A steel door opened in the wall behind him; it had been all but invisible between the two windows before then. A uniformed guard came, took the note, asked me the obvious questions about whom I had told and whether I had any personal enemies, and departed by the same concealed elevator.
“No way of knowing what they’ll find and I detest theorizing in advance of data,” Iphwin said. “Well, back to the problem at hand, then. I assume that if we can adequately clear up this threatening note—that is, we can establish that the person who wrote it cannot harm you, and that I am your real friend and that person is not—you are still interested in the job? And since you don’t know us here at ConTech at all well, I also assume that you will want some proof and evidence of good faith? I know I would in your position.”
In my position, I thought, I still don’t believe that this is happening. I thought at best I might be hired to do statistics for some research project using a mathematical method similar to the abductive statistics I’ve used in my work. I am not accustomed to having a car—even a very friendly and pleasant car—tell me that I am about to meet an international celebrity, less than fifteen minutes before I do. Out loud, I said, “That’s extremely reasonable and it already increases my trust. I’m sure we’ll be able to work something out soon enough. But, sir—”
“Iphwin.”
“Er, yes.” I swallowed hard. “Iphwin, this whole situation makes no sense to me. I’m not a particularly distinguished astronomer. It makes some sort of sense that you want me as a statistician, because that is the one area where I’ve done considerable original work, but all the same there are mathematicians out there who could do rings around me—rings and groups and matrices and tensors, to tell the truth.”
He didn’t laugh; inwardly I cursed whatever it was that had prompted me to make a feeble mathematical pun. Then abruptly he did laugh, and said, “But if they don’t do Abelian groups, they’ll have to live here in the building, since they can’t commute.”
Startled, I laughed.
“You see,” he said, “we have similar senses of humor.”
But yours seems to run on a schedule different from mine, I thought. “Anyway, sir—I mean Iphwin—it just seems to me that you could easily get someone better for whatever job you could possibly have in mind.”
Iphwin hopped up on his desk and crossed his legs, peering at me over his knee, like a small boy about to spring a transparent practical joke. “Who else has even tried to develop a statistics of abduction?”
“Er—eight or nine people. And only four of us are alive. But that’s a pure hobbyhorse of mine. If Utterword weren’t the editor of that little journal, I wouldn’t even be getting published.”
“But you get results.”
“I think I do.”
His smile grew more intense, his eyes twinkled, and he said, “Tell me everything about abduction.”
“That’s a tall order,” I said. “At least let me try to summarize. About 170 years ago, the great American polymath, Charles Sanders Peirce—”
“I thought it was Pierce,” he said, pronouncing it with a long e.
“He pronounced it like ‘purse,’ ” I said. “Anyway, Peirce did an enormous amount of work on logic, developed a very eccentric theory of semiotic, and made contributions to half a dozen sciences and to philosophy, but this is one of his strangest ideas—and he had some very strange ones.”
“Strange but not bad?” Iphwin asked.
“Not bad, or at least not all bad. Peirce said that there were two common kinds of logic—deduction and induction. Deduction is deriving the behavior of the particular case from the general case, like the famous syllogism where you figure out that Socrates is mortal. Induction is the other way round, figuring out general laws from some number of particular cases, like noticing that some energy is always lost irrecoverably as heat in every physical experiment you can run, and coming up with the theory that entropy always increases. Induction gives us general laws, and deduction lets us use them in our particular cases; one gets us ready to cope with a situation and the other is the process of coping. They’ve served humanity pretty well.
“But, Peirce said, that set is incomplete. There’s one more kind of logic not covered there.
“Now one reason he might have thought that is that in Peirce’s thought everything is always organized into threes, so anytime there’s a pair, it’s incomplete, and a third member must be found. It might be no more than that. But Peirce proposed a problem that turns out to be surprisingly difficult to resolve in a satisfactory way, which seems to indicate that there really ought to be one more kind of logic.”
Iphwin jumped up and paced; it was just as if this was all news to him, and yet if he had really been interested in Peirce and in Peircean thought, he could probably have found a Peirce scholar cheap—studies of obscure philosophers do not make for lucrative careers—and gotten a much better exposition than I was giving him. The pacing and gesturing seemed as if he were playing the part of a man consulting an expert, and he expected me to play the role of the expert. “So,” he said, “Peirce proposed a problem?”
With a small tremor of guilt, I realized I had gotten fascinated with watching him, and had not talked for several seconds after his question. “What Peirce proposed was a problem which ought to have a logical solution—that is, one you could arrive at by stepwise objective reasoning that anyone with adequate training could copy or evaluate—for which he could show that both induction and deduction could not lead to the solution. If it was soluble, then it had to be soluble by some other means.” I was warming to the subject, now, I confess, and at the same time I was very worried that I might bore him or begin to lecture and thus lose the friendly warmth he had been beaming at me since I arrived. “What he said was that all logic is basically made up of terms, propositions, and arguments—names of things, statements about names, and groups of statements from which you can generate more statements. ‘Socrates’ is a term, ‘Socrates is a man’ is a proposition, and the syllogism is an argument. Now, Peirce says, it doesn’t matter where we get terms because they’re not subject to logic and are purely arbitrary—all we have to do is remember that we called it a ‘glump’ last time, and we can just go on calling it a ‘glump’ forever. And obviously arguments are deductive or inductive logic, so we know how we get arguments—we take propositions and apply the rules of induction or deduction to connect them with each other.”
“But!” Iphwin shouted. “But!” He leaped up and spun around.
By then I was about half ready to join him; his enthusiasm was so contagious and it would have made as much sense as anything else. I couldn’t help smiling but I otherwise restrained myself and went on. “We know where we get some propositions—we make them out of other propositions, using arguments. But where do the starter propositions come from? How do we link terms to form propositions without going through the stage of argument—since we can’t make arguments if we have no propositions? And Peirce’s answer was that we must have a way of choosing propositions out of the whole vast welter of possible ideas, and of knowing that some propositions are more likely to yield worthwhile results than others. And that way of choosing is his third kind of logic—which he calls abduction. ‘Deduction’ is Latin for leading an idea down—that is, down from general to particular. ‘Induction’ is Latin for leading an idea to or into something—that is, to or into the general from the particular. But abduction is leading away—taking some combination of words, symbols, thoughts, or whatever out of the vast swamp of what it’s possible to think of, and picking one that has a chance of being true, so that when we perform induction and deduction on it, we stand a good chance of gaining either a general law or an understanding of a particular situation.”