THE LOGIC OF MULTIPLE-CHOICE-QUESTIONS
C. S. Peirce once said, science offers tentative hypotheses, indeed questionable hypotheses, sometimes even ‘almost incredibly wild’ ones, which are thus almost-questions: questions are doubts, and assertions are beliefs, he said.
Not so, say Popper, Bunge, Bromberger, Lakatos, and others. We may accept a hypothesis for the purpose of finding an object of belief, and we may accept a hypothesis for the sake of finding an object of study and examination. Should I invest the next few years of my life in question x? or, will it soon turn out to be a worthless question? Or, still worse, will it turn out to be worthless only years later?Popper said once, we need to fall in love with a problem. I am very dissatisfied with this. One must fall in love with a problem, to be sure, but one may try to make it the right one! Indeed, Popper’s theory of degree of falsifiability says more. It says look for as highly testable a hypothesis as possible. This, surely, relates to the choice of problems. How exactly is not yet clear - it is being studied. The logic of questions keeps pressing and now people are working on a technique to embed it. Thus, techniques suggest questions but also questions recommend developing techniques. In 1955 the Priors said that this cannot be done within formal logic. Yet Hamblin started the trend, I think, with the use of simple ideas from logic and information theory. Roughly, Hamblin equated (already in his doctoral dissertation, University of London, 1957) a question with a set of alternatives plus the instruction to choose one: e.g. ‘What is the color of my horse?’ means, choose between ‘the color of my horse is white, is brown, etc.’ Now the disjunction may be complete and so a tautology - at least until challenged in accord with Arthur Pap’s posthumous paper in Mind about the synthetic a priori character of the complete list of colors.
We may, however, exclude green on the basis of the background knowledge that no horse is green. The disjunction sans green, then, presupposes ‘no horse is green’, and from this Harrah concluded that questions presuppose information. If the information be false, Belnap and Aqvist add, we do not answer the question, but criticize it, correct it, rectify it, or pseudo-answer it. This, of course, is more interesting and more dialectical. It is, indeed, very significant that for the first time use is made of the truism, a question well-put, is a question half-answered. But this is only a beginning. Erotetic logicians can handle some yes-no questions, though this takes some effort. Also, they can handle questions of the kind, which of a given set of alternatives is true. This kind of question includes who, which, when, etc. questions, which Carnap has called W-questions. If the list of people is not complete, who questions may be cumbersome, or unanswereable as yet, but still not seriously problematic.A little reflection will make this quite plausible. When a customer asks an airline computer which flight to book from a to b? the computer gives no anser to the question. Rather, the computer can translate the question into a multiple-choice question, and the customer then decides the answer. The multiple-choice list may be incomplete on various counts, or complete (relative to given background-knowledge!), as the case may be, with both question and answer subject to certain constraints (explicit or embedded in the given background-knowledge).
What this indicates is, first and foremost, that contemporary erotetics is a logic of questions, hardly of the choice of an answer or of a decision. This may explain the fact that, contrary to Collingwood’s expectation, so much of it could be developed within traditional formal logic.
This, however, is not to say that all is smooth within the logic of questions : as I have hinted, the situation is more of work in progress than of a job completed.
Even when we restrict the study to seemingly trivial cases, we may get a number of interesting results. Peirce has translated Ts this the way to the city?’ into ‘This is the way to the city, eh?’, which is the same as the request to determine the truth-value of the statement ‘This is the way to the city’. This sounds perfectly straightforward and quite unproblematic, until one tries to embed it in a formal system with requests and knowing what constitutes an answer to a question (i.e. turning it into multiple-choice) and presuppositions. It soon transpires that some questions are risky, even yes-no questions (have you stopped asking risky questions?), as we have seen already.Thus, much of present-day erotetic logic renders questions into multiplechoice questions, their transformations, and the limits of their satisfactoriness. But we have a completely different kind of question, which Bromberger has labelled ^-predicaments, with p for perplexity or puzzlement. When we ask, why?, we may know whether a particular statement would count as an answer. Bromberger has also introduced the term ^-questions - b for beyond our capacity - for example questions which were asked by classical physicists but could not be answered prior to the rise of quantum theory. I shall discuss the difference below.
How do we go about suchp and b questions? How do we explain? i.e. how do we answer why questions? Popper says, we cannot answer this question at all - there is no method of discovering answers. But even he admits that there exist partial methods, though he is reluctant to discuss these. To my surprise I have found that my own study of the existing partial methods (particularly of Faraday’s field-theoretical method of raising new kinds of questions and of looking for new kinds of solutions to them), have led me to dissent from a few details of Popper’s view of the methods of science. Let me sketch here briefly a theory of partial methods, and contrast it with Popper’s theory of explanations. But before that I wish to discuss the theory of explanation in general.
VIII.