two propositions, weconclude, by Barbara, that 'I isI.' Such copulas are, forexample, 'equal to,' and 'of the same colour as.' For any such copula therewill be some relative termr, such that the proposition 'SisP' will be precisely equivalent to 'S isr to everything,and only to everything, to whichP isr.' Such a copula maybe called a copula of correlative identity. If the last proposition followsfrom the last but one, no matter what relativer may be, the copulais thecopula of identity used by Thomson, Hamilton, Baynes, Jevons,and many others.

It has been demonstrated by Peirce that the copula of inclusion is logicallysimpler than that of identity.

Diagram: see LOGICAL DIAGRAM.

Dialogism. A form of reasoning in which from a single premisea disjunctive, or alternative, proposition is concluded introducing anadditional term; opposed to a syllogism, in which from a copulative propositiona proposition is inferred from which a term is eliminated.

Syllogism: All men are animals, and all animals are mortal;  All men are mortal.

Dialogism: Some men are not mortal;  Either some men are not animals, or some animals are not mortal.

Dimension. An element or respect of extension of a logical universeof such a nature that the same term which is individual in one such elementof extension is not so in another. Thus, we may consider different personsas individual in one respect, while they may be divisible in respect totime, and in respect to different admissible hypothetical states of things,&c. This is to be widely distinguished from different universes, as,for example, of things and of characters, where any given individual belongingto one cannot belong to another. The conception of a multidimensional logicaluniverse is one of the fecund conceptions which exact logic owes to O.H. Mitchell. Schröder, in his then second volume, where he is farbelow himself in many respects, pronounces this conception 'untenable.'But a doctrine which has, as a matter of fact, been held by Mitchell, Peirce,and others, on apparently cogent grounds, without meeting any attempt atrefutation in about twenty years, may be regarded as being, for the present,at any rate, tenable enough to be held.

Dyadic relation. A fact relating to two individuals. Thus, thefact thatA is similar toB, and the fact thatA isa lover ofB, and the fact thatA andB are both men,are dyadic relations; while the fact thatA givesB toCis a triadic relation. Every relation of one order of relativity may beregarded as a relative of another order of relativity if desired. Thus,manmaybe regarded asman coexistent with, and so as a relative expressinga dyadic relation, although for most purposes it will be regarded as amonad or non-relative term.

Index (in exact logic): see sub verbo.

Many other technical terms are to be found in the literature of exactlogic.

Literature: for the study of exact logic in its more recent development, excluding probability, the one quite indispensable book is SCHRÖDER, Algebra d. Logik; and the bibliography therein contained is so exhaustive that it is unnecessary to mention here any publications previous to 1890. Schröder's pains to give credit in full measure, pressed down and running over, to every other student is hardly less remarkable than the system, completeness, and mathematical power of his work, which has been reviewed by C. S. PEIRCE in the Monist, vii. 19-40, 171-217. See also C. S. PEIRCE, Studies in Logic; Pop. Sci. Mo., xii. 1; and Proc. Amer. Acad. Arts and Sci., vii. 287. Cf. SCIENTIFIC METHOD. (C.S.P.)

Logic (of chance): see PROBABILITY.

Logic(of emotion): see TERMINOLOGY,English, 'Affective Logic.'

Logic(social): see SOCIAL LOGIC.

Logic(symbolic): see SYMBOLICLOGIC.

Logical [Lat.logicalis, fromlogica,logic]: Ger.logisch; Fr.logique; Ital.logico. Irrespectiveof any facts except those of which logic needs to take cognizance, suchas the facts of doubt, truth, falsity, &c.

Logical possibility is, according to usage, freedom from allcontradiction, explicit or implicit; and any attempt to reform the inaccuracywould only bring confusion.

Logical necessity is the necessity of that whose contrary isnot logically possible.

Logical induction is an induction based on examination of everyindividual of the class to which the examination relates. Thus, conclusionsfrom a census are logical inductions. While this mode of inference is adegenerate form of induction, it also comes into the class of dilemmaticreasoning.

Logical truth is a phrase used in three senses, rendering italmost useless.

1. The harmony of a thought with itself. Most usually so defined, butseldom so employed. So far as this definition is distinct, it makes logicaltruth a synonym for logical possibility; but, no doubt, more is intended(Hamilton,Lects.on Logic, xxvii).

2. The conformity of a thought to the laws of logic; in particular,in a concept, consistency; in an inference, validity; in a proposition,agreement with assumptions. This would better be calledmathematicaltruth, since mathematics is the only science which aims at nothingmore (Kant,Krit.d.reinen Vernunft, 1st ed., 294).

3. More properly, the conformity of a proposition with the reality,so far as the proposition asserts anything about the reality. Opposed,on the one hand, to metaphysical truth, which is an affection of theens,and on the other hand to ethicaltruth, which is telling what awitness believes to be true (Burgersdicius,Inst.Met., chap.xviii).

Logical parts and whole. Parts and whole of logical extension.

Logical reasoning. Reasoning in accordance with a LEADING PRINCIPLE(q.v.) which thorough analysis, discussion, and experience have shown mustlead to the truth, in so far as it is relied upon. But what Aristotle understoodby a logical demonstration may be seen in hisDe generatione animalium,Lib. II. cap. viii.

Logical presumption. A Wolffian term for synthetic reasoning,that is, induction and analogy; for hypothetic reasoning was not recognizedas reasoning at all. The uniformity of nature is called theprincipleof logical presumption.

Logical division. Division into logical parts.

Logical distinctness. That distinctness which results from logicalanalysis.

Logical actuality. Kant, in theLogik by Jäsche (Einleitung,vii), defines logical actuality as conformity to the principle of sufficientreason, consisting of the cognition having reasons and having no falseconsequences; and he makes this, along with logical possibility, to constitutelogical truth, which is thus used in its second sense. But in theCriticof the Pure Reason, in discussing the functions of judgments (1st ed.,75), he says that an assertoric proposition asserts logical actuality (Wirklichkeit,which Max Müller wrongly translates 'reality'), and makes this phrasesynonymous with logical truth (which is thus used in its third, and proper,sense).

Logical definition. A strict definition by genus and specific difference. Ockham and his followers objected to the designation on the ground that the logician, as such, had no occasion to define any ordinary term, such as man (Tractatus logices, Pt. I. chap. xxvi). (C.S.P.)

Logical Diagram (orGraph):Ger.logische Figur; Fr.diagramme logique; Ital.diagrammalogico. A diagram composed of dots, lines, &c., in which logicalrelations are signified by such spatial relations that the necessary consequencesof these logical relations are at the same time signified, or can, at least,be made evident by transforming the diagram in certain ways which conventional'rules' permit.

In order to form a system of graphs which shall represent ordinary syllogisms,it is only necessary to find spatial relations analogous to the relationsexpressed by the copula of inclusion and its negative and to the relationof negation. Now all the formal properties of the copula of inclusion areinvolved in the principle of identity and thedictum de omni. Thatis, ifr is the relation of the subject of a universal affirmativeto its predicate, then, whatever termsX,Y Zmay be, EveryXisr to anX; and if everyX isr to aY,and everyY isr to aZ, everyX isrto aZ. Now, it is easily proved by the logic of relatives, thatto say that a relationr is subject to these two rules, impliesneither more nor less than to say that there is a relationl, suchthat, whatever individualsA andB may be.

If nothing is in the relationl toA without being alsoin the same relationl toB, thenA is in the relationrtoB; and conversely, that, IfA isr toB,there is nothing that isl toA except what isl toB.

Consequently, in order to construct such a system of graphs, we must find some spatial relation by which it shall appear plain to the eye whether or not there is anything that is in that relation to one thing without being in that relation to the other. The popular Euler's diagrams fulfil one-half of this condition well by representingA as an oval inside the ovalB. Then,l is the relation of being included within; and it is plain that nothing can be inside ofA without being insideB. The relation of the copula is thus represented by the spatial relation of 'enclosing only what is enclosed by.' In order to represent the negation of the copula of inclusion (which, unlike that copula, asserts the existence of its subject), a dot may be drawn to represent some existing individual. In this case the subject and predicate ovals must be drawn to intersect each other, in order to avoid asserting too much. If an oval already exists cutting the space in which the dot is to be placed, the latter should be put on the line of that oval, to show that it is doubtful on which side it belongs; or, if an oval is to be drawn through the space where a dot is, it should be drawn though the dot; and it should further be remembered that if two dots lie on the boundaries of one compartment, there is nothing to prevent their being identical. The relation of negation here appears as 'entirely outside of.' For a later practical improvement see Venn,Symbolic Logic, chap. xi. (C.S.P.)

Logical Machine:Ger.logische Machina; Fr.machine logique; Ital.macchine logistiche(E.M.). An instrument devised to facilitate by mechanical means the handling of logical symbols or diagrams.

There are three such instruments which merit attention: --

(1) The first was constructed by W. Stanley Jevons in 1869 (announcedin hisSubstitution of Similars, 1869, 60; described inPhilos,Trans.Roy.Soc.,1870, 497-518; brief description inProc.Roy.Soc.,1870, 166-9, andPrinc.of Sci., 1874, 123-31). This instrumentwas preceded by the logical slate and the logical ABACUS (q.v.) (Proc.ManchesterLit.and Philos.Soc., Apr. 1866, 161;Substitutionof Similars, 1869, 54-9). In the logical slate the combinations ofletters, representing all the possible combinations of a definite numberof characters or qualities in a logical universe, were engraved in verticalcolumns upon a common writing-slate. The combinations inconsistent withgiven premises were then crossed off with a slate pencil, and the conclusionsread off from the untouched combinations.

In the logical abacus the combinations were marked on flat slips ofwood arranged in horizontal lines on an inclined blackboard having a seriesof ledges. The slips of wood were furnished with pins, so that those whichrepresented combinations consistent with the premises could be lifted bymeans of a ruler to the ledge above.

In the logical slate, great care was necessary to cross off all theinconsistent combinations, and in the logical abacus similar care was requiredin picking out all the consistent combinations. The logical machine ofJevons is a logical abacus in which all that is required of the operatoris to press the premises upon a series of keys; the operation of liftingthe combinations consistent with the premises to the higher level beingaccomplished mechanically by a series of levers. By means of a lattice-workwith horizontal slits, the combinations expressed in the premises and consistentwith them, and these only, are exhibited to view. This machine, while manifestingconsiderable ingenuity on the part of the contriver, was nevertheless acumbersome piece of mechanism. The keyboard required two sets of keys,one series for the subject and one for the predicate, and four operationkeys, known as the finis, conjunction, copula, and full-stop keys. Thecombinations were marked upon vertical rods, and a double set of theserods was required. The complex character of this machine rendered it unfitto be extended to problems involving more than four terms. At one timeJevons contemplated constructing a machine like it for ten terms, but foundthat he would have to sacrifice the entire wall-space of one side of hislibrary.

(2) John Venn in 1881 devised a more compact instrument, which he calleda logical diagram machine (Symbolic Logic, 1881, 122). It was alsoconstructed for problems of four terms. For problems of three terms hehad used diagrams consisting of intersecting circles, shading out thoseportions which represented combinations inconsistent with given premises.For four terms, circles were impracticable, hence he used ellipses. Hislogical diagram machine represents four intersecting ellipses, arrangedso that each section represents one of the sixteen possible combinations.These sections are arranged so as to fall below their original level whenthey are to be rejected as inconsistent with the premises. They are heldin place by pins, and when required to fall, the appropriate pin must beremoved. What corresponds to the key-board is therefore a series of sixteenpins, each of which must be individually manipulated. There is no deviceby which a number of sections may be moved at once. The machine is thereforemerely a more cumbersome diagram. The method involved is also practicallylimited to problems of four terms, since the intersections made by fourellipses are already complex enough. An extension of this system would,in the words of Venn, be probably distasteful to any but a mathematician.

(3) A third logical machine was constructed by Allan Marquand in 1881(announced inJohns Hopkins University Studies in Logic, 1883, 16;published inAmer.Acad.Arts and Sci., 1885, 303-7).It is based upon his logical diagrams London, Edinburgh, and Dublin,Philos.Mag.,Oct. 1881, 266-70). These consist of large squares, subdivided verticallyand horizontally into a series of smaller squares, each of which representsone of the logical combinations. The squares which represent combinationsinconsistent with the premises may then be shaded off. In his logical machinethe combinations are represented by indicators which are arranged likethe squares in his logical diagrams. At the outset the indicators are allpointing in a horizontal direction; the premises are then pressed upona key-board of eight letter and two operation keys, and the indicatorswhich represent combinations inconsistent with the premises fall to thevertical position.

In 1882 Marquand constructed from an ordinary hotel annunciator anothermachine in which all the combinations are visible at the outset, and theinconsistent combinations are concealed from view as the premises are impressedupon the keys. He also had designs made by means of which the same operationscould be accomplished by means of electro-magnets.

The characteristic of this machine lies in its simplicity, which maybe the better appreciated as the machine is extended for problems involvingmore than four terms. For problems of ten terms Venn would require a newdiagram of complicated form, and 1,024 keys to operate the instrument.Jevons for a ten-term machine would require 10,240 letters for his combinations,and a key-board with forty-four keys. Marquand's machine for ten termsneeds only 124 letters and twenty-two keys.

There is a further difference between the machines. Jevons' presentsas the conclusion not all the combinations consistent with the premises,but only those which involve the terms of the premises. For example, ina series of premises, he assumes that the only conclusion desired is therelation of the first to the last term in the series. In Venn's and Marquand'smachines the inconsistent combinations only are thrown out, and all thecombinations consistent with the premises are exhibited as the conclusion.Hence any term or combination of terms may be made the subject of the conclusion.

In 1883 Marquand published an account of a machine for producing syllogisticvariations, which he constructed in 1881 (Johns Hopkins University Studiesin Logic, 1883, 12-5). The two premises and the conclusion of a syllogismare written on three rectangular flaps, which are made so as to revolveon a horizontal axis. The contraposed forms of premises and conclusionare then written on the backs of the flaps. By turning a crank, the eightpossible combinations of premises and conclusion are then exhibited toview.

This mechanism could be readily extended so as to exhibit similar variations for arguments involving a larger number of premises or conclusions. Marquand's logical machines are now in the Princeton Psychological Laboratory. (J.M.B.)

Logo-,&c. [Gr. , discourse, lore]: Ger.Logo-; Fr.logo-; Ital.logo-. Logo- (in combination) refers to the intellectual processes, and often specifically to the process introductory to speech. Thus logopathy has been used to indicate a disorder in the formation of thought for the purpose of speaking. On the other hand, logoneurosis is used as well to refer to general mental affections; while logorrhea refers to the excessive flow of words, a common symptom in cases of mania; and logomania to the form of mania in which this occurs. (J.J.)

Logomachy [Gr., taken from the FirstEpistle of Paul to Timothy, vi. 4 , doting about questions and strifes of words]: Ger.Logomachie,Wortstreitigkeit; Fr.logomachie; Ital.contesa di parole. A contention (in which it is not essential thattwo parties should be active) not professedly relating to the use of wordsand phrases, but in which proper care exercised to make the ideas clearwill show the critic, either that there is no important difference betweenthe position attacked and that defended, or if there is, that the argumentationdoes not relate to such points.

Theology and subjects connected with it, such as the freedom of the will, have been the great theatre of such war. At present it is still kept up in logic; and other branches of philosophy are not entirely freed from it. Disputes about the propriety of modes of speech, however hot and silly they may be, are not logomachy. (C.S.P.)

Logos [Gr.]: Ger.Logos; Fr.Logos;Ital.Il verbo. (1) REASON (q.v.).

(2) The eternal Son of God, in whom the wisdom and power of God aremanifested, and who became incarnate in the person of the historic Jesus.

In Greek thought in its earlier stages the Logos is the universal ordivine reason of the world. In later Greek thought under theosophic impulsesthe Logos acquired a quasi personality. It is hypostatized, at least inthe thought of Philo of Alexandria, who ascribes to it some mediating functionsbetween God and the world. The Christian idea of the Logos is containedin the prologue to the Gospel of St. John, in which it is identified withthe eternal Christ, who became flesh in the person of Jesus Christ. Outof this germ the Christology of the early Church developed, and was embodiedin the historic creeds.

Literature: HEINZE, Die Lehre vom Logos in d. griechischen Philos. (1872); ZELLER, Philos. d. Griechen, iii; DORNER, Hist. of the Devel. of the Doctrine of the Person of Christ. (A.T.O.)

Lombard, Peter.(cir. 1100-63 or64.) Educated in theology at Bologna, Rheims, and (under Abelard) Paris.Taught theology successfully at Paris, and became bishop of Paris, 1159.For his workSententiarum LibriIV, he received the title'Magister Sententiarum.'

Lotze, Hermann Rudolf.(1817-81.)Born at Bautzen, Saxony; studied medicine, natural philosophy, and metaphysicsat Leipzig, where be became professor of mental philosophy in 1843. Calledto Göttingen, 1844, and to Berlin, 1881, where he died soon after.He belongs to the group of philosophers known as 'Real-Idealists,' opposingHegel on the one hand and materialism on the other hand; and he is stilla most potent influence. His philosophy is characterized by subtle criticismof the concepts of physical and mental science. He was also one of thepioneers of physiological psychology.

Love[AS.lufian, to love]: Ger.Liebe; Fr.amour; Ital.amore. Dispositional INTEREST (q.v.) of an exclusive kind, having a person for its object, and manifesting itself in the following emotional states: (1) pleasure in the presence of a person or other communion with him, and in the thought of him; (2) pain occasioned by his absence or estrangement; (3) pleasure in his welfare; (4) pain occasioned by injury to him. (G.F.S.-J.M.B.)

The word seems generally to imply exclusive interest in an individual -- an interest of such a nature that no other than the particular person loved can satisfy it. There is, however, another meaning. It is possible to say I love Americans, soldiers, or 'the brethren.' It is also possible in ordinary language to use the term in connection with impersonal objects, as when we speak of 'love of truth' or 'love of beauty.' The emotions in which such interests manifest themselves are more or less analogous to those connected with attachment to persons. But the word is most properly applied to personal relations, and other usages may be regarded as derivative and metaphorical. (G.F.S.,J.M.B.)

The most important distinctions, of a psychological sort, are those(1) between love which involves the natural affections and that which isindependent of them; the former is based upon predispositions of a hereditarysort, as is most strongly instanced in maternal affection. The latter sortof love is extremely complex, seeming to involve the whole range of possibleinterests in persons -- impulsive, sensuous, intellectual, aesthetic, moral.Another distinction (2) is that typified by the difference between thelove for persons respectively of the opposite and of the same sex. Theformer is often called 'romantic' love, and the latter 'fraternal' or 'brotherly'love; and the latter is more akin to the natural affections. Romantic lovemay exist, however, between persons of the same sex. Romantic love hasbeen the subject of the analysis of novelists, notably of the later 'psychological'school. Psychologists usually agree in recognizing in it at least the matingand the sensuous aesthetic impulse, however they may individually disagreein respect to which of these is more fundamental, if either, and in respectto the other more refined factors which contribute to the dispositionsinvolved. Groos connects it with coyness, by which the mating instinctis regulated. The exclusiveness of the interest is must stronger in romanticlove.

In romantic love the conative ingredient is very strongly shown -- intrudingitself into consciousness -- in what is called 'longing' or 'desire' forthe loved one, being a condition of extreme restlessness and mental distractionwhich gives peculiar quality to the pain of absence or estrangement. Thisis not prominent in other forms of affection or friendship -- at leastto the same degree. A recent writer has said: 'Friendship is a satisfaction,love is a desire.'

Literature: perhaps the most painstaking analysis is that of BAIN, Emotions and Will (4th ed.); the exclusiveness of the interest involved has been emphasized by ROYCE, The Conception of God, v. Pt. III. vi. See also GROOS, Play of Man, Eng. trans., 252 ff.; STENDHAL, L'Amour (1822); MICHELET, L'Amour (1858); DE ROBERTO, L'Amore (1897). For the psychopathology of love, see KRAFFT-EBING, Psychopathia sexualis (10th ed.). See also most of the textbooks of psychology, and many of the treatises given under EMOTION. Cf. SHYNESS. (J.M.B.)

Love(metaphysical): see NEO-PLATONISM,and MYSTICISM.

Love(in theology). That attributeof the divine nature by virtue of which God rejoices in and conserves thegood of his creatures.

Among the divine attributes love holds the place of supremacy, inasmuchas it is an all-comprehending emotional principle, which unites God inhis creative and conserving activities with the whole creation. The speciallove of God for his rational creatures is one of the central doctrinesof the Christian theology.

Literature: see ATTRIBUTES (of God). (A.T.O.)

Loyalty (political): see PATRIOTISM.

Lucidity [Lat.lucidus, light,clear]: Ger. (1)Lucidität, (2)Hellsichtigkeit; Fr.lucidité; Ital.lucidità. (1) In referenceto mental disease: the ability to think clearly and appreciate existingrelations. A lucid interval in insanity is thus the throwing off of thedelusions and morbid habits of thought incident to the disease, and theresumption of the normal habit. Lucid intervals are common in mania, butmust not be confused with the mere remission of paroxysms or the intervalsbetween recurrences of mania. The term is also important in a medico-legalsense.

(2) The alleged power claimed by the 'somnambulists,' the successors to Puysegur, by 'spiritists' and others, of transcending the ordinary powers of the senses, overcoming the ordinary visual limitations, and seeing things at a distance and through opaque mediums. The theory has been revived by Richet and others in the discussion of experiments in THOUGHT-TRANSFERENCE (q.v.). See CLAIRVOYANCE. (J.J.)

Lucretius, Titus LucretiusCarus.(cir. 97-53 B.C.) Little is known as to his life. Roman citizenof noble rank. He may have studied in Athens, becoming familiar with Greekphilosophy. His poem,De rerum Natura, revised by Cicero, and stillextant, is considered the completest exposition of the theories of Epicurus.Cf. EPICUREANISM.

Ludicrous:see COMIC.

Lul, Raimon,orLullus, Ramundus,orLully, Raymond,alsoLullius,andLulli.(1235-1315.)Indifferently educated, although of an aristocratic Catalonian family,on the island of Majorca. Became grand seneschal at the court of King Jacobof Majorca. In 1266 he was converted to Christianity, sold most of hisproperty, devoted himself for nine years to ascetic practices and the studyof Arabic. He formed the plan of converting the Moslems to Christianityby appealing to their higher reason. In 1276 he succeeded in having a collegeestablished at Miramar for thirteen Minorite friars, who were to studyArabic and fit themselves for missionary work. To expedite matters he soughta universal and infallible formula or rule, by which doubtful questionsof faith could be settled. This came, he believed, as a revelation fromGod on Mount Randa. He wrote in three languages, his devotional poems inCatalan being of high order. Tried several times to interest the pope inhis missionary plans, but failed. He wandered about teaching from placeto place, making three unsuccessful efforts in Tunis to convert the Moslems,in the last of which he was martyred.

Lumen(naturale, gratiae,&c.)[Lat.]. Light; e.g. of nature (naturale), the natural facultiesas affording knowledge, wisdom, &c.; contrasted with light of grace(gratiae), the illumination due to divine grace. See LIGHT OF NATURE.

The term is a scholastic and theological one, and is applied also to the various sources of 'light' or 'leading,' as light of faith (fidei), of knowledge (scientiae). Cf. Eisler,Wörterb.d.philos.Begriffe, sub verbo, for extensive citations. (J.M.B.)

Lunacy [Lat.luna, the moon]: Ger.Irrsinn,Mondsucht (popular); Fr.folie; Ital.pazzia,lunatico (lunatic, pop.). The term reflects a bygone notion of anintermittent form of insanity affected by the moon. It is used popularlyas synonymous with insanity, and is especially prominent in the discussionof the legal relations of insanity. A lunatic is a person who comes underthe legal qualifications of insanity.

The law of lunacy, the commissioners in lunacy, lunatic asylum, suggest the use of the term in its general application to insanity. The laws defining lunacy and the proceedings necessary to commit an affected person as a lunatic differ in various countries, but in almost all cases the ability to manage one's own affairs is the important consideration. See INCAPACITY, and INSANITY (and the literature there cited). (J.J.)

Lust[AS. and Ger.lust, desire]: Ger.(1)Gelüst, (2)Wollust; Fr. (1)convoitise(covetousness),(2)impureté; Ital. (1)appetiti (bassi), (2)concupiscenza. (1) Craving for immoderate self-indulgence of anysort.

(2) Restricted in popular usage and in law to inordinate sexual passion.

Usage (1) is that of the theologians, who extend the term to include 'unsanctified' desire for earthly pleasure of any sort; and of ethical writers, who, however, emphasize the lower appetences by the term and so lead to the usage (2). Cf. the New Testament (John viii. 44) for usage (1), and the 'Sermon on the Mount' (Matt. v. 28) for usage 2. (J.M.B.)

Lustre [Lat.lucere, to shine, throughFr.]: Ger.Glanz; Fr.lustre; Ital.lustro'We terma surface lustrous when the reflection-image which it gives is intrinsicallyexceedingly indistinct, or when the clear apprehension of it is preventedby irregularities of the reflecting surface. For the most part the twoconditions are found together' (Wundt,Physiol.Psychol.,4th ed., ii. 205).

Two illusions of lustre may be noticed: (1) Binocular. A sheen or polisharises when one half of the strereoscopic field is white and the otherblack or coloured. This is due to the associative transference of the conditionsof objective lustre to the field seen. (2) Monocular. A similar effectcan be obtained monocularly by Lambert's method of COLOUR MIXTURE (q.v.).

Literature: SANFORD, Course in Exper. Psychol., expt. 166; KIRSCHMANN, Philos. Stud., xi. 147 (to whom metallic lustre depends on the parallax of indirect vision); HERING, in Hermann's Handb. d. Physiol., III. i. 575; AUBERT, Physiol. Optik, 553; HELMHOLTZ, Physiol. Optik (2nd ed.), 932-6, 944. Stereoscopic lustre was discovered by DOVE, Berl. Akad. Berichte (1851), 246; and Pogg. Ann. (1851), 1xxxiii. 480. (E.B.T.)

Luther, Martin.(1483-1546.) Bornat Eisleben, Saxony. Educated at the schools in Magdeburg and Eisenachand at the University at Erfurt. Began the study of law, but changed hiscourse, and in 1505 entered an Augustinian monastery. Ordained priest in1507. Professor of philosophy at Wittenberg, 1508; at Erfurt, 1509; professorof theology at Wittenberg, 1510; sent to Rome (1510) on business for theAugustinian order; provincial vicar of Meissen and Thuringia, 1515. Hefirst preached against the sale of indulgences, and in 1517 nailed hisfamous ninety-five theses on the door of the castle church at Wittenberg.Tried by the Diet of Augsburg, 1518; held his disputation at Leipzig withEck, 1519; excommunicated, and burned the papal bull before his studentsat Wittenberg, 1520; refused to recant before the Emperor Charles V, andwas seized by friends in disguise and carried to Wartburg Castle for security,1521; returned to Wittenberg in 1522, and resumed his duties in the University.See LUTHERANISM, and REFORMATION.

Lutheranism [Lutheran, an adherentof Luther]: Ger.Lutherthum; Fr.Luthéranisme; Ital.Luteranismo. The system of the Lutheran Church, embracing a formof government and worship, and a confession in which the doctrines of justificationby faith, supreme authority of Scriptures, total depravity and inabilityof man, vicarious and unlimited atonement, and real presence of Christin the Eucharist, are essential features.

Luther stood for the reform of abuses, an open and authoritative Bible,freedom of private judgment, and justification by faith without penance.The Lutheran Church, which is the oldest and largest of the Reformed communions,adopts as its symbols the Apostles', Nicene, and Athanasian Creeds, theAugsburg Confession, which contains its charter, together with Luther'scatechisms and various modifications of the Augsburg Symbol. Holding manypoints in common with Calvinism, it differs from that system in less insistenceon the divine sovereignty and the decrees, in the denial of limited atonement,in the doctrine of the real presence of Christ in the Eucharist, and inthe greater emphasis it places on the historic evolution of the symbolsof faith.

Literature: F. C. BAUER, Lehrb. d. Dogmatengesch. (2nd ed., 1857); KRAUT, Christenthum u. Lutherthum (1871); H. F. JACOBS, in Johnson's Univl. Cyc.; SCHAFF, in the Schaff-Herzog Cyc. of Eccles. Lit. (A.T.O.)

Luxury [Lat.luxus]: Ger.Luxus;Fr.luxe; Ital.lusso. Commodities which do not produce,in those who use them, economic efficiency proportional to their cost.

A thing is a luxury if it involves a using up of accumulated power without permanent equivalent for the future. We must beware of defining luxury in terms of pleasure. The more real pleasure a thing gives, the less likelihood is there that it can be described as a luxury; for the presumption is that it will tend to increase the productive power of those who enjoy it. A pleasure becomes a luxury (1) when it is harmful to the physical or moral constitution of those who enjoy it; (2) when it involves a waste of capital or of labour power beyond what the recipient of the pleasure is stimulated by it to replace. (A.T.H.)

Lymph [Lat.lympha, clear water]:Ger.Lymphe; Fr.lymphe; Ital.linfa. The fluid portionof the blood which has filtered through the walls of the blood-vessels,has nourished the various tissue elements, received from them their wasteproducts, and which is collected in lymphatic vessels and finally returnedto the blood.

In addition to fluid constituents, lymph contains colourless lymph corpuscules which have wandered (diapedesis) through the walls of the blood-vessels, and which are also added to the lymph stream by numerous lymph nodules located in the course of the lymphatic vessels. Lymph is thus to be distinguished from plasma, which is the fluid portion of circulating or freshly shed blood, and also from serum, which is the fluid portion of coagulated blood. (C.F.H.)