So much contemporary research in psychology focuses on the flaws in our thinking and the errors in our decision making. There is something refreshing therefore in a new study by
Louis Lee and colleagues who have used the digit-placement puzzle
Sudoku to argue, contrary to many others, that untrained people are capable of pure deductive reasoning - this is the ability to arrive at a logical conclusion by following the implications of one or more premises.
In an initial experiment, ten Chinese Hong Kong university students who'd never played Sudoku before were presented with an easy, difficult and fiendish version of the puzzle. They were told the rules, but weren't given any advice on strategies to follow. As the participants filled in the missing digits, they were asked to explain how they'd identified their solutions.
The participants solved only two digits per puzzle, thus showing how hard the puzzle is for naive players. However, for the answers they did find, the students were able to explain their deductive reasoning. "...[T]he solution to the puzzle Sudoku yields an insight into human competence that is in stark contrast to many psychological theories," the researchers argued. "Reasoners readily acquire the ability to make deductions about abstract contents, which are far removed from the exigencies of daily life and from the environment of our evolutionary ancestors."
Further experiments by the researchers showed that the initial deductive reasoning strategies that players deploy can only get them so far. To solve difficult and fiendish puzzles, players have to deduce several possible missing digits at once, and use those possible digits to deduce the answers to other parts of the puzzle. Some of us give up before making this transition. But for those of us who move onto this more advanced stage, Lee's team said "this shift in strategy is analogous to shifting from proofs in the first-order predicate calculus to proofs in the first-order modal predicate calculus" - in other words, it's a pretty impressive display of logical prowess and further evidence of our ability to "make deductions about abstract matters remote from our mundane life".
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N.Y. Louis Lee, Geoffrey Goodwin, P. N. Johnson-Laird (2008). The psychological puzzle of Sudoku. Thinking & Reasoning, 14 (4), 342-364 DOI: 10.1080/13546780802236308
译文:
Sudoku难题表明我们有演绎推理的能力
当代有关心理学诸多研究集中关注我们思考中的缺陷和我们作出决定时的错误。Louis Lee 和同事使用了数字填空难题Sudoku进行辩论，最后提出一个耳目一新的观点。同其他许多人的观点相反，那些没有经过训练的人有能力进行纯粹的演绎推理——这是一种通过一个货多个前提推断得到逻辑结论的能力。
在最初的试验中，十名之前没有玩过Sudoku的中国香港大学学生将要面对一个简单、困难、极难版本的游戏。首先让他们了解游戏规则，但是没有提供他们可遵循的策略建议。当参与者在空白处填入数字时，他们还要解释确定这些数字的方法。
参与者只做出了每道难题的两个数字，由此可见，对于初次玩家来说，要做出这些题目是多么的困难。然而，根据他们找到的答案，这些学生可以对他们的演绎推理能力作出解释。研究人员争论“从Sudoku难题的答案中，我们可以洞察到人类这种能力，这同许多心理学家的理论完全相反。”“研究人员对抽象内容具备进行演绎的能力，这同日常生活的紧急事件和祖先进化的环境没有任何联系。”
研究人员进一步的试验显示：玩家应用的最初演绎推理策略可以帮助他们继续玩下去。为了解决困难和极难的问题，玩家不得不立即推断出若干空格上可能的数字，然后使用那些可能的数字来推断难题中其他部分的答案。我们中的有些人在作出这次过渡前就已经放弃了尝试。但是我们中的那些进入更高等级的玩家，Lee的团队说，“这次策略的转换同从一阶谓词演算证据到一阶情态谓词演算证据非常类似”——换句话说，这是一次令人印象深刻的展示：逻辑的力量和我们具备对“远离日常生活的抽象事物进行演绎”的能力。
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N.Y. Louis Lee, Geoffrey Goodwin, P. N. Johnson-Laird (2008). Sudoku心理难题。思考&推理，14 (4), 342-364 DOI: 10.1080/13546780802236308