Editorial
Second-Order Logic?
At various times in these pages, we've kicked around the problem of logic and thinking—and that "we" isn't the editorial variety, either. See Brass Tacks—and join in the discussion if you've a mind to. The world's prize stupid oaf is the man who thinks he already has all the answers; so far, I don't qualify for that one.
Let's try a new tack on this problem of Aristotelian vs. Non-Aristotelian logic. The concept of A vs. Non-A logic is, of course, strictly Aristotelian in that anything that isn't A-logic must be Non-A—which makes it somewhat easy for the Non-A advocates. They do fine by defining in the negative; they need only tell you what they do not mean to be left an infinity of possible meanings. I can with the most complete assurance make the statement: "This magazine is not an apple." Whether that helps you to understand what it is or not . . . well, that's a different problem, I suppose. But my statement is unquestionably correct; no one can challenge me on that.
Such statements are safe, to be sure—but are they useful?
It is useful to recognize that Aristotelian logic is not adequate—that it's necessary but not sufficient. But that statement is itself necessary, but not sufficient; if A-type logic is not sufficient, then what is? Define positively, not negatively, the Non-A logic that will do the required job.
All right—let's make a try at it.
It's long been held that truly logical thinking about a problem requires an objective viewpoint; you must remove your own feelings and biases about the problem from consideration, and think about the problem as though you were not involved in it. Don't let the problem influence your feelings, or
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Astounding Science-Fiction
