Classics in the History of Psychology

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Definitions Lod - Lz

Posted July 2001

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

An approach to such a classification is made by every man whenever he reasons, in the proper sense of that term. It is true that the contemplation of a state of things believed to be real may cause the contemplator to believe something additional, without making any classification of such sequences. But in that case he does not criticize the procedure, nor so much as distinctly reflect that it is just. He can, consequently, not exercise any control over it. Now, that which is uncontrollable is not subject to any normative laws at all; that is, it is neither good nor bad; it neither subserves an end nor fails to do so. But it is only the deliberate adoption of a belief in consequence of the admitted truth of some other proposition which is, properly speaking, reasoning. In that case the belief is adopted because the reasoner conceives that the method by which it has been determined would either in no analogous case lead to a false conclusion from true premises, or, if steadily adhered to, would at length lead to an indefinite approximation to the truth, or, at least, would assure the reasoner of ultimately attaining as close an approach to the truth as he can, in any way, be assured of attaining. In all reasoning, therefore, there is a more or less conscious reference to a general method, implying some commencement of such a classification of arguments as the logician attempts. Such a classification of arguments, antecedent to any systematic study of the subject, is called the reasoner's logica utens, in contradistinction to the result of the scientific study, which is called logica docens. See REASONING.

That part of logic, that is, of logica 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. kritikh. According to Diogenes Laertius, Aristotle divided logic into three parts, of which one was proV krisin). This word, used by Plato (who divides all knowledge into epitactic and critic), 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 initial c 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 antecedes what we have called critic. It considers, for example, in what sense and how there can be any true proposition and false proposition, and what are the general conditions to which thought or signs of any kind must conform in order to assert anything. Kant, who first raised these questions to prominence, called this doctrine transcendentale Elementarlehre, and made it a large part of his Critic of the Pure Reason. But the Grammatica Speculativa of Scotus is an earlier and interesting attempt. The common German word is Erkenntnisstheorie, sometimes translated EPISTEMOLOGY (q.v.).

It is further generally recognized that another doctrine follows after critic, and which belongs to, or is closely connected with, logic. Precisely what this should contain is not agreed; but it must contain the general conditions requisite for the attainment of truth. Since it may be held to contain more, one hesitates to call it heuristic. It is often called Method; but as this word is also used in the concrete, methodic or methodeutic would be better.

For deciding what is good logic and what is bad, appeal is made by different writers to one or more, generally several, of these eight sources: to direct dicta of consciousness, to psychology, to the usages of language, to metaphysical philosophy, to history, to everyday observation, to mathematics, and to some process of dialectic. In the middle ages appeal was frequently made to authority.

The appeal to direct consciousness consists in pronouncing certain reasoning to 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 repulsion against contradiction, or, as he calls it, 'the immediate feeling of necessity' (Logic § 3, 2). Those who think it worth while to make any defence at all of this proceeding urge, in effect, that, however far the logician may push his criticisms of reasoning, still in doing so, he must reason, and so must ultimately rely upon his instinctive recognition of good and bad reasoning. Whence it follows that, in Sigwart's words, 'every system of logic must rest upon this principle.' It is, however, to be noted that among the dicta of direct consciousness, many pronounce certain reasonings to be bad. If, therefore, such dicta are to be relied upon, man not only usually has a tendency to reason right, but also sometimes has a tendency to reason wrong; and if that be so, the validity of a reasoning cannot consist in a man's having a tendency to reason in that way. Some say that the validity of reasoning consists in the 'definitive dictum' of consciousness; but it has been replied that certain propositions in Euclid were studied for two thousand years by countless keen minds, all of whom had an immediate feeling of evidence concerning their proofs, until at last flaws were detected in those proofs, and are now admitted by all competent persons; and it is claimed that this illustrates how far from possible it is to make direct appeal to a definitive pronouncement. Besides, say those who object to this method, all reasoning and inquiry expects that there is such a thing as 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 appeal can be made may opine about that question. A fortiori it does not depend upon whether I am satisfied with it or not. It is further insisted that there can be no genuine criticism of a reasoning until that reasoning is actually doubted; and no sooner is it actually doubted than we find that consciousness has revoked her dictum in its favour, if she ever made any. It is, indeed, maintained that so far from true is it that every system of logic must be based upon any instinctive recognition of good and bad reasoning, that it is quite impossible for any reasoning to be 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 nothing but itself is to rest it on nothing at all. If the fact that we must use our reasoning instinct in criticizing reasoning proves that we must appeal to nothing else in such criticism, it equally proves that we ought to follow the lead of that instinct without any logical control at all, which would be as much as to say that we ought not to reason at all. A man cannot criticize every part of his reasoning, since he cannot criticize the act of reasoning he is performing in the criticism, it is true. But he can criticize steps whose validity he doubts; and in doing so, ought to consider in what characters the validity of reasoning consists, and whether the reasoning in question possesses those characters.

Under an appeal to psychology is not meant every appeal to any fact relating to the mind. For it is, for logical purposes, important to discriminate between facts of that description which are supposed to be ascertained by the systematic study of the mind, and facts the knowledge of which altogether antecedes such study, and is not in the least affected by it; such as the fact that there is such a state of mind as doubt, and the fact that the mind struggles to escape from doubt. Even facts like these require to be carefully examined by the logician before he uses them as the basis of his doctrine. But many logicians have gone much further, and have avowedly based their systems upon one or another theory of psychology. Another class of logicians have professed to base logic upon a psychological theory of cognition. Of course, if this is done, such psychological doctrine is placed above logical criticism, or, at any rate, above logical support. For if the truth of a conclusion is known only from certain premises, it cannot be used to support those premises. Now, it may be doubted whether psychology is not, of all the special sciences, the one which stands most in need of appeal to a scientific logic.

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

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

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

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

The boundary between some parts of logic and pure mathematics in its modern treatment is almost evanescent, as may be seen in Dedekind's Was sind 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 made to mathematical results, such as Bernoulli's law of high numbers. It seems to be the general opinion that nothing so difficult as mathematics can be admitted into, or be appealed to by, the science of logic, which has the peculiarity of consisting chiefly of truisms.

In mathematical reasoning there is a sort of observation. For a geometrical diagram or array of algebraical symbols is constructed according to an abstractly stated precept, and between the parts of such diagram or array certain relations are observed to obtain, other than those which were expressed in the precept. These being abstractly stated, and being generalized, so as to apply to every diagram constructed according to the same precept, give the conclusion. Some logicians hold that an equally satisfactory method depends upon a kind of inward observation, which is not mathematical, since it is not diagrammatic, the development of a conception and its inevitable transformation being observed and generalized somewhat as in mathematics; and those logicians base their science upon such a method, which may conveniently be termed, and is sometimes termed, a Dialectic. Other logicians regard such a method as either extremely insecure or as altogether illusory.

The generally received opinion among professors of logic is that all the 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's Logik): see HEGEL'S TERMINOLOGY, II. b.

Logic (exact): Ger. exakte Logik; Fr. logique exacte; Ital. logica esatta. The doctrine that the theory of validity and strength of reasoning ought to be made one of the 'exact sciences,' that is, that generalizations from ordinary experience ought, at an early point in its exposition, to be stated in a form from which by mathematical, or expository, REASONING (q.v.), the rest of the theory can be strictly deduced; together with the attempt to carry this doctrine 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), La Place (1749-1827), De Morgan (1806-71), Boole (1815-64), and many others; and a few men in different countries continue the study of the problems opened by the last two named logicians, as well as those of the proper foundations of the doctrine and of its application to inductive reasoning. The results of this method, thus far, have comprised the development of the theory of probabilities, the logic of relatives, advances in the theory of inductive reasoning (as it is claimed), the syllogism of transposed quantity, the theory of the Fermatian inference, considerable steps towards an analysis of the logic of continuity and towards a method of reasoning in topical geometry, contributions towards several branches of mathematics by applications of 'exact' logic, the logical graphs called after Euler and other systems for representing in intuitional form the relations of premises to conclusions, and other things of the same general nature.

There are those, not merely outside the ranks of exact logic, but even within it, who seem to suppose that the aim is to produce a calculus, or semi-mechanical method, for performing all reasoning, or all deductive inquiry; but there is no reason to suppose that such a project, which is much more consonant with the ideas of the opponents of exact logic than with those of its serious students, can ever be realized. The real aim is 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 necessarily the first in the order of inquiry) is to formulate with mathematical precision, definiteness, and simplicity, the general facts of experience which logic has to take into account.

The employment of algebra in the investigation of logic is open to the danger of degenerating into idle trifling of too rudimentary a character to 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 employed may be mistaken for first principles of logic. An algebra which brings along with it hundreds of purely formal theorems of no logical import whatever must be admitted, even by the inventor of it, to be extremely defective in that respect, however convenient it may be for certain purposes. On the other hand, it is indisputable that algebra has an advantage over speech in forcing us to reason explicitly and definitely, if at all. In that way it may afford very considerable aid to analysis. It has been employed with great advantage in the analysis of mathematical reasonings.

Algebraic reasoning involves intuition just as much as, though more insidiously than, does geometrical reasoning; and for the investigation of 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 of the logical trifler. In the opinion of some exact logicians, they lead more directly to the ultimate analysis of logical problems than any algebra yet devised. See LOGICAL DIAGRAM (or GRAPH).

It is logical algebra, however, which has chiefly been pursued. De Morgan invented a system of symbols, which had the signal advantage of being entirely new and free from all associations, misleading or otherwise. Although he employed them for synthetical purposes almost exclusively, yet the great generality of some of the conceptions to which they led him is sufficient to show that they might have been applied with great advantage in analysis. Boole was led, no doubt from the consideration of the principles of the calculus of probabilities, to a wonderful application of ordinary algebra to the treatment of all deductive reasoning not turning upon any relations other than the logical relations between non-relative terms. By means of this simple calculus, he took some great steps towards the elucidation of probable reasoning; and had it not been that, in his pre-Darwinian day, the notion that certain subjects were profoundly mysterious, so that it was hopeless, if not impious, to seek to penetrate them, was still prevalent in Great Britain, his instrument and his intellectual force were adequate to carrying him further than he actually went. Most of the exact logicians of to-day are, from the nature of the case, followers of Boole. They have modified his algebra by disusing his addition, subtraction, and division, and by introducing a sign of logical aggregation. This was first done by Jevons; and he proposed .|. , a sign of division turned up, to signify this operation. Inasmuch as this might easily be read as three signs, it would, perhaps, be better to join the two dots by a light curve, thus Y. Some use the sign + for logical aggregation. The algebra of Boole has also been amplified so as to fit it for the logic of relatives. The system is, however, far from 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, called aggregants, to produce an aggregate term or proposition which is true of everything of which any aggregant is true, and false of everything of which all the aggregants are false. It is opposed to composition, which is the operation of producing from two or more terms or propositions, called the components, a new term or proposition, called their compound, which is true of all of which all the components are true, and false of all of which any are false.

Absorption, law of (Ger. Absorptionsgesetz). The proposition 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 Aulus Gellius, understood to imply that one, and one only, of the alternatives is true. At the same time, the standard traditional example of a disjunctive was 'Socrates currit vel Plato disputat,' and the rule was 'Ad veritatem disiunctivae sufficit alteram partem esse veram.' Nevertheless, the narrower sense was also recognized, and the term alternative is perhaps preferable.

Associative. An operation combining two elements is associative if, and only if, in combining the result with a third element, it makes no difference whether the middle element be first combined with the last and the result with the first, or the other way, so long as the order of sequence is preserved. Addition and multiplication are associative, while involution 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 an algebra in which multiplication is associative.

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

Composition: see Aggregation, above.

Compound: see Aggregation, above.

Copula is often defined as that which expresses the relation between the subject-term and the predicate-term of a proposition. But this is not sufficiently accurate for the purposes of exact logic. Passing over the objection that it applies only to categorical propositions, as if conditional and 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 essentially the same as 'A translated favoured patriarch is'; and 'Every mother is a lover of that of which she is a mother' is the same as 'A mother of something not loved by her is not.' In the second and fourth forms, the copula connects no 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 general term or terms to the universe. The universe must be well known and mutually known to be known and agreed to exist, in some sense, between speaker and hearer, between the mind as appealing to its own further consideration and the mind as so appealed to, or there can be no communication, or 'common ground,' at all. The universe is, thus, not a mere concept, but is the most 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 sort of sign or thought; for such a relation must, if it subsist, exist quite otherwise than a relation between mere concepts. This, then, is what the copula essentially does. This it may do in three ways: first, by a vague reference to the universe collectively; second, by a reference to all the individuals existent in the universe distributively; third, by a vague reference to an individual of the universe selectively. 'It is broad daylight,' I exclaim, as I awake. My universe is the momentary experience as a whole. It is that which I connect as object of the composite photograph of daylight produced in my mind by all my similar experiences. Secondly, 'Every woman loves something' is a description of every existing individual in the universe. Every such individual is said to be coexistent only with what, so far as it is a woman at all, is sure to be a lover of some existing individual. Thirdly, 'Some favoured patriarch is translated' means that a certain description applies to a select individual. A hypothetical proposition, whether it be conditional (of which the alternative, or disjunctive, proposition is a mere species, or vice versa, as we choose to take it) or copulative, is either general or ut nunc. A general conditional is precisely equivalent to a universal categorical. 'If you really want to be good, you can be,' means 'Whatever determinate state of things may be admissibly supposed in which you want to be good is a state of things in which you can be good.' The universe is that of determinate states of things that are admissable hypothetically. It is true that some logicians appear to dispute this; but it is manifestly indisputable. Those logicians belong to two classes: those who think that logic ought to take account of the difference between one kind of universe and another (in which case, several other substantiae of propositions must be admitted); and those who hold that logic should distinguish between propositions which are necessarily true 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 system of expression, to afford different ways of expressing the same state of facts; although this defect may be less important than a definite advantage gained by it. The copulative proposition is in a similar way equivalent to a particular categorical. Thus, to say 'The man might not be able voluntarily to 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 admissible in which a man tries to act one way and voluntarily acts another way in consequence of physical causes. As to hypotheticals ut nunc, they refer to no range of possibility, but simply to what is true, vaguely taken collectively.

Although it is thus plain that the action of the copula in relating the subject-term to the predicate-term is a secondary one, it is nevertheless necessary to distinguish between copulas which establish different relations between these terms. Whatever the relation is, it must remain the same in all propositional forms, because its nature is not expressed in the proposition, but is a matter of established convention. With that proviso, the copula may imply any relation whatsoever. So understood, it is the abstract copula of De Morgan (Camb. Philos. Trans., x. 339). A transitive copula is one for which the mood Barbara is valid. Schröder has demonstrated the remarkable theorem that if we use IS in small capitals to represent any one such copula, of which 'greater than' is an example, then there is some relative term r, such that the proposition 'S IS P' is precisely equivalent to 'S is r to P and is r to whatever P is r to.' A copula of correlative inclusion of one for which both Barbara and the formula of identity hold good. Representing any one such copula by is in italics, there is a relative term r, such that the proposition 'S is P' is precisely equivalent to 'S is r to whatever P is r to.' If the last proposition follows from the last but one, no matter what relative r may be, the copula is called the copula of inclusion, used by C. S. Peirce, Schröder, and others. De Morgan uses a copula defined as standing for any relation both transitive and convertible. The latter character consists in this, that whatever terms I and J may be, if we represent this copula by is in black = letter, then from 'I is J' it follows that 'J is I.' From these two propositions, we conclude, by Barbara, that 'I is I.' Such copulas are, for example, 'equal to,' and 'of the same colour as.' For any such copula there will be some relative term r, such that the proposition 'S is P' will be precisely equivalent to 'S is r to everything, and only to everything, to which P is r.' Such a copula may be called a copula of correlative identity. If the last proposition follows from the last but one, no matter what relative r may be, the copula is the copula of identity used by Thomson, Hamilton, Baynes, Jevons, and many others.

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


Dialogism. A form of reasoning in which from a single premise a disjunctive, or alternative, proposition is concluded introducing an additional term; opposed to a syllogism, in which from a copulative proposition a 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 universe of such a nature that the same term which is individual in one such element of extension is not so in another. Thus, we may consider different persons as individual in one respect, while they may be divisible in respect to time, 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 belonging to one cannot belong to another. The conception of a multidimensional logical universe is one of the fecund conceptions which exact logic owes to O. H. Mitchell. Schröder, in his then second volume, where he is far below 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 at refutation 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, the fact that A is similar to B, and the fact that A is a lover of B, and the fact that A and B are both men, are dyadic relations; while the fact that A gives B to C is a triadic relation. Every relation of one order of relativity may be regarded as a relative of another order of relativity if desired. Thus, man may be regarded as man coexistent with, and so as a relative expressing a dyadic relation, although for most purposes it will be regarded as a monad or non-relative term.

Index (in exact logic): see sub verbo.

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

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 SYMBOLIC LOGIC.

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

Logical possibility is, according to usage, freedom from all contradiction, explicit or implicit; and any attempt to reform the inaccuracy would only bring confusion.

Logical necessity is the necessity of that whose contrary is not logically possible.

Logical induction is an induction based on examination of every individual of the class to which the examination relates. Thus, conclusions from a census are logical inductions. While this mode of inference is a degenerate form of induction, it also comes into the class of dilemmatic reasoning.

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

1. The harmony of a thought with itself. Most usually so defined, but seldom so employed. So far as this definition is distinct, it makes logical truth 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 called mathematical truth, since mathematics is the only science which aims at nothing more (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 the ens, and on the other hand to ethical truth, which is telling what a witness 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 must lead to the truth, in so far as it is relied upon. But what Aristotle understood by a logical demonstration may be seen in his De generatione animalium, Lib. II. cap. viii.

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

Logical division. Division into logical parts.

Logical distinctness. That distinctness which results from logical analysis.

Logical actuality. Kant, in the Logik by Jäsche (Einleitung, vii), defines logical actuality as conformity to the principle of sufficient reason, consisting of the cognition having reasons and having no false consequences; and he makes this, along with logical possibility, to constitute logical truth, which is thus used in its second sense. But in the Critic of 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 phrase synonymous 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 (or Graph): Ger. logische Figur; Fr. diagramme logique; Ital. diagramma logico. A diagram composed of dots, lines, &c., in which logical relations are signified by such spatial relations that the necessary consequences of 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 relations expressed by the copula of inclusion and its negative and to the relation of negation. Now all the formal properties of the copula of inclusion are involved in the principle of identity and the dictum de omni. That is, if r is the relation of the subject of a universal affirmative to its predicate, then, whatever terms X, Y Z may be, Every X is r to an X; and if every X is r to a Y, and every Y is r to a Z, every X is r to a Z. Now, it is easily proved by the logic of relatives, that to say that a relation r is subject to these two rules, implies neither more nor less than to say that there is a relation l, such that, whatever individuals A and B may be.

If nothing is in the relation l to A without being also in the same relation l to B, then A is in the relation r to B; and conversely, that, If A is r to B, there is nothing that is l to A except what is l to B.

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 representing A as an oval inside the oval B. Then, l is the relation of being included within; and it is plain that nothing can be inside of A without being inside B. 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 (announced in his Substitution of Similars, 1869, 60; described in Philos, Trans. Roy. Soc., 1870, 497-518; brief description in Proc. Roy. Soc., 1870, 166-9, and Princ. of Sci., 1874, 123-31). This instrument was preceded by the logical slate and the logical ABACUS (q.v.) (Proc. Manchester Lit. and Philos. Soc., Apr. 1866, 161; Substitution of Similars, 1869, 54-9). In the logical slate the combinations of letters, representing all the possible combinations of a definite number of characters or qualities in a logical universe, were engraved in vertical columns upon a common writing-slate. The combinations inconsistent with given premises were then crossed off with a slate pencil, and the conclusions read off from the untouched combinations.

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

In the logical slate, great care was necessary to cross off all the inconsistent combinations, and in the logical abacus similar care was required in picking out all the consistent combinations. The logical machine of Jevons is a logical abacus in which all that is required of the operator is to press the premises upon a series of keys; the operation of lifting the combinations consistent with the premises to the higher level being accomplished mechanically by a series of levers. By means of a lattice-work with horizontal slits, the combinations expressed in the premises and consistent with them, and these only, are exhibited to view. This machine, while manifesting considerable ingenuity on the part of the contriver, was nevertheless a cumbersome piece of mechanism. The keyboard required two sets of keys, one series for the subject and one for the predicate, and four operation keys, known as the finis, conjunction, copula, and full-stop keys. The combinations were marked upon vertical rods, and a double set of these rods was required. The complex character of this machine rendered it unfit to be extended to problems involving more than four terms. At one time Jevons contemplated constructing a machine like it for ten terms, but found that he would have to sacrifice the entire wall-space of one side of his library.

(2) John Venn in 1881 devised a more compact instrument, which he called a logical diagram machine (Symbolic Logic, 1881, 122). It was also constructed for problems of four terms. For problems of three terms he had used diagrams consisting of intersecting circles, shading out those portions which represented combinations inconsistent with given premises. For four terms, circles were impracticable, hence he used ellipses. His logical diagram machine represents four intersecting ellipses, arranged so that each section represents one of the sixteen possible combinations. These sections are arranged so as to fall below their original level when they are to be rejected as inconsistent with the premises. They are held in place by pins, and when required to fall, the appropriate pin must be removed. What corresponds to the key-board is therefore a series of sixteen pins, each of which must be individually manipulated. There is no device by which a number of sections may be moved at once. The machine is therefore merely a more cumbersome diagram. The method involved is also practically limited to problems of four terms, since the intersections made by four ellipses 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 in Johns Hopkins University Studies in Logic, 1883, 16; published in Amer. 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 vertically and horizontally into a series of smaller squares, each of which represents one of the logical combinations. The squares which represent combinations inconsistent with the premises may then be shaded off. In his logical machine the combinations are represented by indicators which are arranged like the squares in his logical diagrams. At the outset the indicators are all pointing in a horizontal direction; the premises are then pressed upon a key-board of eight letter and two operation keys, and the indicators which represent combinations inconsistent with the premises fall to the vertical position.

In 1882 Marquand constructed from an ordinary hotel annunciator another machine in which all the combinations are visible at the outset, and the inconsistent combinations are concealed from view as the premises are impressed upon the keys. He also had designs made by means of which the same operations could be accomplished by means of electro-magnets.

The characteristic of this machine lies in its simplicity, which may be the better appreciated as the machine is extended for problems involving more than four terms. For problems of ten terms Venn would require a new diagram 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 terms needs only 124 letters and twenty-two keys.

There is a further difference between the machines. Jevons' presents as the conclusion not all the combinations consistent with the premises, but only those which involve the terms of the premises. For example, in a series of premises, he assumes that the only conclusion desired is the relation of the first to the last term in the series. In Venn's and Marquand's machines the inconsistent combinations only are thrown out, and all the combinations 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 syllogistic variations, which he constructed in 1881 (Johns Hopkins University Studies in Logic, 1883, 12-5). The two premises and the conclusion of a syllogism are written on three rectangular flaps, which are made so as to revolve on a horizontal axis. The contraposed forms of premises and conclusion are then written on the backs of the flaps. By turning a crank, the eight possible combinations of premises and conclusion are then exhibited to view.

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. logoV, 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 First Epistle of Paul to Timothy, vi. 4 noswn peri xhthseiV kai logomaciaV, doting about questions and strifes of words]: Ger. Logomachie, Wortstreitigkeit; Fr. logomachie; Ital. contesa di parole. A contention (in which it is not essential that two parties should be active) not professedly relating to the use of words and phrases, but in which proper care exercised to make the ideas clear will show the critic, either that there is no important difference between the position attacked and that defended, or if there is, that the argumentation does 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 are manifested, and who became incarnate in the person of the historic Jesus.

In Greek thought in its earlier stages the Logos is the universal or divine reason of the world. In later Greek thought under theosophic impulses the Logos acquired a quasi personality. It is hypostatized, at least in the thought of Philo of Alexandria, who ascribes to it some mediating functions between God and the world. The Christian idea of the Logos is contained in the prologue to the Gospel of St. John, in which it is identified with the eternal Christ, who became flesh in the person of Jesus Christ. Out of this germ the Christology of the early Church developed, and was embodied in 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 or 64.) Educated in theology at Bologna, Rheims, and (under Abelard) Paris. Taught theology successfully at Paris, and became bishop of Paris, 1159. For his work Sententiarum Libri IV, he received the title 'Magister Sententiarum.'

Lotze, Hermann Rudolf. (1817-81.) Born at Bautzen, Saxony; studied medicine, natural philosophy, and metaphysics at Leipzig, where be became professor of mental philosophy in 1843. Called to Göttingen, 1844, and to Berlin, 1881, where he died soon after. He belongs to the group of philosophers known as 'Real-Idealists,' opposing Hegel on the one hand and materialism on the other hand; and he is still a most potent influence. His philosophy is characterized by subtle criticism of the concepts of physical and mental science. He was also one of the pioneers 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 is independent of them; the former is based upon predispositions of a hereditary sort, as is most strongly instanced in maternal affection. The latter sort of love is extremely complex, seeming to involve the whole range of possible interests in persons -- impulsive, sensuous, intellectual, aesthetic, moral. Another distinction (2) is that typified by the difference between the love for persons respectively of the opposite and of the same sex. The former is often called 'romantic' love, and the latter 'fraternal' or 'brotherly' love; and the latter is more akin to the natural affections. Romantic love may exist, however, between persons of the same sex. Romantic love has been the subject of the analysis of novelists, notably of the later 'psychological' school. Psychologists usually agree in recognizing in it at least the mating and the sensuous aesthetic impulse, however they may individually disagree in respect to which of these is more fundamental, if either, and in respect to the other more refined factors which contribute to the dispositions involved. Groos connects it with coyness, by which the mating instinct is regulated. The exclusiveness of the interest is must stronger in romantic love.

In romantic love the conative ingredient is very strongly shown -- intruding itself into consciousness -- in what is called 'longing' or 'desire' for the loved one, being a condition of extreme restlessness and mental distraction which gives peculiar quality to the pain of absence or estrangement. This is not prominent in other forms of affection or friendship -- at least to 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 attribute of the divine nature by virtue of which God rejoices in and conserves the good of his creatures.

Among the divine attributes love holds the place of supremacy, inasmuch as it is an all-comprehending emotional principle, which unites God in his creative and conserving activities with the whole creation. The special love of God for his rational creatures is one of the central doctrines of 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 reference to mental disease: the ability to think clearly and appreciate existing relations. A lucid interval in insanity is thus the throwing off of the delusions and morbid habits of thought incident to the disease, and the resumption of the normal habit. Lucid intervals are common in mania, but must not be confused with the mere remission of paroxysms or the intervals between recurrences of mania. The term is also important in a medico-legal sense.

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

Ludicrous: see COMIC.

Lul, Raimon, or Lullus, Ramundus, or Lully, Raymond, also Lullius, and Lulli. (1235-1315.) Indifferently educated, although of an aristocratic Catalonian family, on the island of Majorca. Became grand seneschal at the court of King Jacob of Majorca. In 1266 he was converted to Christianity, sold most of his property, devoted himself for nine years to ascetic practices and the study of Arabic. He formed the plan of converting the Moslems to Christianity by appealing to their higher reason. In 1276 he succeeded in having a college established at Miramar for thirteen Minorite friars, who were to study Arabic and fit themselves for missionary work. To expedite matters he sought a universal and infallible formula or rule, by which doubtful questions of faith could be settled. This came, he believed, as a revelation from God on Mount Randa. He wrote in three languages, his devotional poems in Catalan being of high order. Tried several times to interest the pope in his missionary plans, but failed. He wandered about teaching from place to 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 faculties as 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 an intermittent form of insanity affected by the moon. It is used popularly as synonymous with insanity, and is especially prominent in the discussion of the legal relations of insanity. A lunatic is a person who comes under the 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 any sort.

(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, through Fr.]: Ger. Glanz; Fr. lustre; Ital. lustro 'We term a surface lustrous when the reflection-image which it gives is intrinsically exceedingly indistinct, or when the clear apprehension of it is prevented by irregularities of the reflecting surface. For the most part the two conditions are found together' (Wundt, Physiol. Psychol., 4th ed., ii. 205).

Two illusions of lustre may be noticed: (1) Binocular. A sheen or polish arises when one half of the strereoscopic field is white and the other black or coloured. This is due to the associative transference of the conditions of objective lustre to the field seen. (2) Monocular. A similar effect can 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.) Born at Eisleben, Saxony. Educated at the schools in Magdeburg and Eisenach and at the University at Erfurt. Began the study of law, but changed his course, and in 1505 entered an Augustinian monastery. Ordained priest in 1507. Professor of philosophy at Wittenberg, 1508; at Erfurt, 1509; professor of theology at Wittenberg, 1510; sent to Rome (1510) on business for the Augustinian order; provincial vicar of Meissen and Thuringia, 1515. He first preached against the sale of indulgences, and in 1517 nailed his famous ninety-five theses on the door of the castle church at Wittenberg. Tried by the Diet of Augsburg, 1518; held his disputation at Leipzig with Eck, 1519; excommunicated, and burned the papal bull before his students at Wittenberg, 1520; refused to recant before the Emperor Charles V, and was 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 adherent of Luther]: Ger. Lutherthum; Fr. Luthéranisme; Ital. Luteranismo. The system of the Lutheran Church, embracing a form of government and worship, and a confession in which the doctrines of justification by faith, supreme authority of Scriptures, total depravity and inability of man, vicarious and unlimited atonement, and real presence of Christ in 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, the Augsburg Confession, which contains its charter, together with Luther's catechisms and various modifications of the Augsburg Symbol. Holding many points in common with Calvinism, it differs from that system in less insistence on 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 in the greater emphasis it places on the historic evolution of the symbols of 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 portion of the blood which has filtered through the walls of the blood-vessels, has nourished the various tissue elements, received from them their waste products, and which is collected in lymphatic vessels and finally returned to 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.)