The Psychology of Proof by Lance J. Rips
Suppose some future psychologists are asked to investigate the mental faculties of a newly discovered intelligent life form. Sent to the planet that these creatures inhabit, the psychologists make observations, conduct experiments, administer tests, and Anally compose a report for the Journal of Extraterrestrial Psychology.
In reading this report, we would probably not be too surprised to And that the creatures have visual systems different from ours, and perhaps different perceptual experiences. Nor is it hard to imagine these creatures having vastly greater (or smaller) memory capacity. But suppose we are also told that the creatures reject simple, familiar inference principles in favor of equally simple but to our minds obviously incorrect principles.
To us earthlings, an intuitively straightforward inference principle is the one logicians call modus ponens. According to this principle, the proposition IF so-and-so THEN such-and-such and the proposition So-and-so jointly entail the proposition Such-and-such.1 For example, from the propositions IF Calvin deposits 50 cents THEN Calvin will get a coke and Calvin deposits 50 cents, it follows that Calvin will get a coke. We can write this in the form shown in (IX where the sentences above the line are called premises and the sentence below the line the conclusion.
(1) If Calvin deposits 50 cents, Calvin will get a coke.
Calvin deposits 50 cents.
Calvin will get a coke.
Now suppose that our extraterrestrials have exactly the same inference skills that we do, but with one important exception. They reject all modus ponens arguments, such as (1), and adopt instead a contrary principle we might call modus shmonensr. From IF so-and-so THEN such-and-such and So-and-so, they conclude NOT such-and-such. For instance, they would say that the conclusion of (1) doesn’t follow from its premises, but that the conclusion of (2) does.
(2) If Calvin deposits 50 cents, Calvin will get a coke.
Calvin deposits 50 cents.
Calvin will not get a coke.
The existence of creatures who systematically deny modus ponens and accept modus shmonens would be extremely surprising—much more surprising than the existence of creatures who differ from us in basic perceptual or memory abilities. In a situation like this one, we would probably be more apt to blame the translation into English from whatever language the creatures speak than to accept the idea that they sincerely believe in modus shmonens .
Indeed, our reluctance to attribute exotic inferences even to exotic creatures is an interesting property of our thought processes. Modus pone ns and other inference principles like it are so well integrated with the rest of our thinking—so central to our notion of intelligence and rationality—that contrary principles seem out of the question.
As Lear puts it, “We cannot begin to make sense of the possibility of someone whose beliefs are uninfluenced by modus ponens: we cannot get any hold on what his thoughts or actions would be like.” Deep-rooted modes of thought such as these are important objects of psychological investigation, since they may well turn out to play a crucial organizing role for people’s beliefs and conjectures—or so I will try to argue.
This book leads up to the conclusion that cognitive scientists should consider deductive reasoning as a basis for thinking. That is, it explores the idea—which I call the Deduction-System Hypothesis—that principles such as modus ponens are central to cognition because they underlie many other cognitive abilities.
Part of the content of this proposal is that the mental life of every human embodies certain deduction principles— that these principles are part of the human cognitive architecture and not just the properties of people schooled in logic. This approach also views deduction as analogous to a general-purpose programming system: Just as we can use a computer language such as Basic or Pascal to keep track of our finances or to solve scientific or engineering problems, we can use deductive reasoning to accomplish a variety of mental activities.
In particular, we will see how deduction allows us to answer questions from information stored in memory, to plan actions to obtain goals, and to solve certain kinds of problems. The Deduction-System Hypothesis is necessarily vague at this point, but I hope to clarify it during the course of the book. In the meantime, it may help to think of deduction systems as similar to production systems but incorporating more flexible forms of representation and process.
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