n could only be a necessary linking together of other truths whose
result would be contrary to the truth that one maintains; and consequently
there would be contradiction between the truths, which would be an utter
absurdity. Moreover, albeit our mind is finite and cannot comprehend the
infinite, of the infinite nevertheless it has proofs whose strength or
weakness it comprehends; why then should it not have the same comprehension
in regard to the objections? And since the power and the wisdom of God are
infinite and comprehend everything, there is no pretext for doubting their
scope. Further, M. Descartes demands a freedom which is not needed, by his
insistence that the actions of the will of man are altogether undetermined,
a thing which never happens. Finally, M. Bayle himself maintains that this
experience or this inward sense of our independence, upon which M.
Descartes founds the proof of our freedom, does not prove it: for from the
fact that we are not conscious of the causes whereon we depend, it does not
follow, according to M. Bayle, that we are independent. But that is
something we will speak of in its proper place.

70. It seems that M. Descartes confesses also, in a passage of his
_Principles_, that it is impossible to find an answer to the difficulties
on the division of matter to infinity, which he nevertheless recognizes as
actual. Arriaga and other Schoolmen make well-nigh the same confession: but
if they took the trouble to give to the objections the form these ought to
have, they would see that there are faults in the reasoning, and sometimes
false assumptions which cause confusion. Here is an example. A man of parts
one day brought up to me an objection in the following form: Let the
straight line BA be cut in two equal parts at the point C, and the part CA
at the point D, and the part DA at the point E, and so on to infinity; all
the halves, BC, CD, DE, etc., together make the whole BA; therefore there
must be a last half, since the straight line 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 arg