heresy has always been The ideas of section XII With a very polite bow to

Christian sects the reproach of stuck to the more sensible part. are somewhat difficult to catch. the Church of England, Hume derides the Christian (Catholic) rites-for instance the Lord's Supper-which in his opinion are as absurd as the ideas of paganism. He examines the relation between peoples' creed and their own conjecture about this creed, observing that human conscience includes the greatest contrasts: a concise, scientific range of ideas alongside of the most superstitious notions, a profound psychological remark, which as to the individual consciousness forms the supplement to Hume's assignment of the lower strata which survive unaltered in the people. In agreement with the words of Lucretius Carus,

"Primus in orbe deos fecit timor,"

and with Hobbes's psychology of religion in Leviathan, Hume had emphasized fear as the strongest religious impulse. The gods are created by fear, and fear secondarily begets praise, elevating the gods. But in Hume's opinion this idealization-if it was not idola fori-according to its origin only indicated an enlargement of the power of deity. The gods had to remain on an ethical level with the men who created them in their own image. As set forth in section XII the consequence is that the fear of the god magnifies in proportion as he increases in power. This enlargement of the deity's power is contingent upon no other deities being acknowledged beside him. In each religion there are two poles represented on one hand by the kind, beneficent gods, on the other by the noxious, wicked ones. "The higher the deity is exalted in power the lower is he depressed from an ethical point of view." In the so-called higher religions the tension becomes strongest in the negative pole: a fact illustrated by means of Judaism and Christianity. Hume cautiously screens himself by

Andrew Michael Ramsay (1686-1743) the friend of Fenelon and author of Philosophical Principles of Natural and Revealed Religion, Explained and Unfolded in a Geometrical Order (1749). In section XIV Hume repeats that the ethical idealization of the deities is only a verbal definition. Religion will always contradict morality from the mere cause of its emphasizing other things than an honest life. Were we to suppose a purely moral religion, the only cult of which consisted in sermons of a virtuous conduct of life, the very attendance on these sermons would soon be turned into religion. Any religion is compatible with the greatest baseness, nay it rather produces it, for the fervor of religious passion arises from a range of ideas entirely different from man's sense of truth and goodness. In the last chapter Hume sums up the last six chapters, setting forth the contrast between the doctrine of the higher religious tenets and the life of their adherents. He concludes by maintaining that religions do not give any real answer in reply to the question of life and death, but that the history of religion in showing the mutual struggle of the different religious systems may also be of practical importance in enjoining us to be cautious in our relation to those questions. I believe Hume was right in this particular. What the more abstract criticism of deism failed to reach as to religion may surely be reached more easily by the path of historical investigation. But whether an adherent of Hume's conception of life or not, one is almost bound to grant that the contest between religious and nonreligious conceptions approaches more and more the mere historical domain, a fact proved by the time succeeding Hume's-in spite of the recent American religious psychological humbug, in spite of all its desperate endeavors to make science founded on "mind-cure" and statistics of conversion. Be the expectations and the result as they may, only historical meditations and arguments give value to

attack and defence. But whatever stand we will take in the strife or what special domain within the science of religion we wish to peacefully explore, we ought always to return to the classical work of religious science and bow our heads in reverence to the great founder of this science.

UNIVERSITY OF COPENHAGEN.

ANTON THOMSEN.

A MODERN ZENO.

ENO of Elea is famous mostly for his so-called “argument" to the effect that in a race between Achilles and a tortoise with the latter starting in advance a certain distance, Achilles can never overtake the tortoise although he may run many times as fast as his slow competitor. For, says Zeno, when Achilles reaches the spot where the tortoise started the other will have advanced to another point, and when Achilles has reached this second point the tortoise will have gone on to a third point and just so on and on the race will continue ad infinitum, the tortoise being always a little ahead. It is curious to see how this little non sequitur has perplexed people, many of them of excellent intellectual standing. Thus the famous logician Sir William Hamilton said the "argument" was unanswerable.

It is altogether beside my present theme to state wherein the catch lies, so I will merely say that the conclusion is no consequence at all from the premises. The "argument" stripped of its disguises is just this. Achilles can never overtake the tortoise because he cannot overtake it in any less time than it takes to do so.

Among men there is no habit more inveterate than the persuasion of each individual that he personally is immune from slips in reasoning. All around him during almost every day of his life he takes notice how badly other people reason without ever saying to himself that probably he is

like other people in the same regard. So in view of the incontestable fact that men, yea, even men most eminent in intellectual power and cultivation, do sometimes err in reasoning, I make bold to confess a growing measure of misgiving as to certain geometrical results that have played and are still playing a conspicuous rôle in the mathematics of the present epoch. I refer to the so-called non-Euclidean geometry, and I propose to utter a little note of protest or rather of question. That is to say, some considerable study of the famous brochure of Lobatchevsky on parallels leaves my mind in such a state that I desire greatly some further instruction.

It is generally recognized that the problems of parallelism and of the angle-sum of the triangle are only two different aspects of a single problem. The solution of either involves the solution of the other. Lobatchevsky approaches the problem from a definition of parallelism. He adopts most of the fundamental definitions and conceptions of ordinary geometry and quite a number of the initial theorems. He defines the straight line in an original way saying: "A straight line fits upon itself in all its positions. By this I mean that during the revolution of the surface containing it the straight line does not change its place if it goes through two unmoving points in the surface (i. e., if we turn the surface containing it about two points of the line, the line does not move)."

Now it is one thing to give us an idea of an object and quite another to so define it that its essential quality or qualities shall be definitely stated. Lobatchevsky's definition is no special improvement upon the other current definitions. It is a suggestion rather than a definition. Of late the statement that a straight line is determined by two of its points has gained favor as a definition, and it is true that a single particular straight line is by two points of it determined to be that several and singular straight line