I will first give the example of that kind of induction, then define it, then give the definition of what we do - in the trace of older philosophers - accept as induction, then examplify it with the same matter so as to make the difference most clear.
The Sun has always risen every morning. Therefore it is impossible for the sun not to rise tomorrow, and an omnipotent God who could make an exception is excluded.
1) That induction is from particular to particular. 2) And it claims to be surer than Christianity.
It is, in its first quality, a renovation innovation by John Stuart Mill, who wanted to formalise induction as much as deduction and therefore wanted more variations on the theme "induction". In the second quality, it is the induction of a "sceptic", that is, of a disbeliever in miracles. Is it an accident that JSM was such a person?
Now, there is another kind of induction which we, following Aristotle, even Socrates, do accept. It is the induction of particular examples to make a point about a general principle, which once illustrated by the inductions, we cannot deny.
The Sun has always risen every morning. Therefore, the Sun rises every morning.
That does NOT yet determine whether the sun will rise tomorrow. To do that we need also to state a deduction, from general principle to particular:
The Sun rises every morning. Tomorrow will have a morning as any other day. Therefore the Sun will rise tomorrow.
But, knowing there is one omnipotent God, knowing time has not only a created beginning but a created end, we will not attribute to the conclusion such sureness as to exclude some extraordinary action by God, like a miracle or the day of judgement. Quite obviously, the possibility of such an exception does neither change the fact that we do expect the Sun to rise tomorrow, nor the possibility of making inductions.
Indeed, if we had not accepted the induction that old women do not have babies, we would not have known that the birth of Isaaq, of Our Lady and of St John the Baptist were divine miracles. If we had not accepted the induction that getting pregnant depends on having sex, we would not have known - and St Joseph would not have considered putting away Our Lady - that the Virgin Birth is a miracle. If we had not accepted the induction that the dead do not return to life, we would not have seen the point why St Thomas, on seeing Christ resurrected, called him My Lord and My God.
Without inductions, we would not have been able to determine where we had indications of the action of an Omnipotent God.
Hans-Georg LundahlParis IV, G Pompidou
21/sept/2009, St Matthew, Evangelist;
for Old Calendarists:
8/sept/2009, Our Lady's Birthday