INFINITY
INFINITY
domestic life. Some very delicate questions may arise
in connexion with the last prohibition; for instance, we
may recall the celebrated controversy concerning the
Chinese rites (see China). On the other hand, it is not
forbidden to enter temples and mosques out of mere
curiosity if no act of religion be performed, or to eat
food that has been offered to false gods, provided
this be not done in a temple or as a sacred repast,
and that it be done without scandal; or to observe
customs or perform acts which are not in themselves
religious, even though pagans join superstitious prac-
tices to them. Not only is it not forbidden, but it is
permissible and one might say obligatory to pray even
publicly for infidel princes, in order that God may
grant their subjects peace and prosperity; nothing is
more conformable to the tradition of the Church ; thus
Catholics of the different rites in the Ottoman Empire
pray for the sultan.
In this place mention may be made of the ecclesi- astical law forbidding the faithful to marry infidels, a prohibition which is now a diriment impediment, ren- dering a marriage null and void unless a dispensation has been obtained (see Disp.uiity of Worship). It is easy to see that there is a real danger to the faith and rehgious life of the Catholic party in the intimacy of married life and in the difficulties in the way of a Christian education of the children; and, if that party be the wife, in the excessive authority of the husband and the inferior condition of the wife in infidel coun- tries; consequently, this dispensation is granted only with difficulty and when the precautions dictated by prudence have been taken. The laws regulating the dealings between Catholics and infidels in civil life were inspired also by religious motives, the danger of perversion, and the high idea entertained in the ages of faith of the superiority of Christians to in- fidels. These regulations, of course, did not refer to all acts of civil life; moreover, they were not directed against all infidels indifferently, but only against Jews; at the present day they have fallen almost completely into desuetude. In the early Middle Ages, Jews were forbidden to have Christian slaves; the laws of the decretals forbade Christians to enter the service of Jews, or Christian women to act as their nurses or mid wives; moreover. Christians when Ul were not to have recourse to Jewish physicians. These meas- ures may be useful in certain countries to-day and we find them renewed, at least as recommendations, by recent councils (Council of Gran, in 1858; Prague, in 1800; and Utrecht, ia 1865). As for the Jews, they were ordinarily restricted to certain definite quarters of the towns into which they were admitted, and had to wear a dress by which they might be recognized. Modern legislation has given the Jews the same rights as other citizens and the intercourse between them and Catholics in civil life is no longer governed by ecclesiastical law. (See Jews and Juuais.m; Mo-
HAM.MED AND MOHAMMEDANISM.)
The commentaries of the eanonists on book V, tit. vi of the decretals. "De Judans et Saracenis et eorum servia". An ample collection of texts in the Collectanea S. Congr. de Propa- ganda Fide (Rome, 1893; 2nded., 1907); Saomuller, Lc/iriur/i des kathol. Kirchenrechts (Freiburg im Br., 1904), 15; D'.^nni- BALE, Summula, I, n. 111.
A. BODDINHON.
Infinity (Lat. infinilas; in, not, finis, the end, the boundary) is a concept of the utmost importance in Christian philosophy and theology.
Definition. — The infinite, as the word indicates, is that which has no end, no hmit, no boundary, and therefore cannot be measured by a finite standard, however often applied; it is that which cannot be attained by successive addition, nor exhausted by successive subtraction of finite quantities. Though in itself a nefiative terra, infinity has a very positive meaning. Since it denies all bounds — which are themselves negations — it is a double negation, hence an affirmation, and expresses positively the highest,
unsurpassable reality. Like the concepts of quantity,
limit, boundary, the term infiniti/ applies primarily
to space and time, but not exclusively as Schopen-
hauer maintains. In a derived meaning it may be
applied to every kind of perfection: wisdom, beauty,
power, the fullness of being itself.
The concept of infinity must be carefully distin- guished from the concept of the "all-being". In- finity implies that an infinite being cannot lack any reality in the line in which it is infinite, and that it cannot be surpassed by anything else in that particu- lar perfection; but this does not necessarily mean that no other being can have perfections. " All- being", however, implies that there is no reality out- side of itself, that beyond it there is nothing good, pure, and beautiful. The infinite is equivalent to all other things together; it is the greatest and most beautiful; but, besides it, other things both beautiful and good may exist (for further explanation see below). It is objected that, if there were an infinite bod}', no other body could exist besides it; for the infinite body would occupy all space. But the fact that no other body could exist besides the infinite body would be the result of its impenetrability, not of its infinity. Spinoza defines: " Finite in its kind is that which can be limited by a thing of the same kind" (Ethics, I, def . ii). If he intended only to say: "Finite is that from which another thing of the same kind, by its very existence, takes away perfection", no fault could be found with him. But what he means to say is this: "Finite is that, besides which something else can exist; infinite therefore is that only which includes all things in itself." This definition is false.
Many confound the infinite with the indeterminate. Determination (delerminatio) is negation, limitation (negatio, limitatio), says Spinoza. Generally speak- ing, this is false. Determination is limitation in those cases only where it excludes any further possible perfection, as, for example, the determination of a surface by a geometrical figure; but it is no limitation, if it adds further reality, and does not exclude, but rather requires a new perfection, as, for example, the determination of substance by rationality. The mere abstract being, so well known to metaphysicians, is the most indeterminate of all ideas, and neverthe- less the poorest in content; the infinite, however, is in every way the most determinate idea, in which all possibilities are realized, and which is therefore the richest in content. According to Hobbes, we call a thing infinite if we cannot assign limits to it. This definition is also insufficient : infinite is not that whose limits we cannot perceive, but that which has no limit.
Division. — The different kinds of infinity must be carefully distinguished. The two principal divisions are: (1) the infinite in only one respect [secundum quid) or the partially infinite, and the infinite in every respect (simpliciter) or the absolutely infinite; (2) the actually infinite, and the potentially infinite, which is capable of an indefinite increase. Infinite in only one respect (viz. extension) is ideal space; infinite in only one respect (viz. duration) is the im- mortal soul; infinite in every respect is that being alone, which contains in itself all possible perfections and which is above every species and genus and order. Potentially infinite is (e. g.) the path of a body which moves in free space; potentially infinite is also the duration of matter and energy, according to the law of their conservation. For this motion and this duration will never cease, and in this sense will be without end; nevertheless, the path and the duration up to this instant can be measured at any given point and are therefore in this sense finite. Hence, they are infinite not according to what they actually are at a given moment, but according to what they are not yet and never actually can be; they are infinite in this, that they are ever and forever progressing with- out bounds, that there is always the "and so forth".
