BA finishes at A. But this last half is absurd:  for since it is a line, it will be possible again to cut it in two.  Therefore division to infinity cannot be admitted.  But I pointed out to him that one is not justified in the inference that there must be a last half, although there be a last point A, for this last point belongs to all the halves of its side.  And my friend acknowledged it [113] himself when he endeavoured to prove this deduction by a formal argument; on the contrary, just because the division goes on to infinity, there is no last half.  And although the straight line AB be finite, it does not follow that the process of dividing it has any final end.  The same confusion arises with the series of numbers going on to infinity.  One imagines a final end, a number that is infinite, or infinitely small; but that is all simple fiction.  Every number is finite and specific; every line is so likewise, and the infinite or infinitely small signify only magnitudes that one may take as great or as small as one wishes, to show that an error is smaller than that which has been specified, that is to say, that there is no error; or else by the infinitely small is meant the state of a magnitude at its vanishing point or its beginning, conceived after the pattern of magnitudes already actualized.

71.  It will, however, be well to consider the argument that M. Bayle puts forward to show that one cannot refute the objections which reason opposes to the Mysteries.  It is in his comment on the Manichaeans (p. 3140 of the second edition of his Dictionary).  ‘It is enough for me’, he says, ’that it be unanimously acknowledged that the Mysteries of the Gospel are above reason.  For thence comes the necessary conclusion that it is impossible to settle the difficulties raised by the philosophers, and in consequence that a dispute where only the light of Nature is followed will always end unfavourably for the theologians, and that they will see themselves forced to give way and to take refuge in the canon of the supernatural light.’  I am surprised that M. Bayle speaks in such general terms, since he has acknowledged himself that the light of Nature is against the Manichaeans, and for the oneness of the Principle, and that the goodness of God is proved incontrovertibly by reason.  Yet this is how he continues: 

72.  ’It is evident that reason can never attain to that which is above it.  Now if it could supply answers to the objections which are opposed to the dogma of the Trinity and that of hypostatic union, it would attain to those two Mysteries, it would have them in subjection and submit them to the strictest examination by comparison with its first principles, or with the aphorisms that spring from common notions, and proceed until finally it had drawn the conclusion that they are in accordance with natural light.  It would therefore do what exceeds its powers, it would soar above its [114] confines, and that is a formal contradiction.  One must therefore