Page:The New International Encyclopædia 1st ed. v. 10.djvu/699

* INFINITE. 613 INFLAMMATION. (3) Infinite in another sense is any member of an all-inclusive system of reciprocally deter- mining members. Thus, according to Hegel, all reality is infinite. Hegel justifies the use of the term by pointing out that in a true system any member in being determined by the other meni- liers is really self-determined, because its sys- tematic relation to the other members is an in- tegral constituent of its own nature. These other members exercise no foreign conipulsiun upon it to make it what it is. They determine it only because it is part of its own being to be so deter- mined. They do not set limits to it which it may not pass, but they give it opportunity to be itself. To take one of the apparently most re- fractory instances, the billiard-ball is not infinite in sense la, because though spatial its place is only a part of a larger space from which it is marked off by definite boundaries. But the ball is something more than so much space. It is an object that undergoes various changes under certain conditions — e.g. when struck it rolls. This dependence of its changes upon the action of other objects is often considered another evi- dence of its finitude. But it must be remembered that it is only because it is the nature of the ball to roll when struck that it rolls at all. In rolling it does not succumb to external force, but it acts its own part. Though determined, it is self-determined. Though compelled, it is free. This free, self-determined nature of every nieni- Ix'r of any free system is what Hegel calls infi- nite. He considers the term infinite appropriate because the systematic conditions which deter- mine the ball's action do not limit it in the sense of repressing its spontaneous tendency to act out its own nature. They simply give it a chance to show one side of its nature in a cer- tain definite movement. There is no reason why the term infinite should not be employed in this case. But there is every reason to remember that this sort of infinitude is thoroughlj' compatible with finitude in another sense — e.g. spatial. When Hegel says that the finite is essentially infinite, he means that that which is conditioned I heslimmt) is conditioned because it is its ^pry nature to act in response to these condi- tions; that condition is not restraint {Schranke) of an inherent tendency by an external limit (flrcnze). A reader in philosophy must keep him-^elf always on the alert to detect the various meanings of the word infinite, and then he will be able to understand many paradoxes that at first appear to be illogical contradictions. Wheth- er the infinite really exists depends on the kind of infinite you mean. The existence of infinite

is discussed elsewhere (see XrMBER; Space; Time) ; infinites h. 2 in at least certain eases, and 5 are unquestionable. Infinite .S is, if it does exist, imknowablc. and there is not the sliffhtest reason to assert its existence. Infinite 4 does not exist at any particular time from the very nature of the case, because it is an unattain- able ideal. The infinite process is real at least in the case of time in the sense that the flow of time never ceases; but at no moment has it completed its unending course, and in this sense infinite time does not now exist, nor ever has existed, nor ever will. But when the present tense is used, not specifically, but universally, it is then true that there is infinite time. Any further treatment of the question of infinity would be out of place here. Consult: Royce, The World and the Individual, vol. i., supplementary essay (New York, 1900) ; Bradley, Appearance and Reality (2d cd., Lon- don, 1897); Couturat, De Vinfini mathimatique (Paris, 1896) ; Bosanquet, Logic (Oxford, 1888) ; Bolzano, Paradoxien des Vnendlichen (Leipzig, 1851); Hegel. Wissenschaft der Logih (Berlin, 1841); J. Cohn, Geschichte des Unendlichkeits- problems im abendliindischen Denken his Kant (Leipzig, 1896). INFINITE SERIES. See Series. INFINITY AND THE INFINITESIMAL (Lat. infinitas, from infinitus, boundless). A number conceived to be greater than any a.ssign- able number, however great, is called an infinite number. The symbol a, meaning indefinitely great, cannot be used in operations as a finite number ; e.g. at; — ■ od is not necessarily zero, and ^ is not necessarily 1. A number that varies and becomes and remains smaller in absolute value than any assignable number, however small, is called an infinitesimal numt)cr. The use ot the symbol is also limited; e.g. — h not necessarily 1. (See Fbactioxs. ) In modern geometry the notion of infinite points and in- finite lines has led to great generalization, and supplied the condition for continuity (q.v.) of many relations; e.g. for the statement. "Two co- planar lines are concurrent or parallel." may be substituted, "Two co-planar lines are concurrent in a finite or an infinite point." In modern anal- ysis the infinitesimal has played an important role. From the time of Kepler mathematicians have struggled with the infinitesimal, especially as employed in the differential calculus, and some, notably Lagrange, have tried to avoid its use entirely. But through the efforts of Le- gcndre. Gauss. Carnot, and especially Cauchy. the meaning of the propositions concerning in- finitesimals has been established, and a safe foundation for the differential calculus has been laid. See the article Calculus. INFIRMARY. See Hospital; Dispessaby. INFLAMMATION (Lat. inftammatio, from inflammare, to set on fire, from in, in + flamma. flame; connected with flagrare. Gk. (pXiyctv, phle- gein, to blaze, Skt. bhraj, to be bright). . mor- bid condition characterized by altered function of the elements of the tissue involved, changes in circulation, derangement of local nutrition, and generally an exudation infiltrating the tis- sues affected. It is a process of extreme com- plexity, presenting variations depending upon the exciting cause and upon the kind of tissue in which it occurs. It is therefore impossible to define it satisfactorily. The most obvious .symp- toms or phenomena of inflammation, when it at- tacks an external or visible part, are pain, red- ness, heat, and swelling, together with altered function. The general characters of the process will be best understood by an assumed case. If a healthy man has a splinter of wood or any other foreign body imbedded in any fleshy part, he begins to experience pain at the part, and this is soon succeeded by redness of the skin, a firm and extremely tender swelling at and around the spot, and a sense of abnormal heat. These purely local symptoms are succeeded, if the inflammation reaches a certain degree of in- tensity, by a general derangement of the vascular