Last rites declaration of Ioannes Paulus PP. II (Karol Wojtyla)
2nd April 2005
astonished when they are presented with propositions of which
they understand nothing, and the way to which is through definitions and
axioms so sterile, and which they are not accustomed to see thus in detail,
that they are repelled and disheartened.
But dull minds are never either intuitive or mathematical.
Mathematicians who are only mathematicians have exact minds, provided all
things are explained to them by means of definitions and axioms; otherwise
they are inaccurate and insufferable, for they are only right when the
principles are quite clear.
And men of intuition who are only intuitive cannot have the patience to
reach to first principles of things speculative and conceptual, which they
have never seen in the world and which are altogether out of the common.
2. There are different kinds of right understanding; some have right
understanding in a certain order of things, and not in others, where they go
astray. Some draw conclusions well from a few premises, and this displays an
Others draw conclusions well where there are many premises.
For example, the former easily learn hydrostatics, where the premises are
few, but the conclusions are so fine that only the greatest acuteness can
And in spite of that these persons would perhaps not be great
mathematicians, because mathematics contain a great number of premises, and
there is perhaps a kind of intellect that can search with ease a few
premises to the bottom and cannot in the least penetrate those matters in
which there are many premises.