themselves. I had no time, I very much regret to say, to speak of continuity, which is the principal mathematical conception and the most in need of explanation while its logical importance is far greater than is everything else put together that I could bring into the first six lectures. But there was no possibility of crowding it into this course. In the sixth lecture I was only able to make a few detached remarks concerning statistical deductions. This leaves us but two hours in which to treat of the most important kinds of reasoning Induction and Abduction. Deduction is of small account beside these
but unfortunately these can only be understood in the least in the light of deduction. Without that one could not even comprehend what inductive and abductive reasoning are. All that I have said, therefore, is merely a very inadequate preparation for these last two lectures; and the latter of these will have to be curtailed in a most injurious fashion. Logic, let me tell you, while it is a subject requiring continual stress of mind, is by no means a dry and uninteresting topic. But it becomes so, as any science would, when it has to be compressed to a very injurious and almost fatal degree. Where it differs from other sciences is that fragments
of them can be presented very well, while logic must be given in a certain degree of fulness or else it will not be presented at all.
The course of events by which any new subject gets added to our knowledge is most clearly marked in the case of an addition to our scientific knowledge.
In the first place we are already in a previous state of knowledge. Logic has
absolutely quite nothing to say concerning the primum cognitum. In consequence of this we are in a state of expectation concerning a coming phenomenon,— being that expectation active or passive.
If the phenomenon, when it comes, fulfills that expectation, it strengthens the habits of thinking on which that expectation is based, but teaches us nothing new. But if it involves any surprise, as it mostly does, our habits of thinking are deranged, whether little or much. We then feel the need of a new idea which shall serve to bind the surprising phenomenon to our preëxisting experience. Our usual phrase is that we want the surprising fact explained.
For this pur With this end in view we are led to frame a hypothesis, and the process of reasoning by which we come to set up a hypothesis is the kind of reasoning that I call Abduction. Now this hypothesis is a purely ideal state of things, and upon the