Page:Catholic Encyclopedia, volume 1.djvu/507

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451

AN AN 451 ANAPHORA light into the elementary colours, to dissect an organ- ism, to take a macliine to pieces, is to proceed analyt- ically. Hut frequently actual isolation is iiniwssible. Tims the factors of a movement or of a psychological Frocess cannot be set apart and studied separately, f the process occura at all, it must l>c a complex one. We may, however, reach an analytical result by means of ditTerent successive syntheses, i. e. by variations in the grouping of the elements or cir- cvunstances. In order to;Lscertain the individual nature of any determined element, factor, or cir- cmiLstance, it is maintained in the state of per- manency, while the accompanying elements, factors, or circumstances are eliminated or changed; or, on the contrary, it may Ik; eliminated or modified, while the others remain constant. The four methods of induction belong to this form of analysis. It is also in a large measure the method of jwychological experiment and of introspective analysis. Finally, it may be impossible to effect any real dissociation of a concrete tiling or event, either because it cannot bo reached or controlled, or liecause it is past. Then mental dis.sociatioii and aljstraction are used. In a complex object the mind considers separately some part or feature which cannot in reality be sejiarated. Analogy and comparison of such cases with similar instances in which dissociation has been effected are of great value, and the results already ascertained are applied to the case under examination. This occurs freqviently in physical and jisychological sciences; it is also the metliod used by the historian or the sociologist in the study of events and in- stitutions. โ€” (2) When the complex is an idea, analysis consists in breaking it up into simpler ideas. We are in the abstract order and must rcmam therein; conse<|uently, we do not take into consideration the extension of an idea, that is, its range of applicability to concrete things, but its intension, or connotation, that is, its ideal contents. To analyze an idea is to single out in it other ideas whose ideal complexity, or whose connotation is not so great. The siime must be said of analytical reasonmg. The truth of a proposition or of a complex statement is analytically demonstrated by reverting from the proposition itself to higher principles, from the complex state- ment to a more general truth. And this applies not only to mathematics, when a given problem is solved by showing its necessarj' connection with a proposi- tion already demoiLstrated, or with a self-evident a.xiom, but also to all the .sciences in which from the facts, the effects, and the conditioned we infer the law, the cause, and the condition. Principle, law, cause, nature, condition, are less complex than con- clusion, fact, effect, action, conditioned, since these are concrete applications and further determinations of the former. A physical law, for instance, is a simplified expression of all the facts which it governs. In one word, therefore, we may characterize analysis as a process of resolution and regression; synthesis, as a process of composition and progression. The confusion that has existed and still exists in the definition and use of the teniis analysis and synthesis is due to the diverse natures of the com- plexes which have to be analyzed. Moreover, the same object may be analyzed from different points of view and, consequently, with various results. It is especially important to keep in mind the dis- tinction between the connotation and the denota- tion of an idea. As the two vary in inverse ratio, it is dear that, in an idea, the subtraction of certain connotative elements implies an increase in ex- tension. Hence connotative analysis is necessarily an extensive synthesis, and rice rcrsd. Thus, if my idea of a child is that of "a human being under a certain age", by connotative analysis I may omit the last determination "under a certain age"; what remains is less complex than the idea "child", but I.-29 applies to a greater number of individuals, namely: to all human beings. In order to restrict the ex- tension to fewer individuals, the connotation must be increased, that is, further determinations must be added. In the same manner, a fact, when reduced to a law, either in the physical, the mental, or tin- historical order, is reduced to something which luc- a greater extension, since it is assumed to rule all the facts of the same nature, but the law is less com- plex in connotation, since it does not share the in- dividual characters of the concrete events. The necessity of analysis comes from the fact that knowledge begins with the perception of the con- crete j'.nd the individual, aim that whatever is con- crete is complex. Hence the mind, unable to dis- tinctly grasp the whole reality at once, must divide it, and .study the parts separately. Moreover the innate tendency of the mind towards unification and classification leatls it to neglect certain aspects, ^o as to reach more general truths and laws whose range of application is larger. The relative useful- ness of analysis and sjmthesis in the various sciemcs tiepends on the nature of the problems to be solved, on the knowledge already at hand, on the mind's attitude, and on the stage of development of the science. Induction is 'primarily analytic; deduction, primarily synthetic. In proportion as a natural science becomes more systematic, i. e. when more general laws are forniulated, the synthetic process is more freely used. Previous analysis then enables one to "compose", or deduce future experience. Where, on the contrary, the law has to be dis- covered, observation and analysis are dominant, al- though, even then, synthesis is indispensable for the verification of hypotheses. Some sciences, such as Euclidean geometry, proceed syntheti- cally, from simple notions and a.xioms to more complex truths. Analysis has the advantage of adhering more strictly to the point under investiga- tion; synthesis is in danger of going astray, since from the same principle many different conclusions may be drawn, and a multitude of real or possible events are governed by the same law. For this same reason, however, sjTithesis, in certain sciences at least, is likely to prove more fruitful than analysis. It also has the advantage of starting from that which has a natural priority, for the conditioned prcsu|>- pises the condition. When the result is already known, and the relation between a principle and some one conclusion thus iuscertained, synthesis is a great help in teaching others. In synthesis the strictness of logical reasoning is required. Accura< y and exactness in the olwervation of phenomena, attention to all their details, the power of mental abstraction and generalization are qualities indis- pensable in the analj'tic process. The literature of uiialyniH include.'* all works on lofcic and on the methods of the sciences*. We give only (tome few references. Dugai.d Stewart, Phitottophy of 'the Human Mind, V. II, iv. ยง .3; Wundt, l^iaik (2d ed., Stuttgart, 1895). II, i; DrilA.MKI., Dfli m/ihodra dans leg acienccti de raisunncmtnt (Paris. lH6S-73>; Bai.v. Umir. V. 11, Indiiftion (2d cd.. Lon- don, 1873); UonF.RTSON. art. Amili/tia in Encyclopardia llrilan- nica, 9th wl. โ€” On psychological analvsi.s, see. among others, KoYCE, Oullinci of I'suchology, iv. 5} 40-47 (New York, lUo:i). C. A. DUBR.Y. Anan. See C.vr.mtes. Anaphora (dr., ava<popi, offering, sacrifice), a liturgical tcmi in the (ireek Kite. It is variou.sly used in the liturgies of the Greek Orient to signify that part of the service which corresponils sub- stantially to the Latin Canon of the Mass. It also signifies the offering of Kucharistic bread; the large veil (.see .f.h) that covers the same, and the procession in which the offering is brought to the altar (Mrightman). โ€” 1. In the Greek Kite the .iia- plioras are numerous, while in the Koman Kite the Canon of the Mass is from time immemorial uuitC