计算机问题求解一论题1-2一什么样的推理是正确的？
计算机问题求解– 论题1-2 - 什么样的推理是正确的?
Part I推理过程
Part I 推理过程
One important purpose of mathematical logic is to makeprecise the notion of a proof.Just what is meant by the word proof'? One personsuggested to me that a proof is simply an argument thatconvinces somebody. Not bad, but the trouble is thatdifferent people are convinced by different arguments, sothe concept of proofin that sense is quite subjectiveCan't one, then, find a more objective definition of theword proof'? Well, so far no such definition has beenfound for the general notion of proof, but symbolic logichas done an admirable job in making absolutely precise thenotion of proof'for given axiom systems!-RaymondSmullyan
One important purpose of mathematical logic is to make precise the notion of a proof. Just what is meant by the word “proof”? One person suggested to me that a proof is simply an argument that convinces somebody. Not bad, but the trouble is that different people are convinced by different arguments, so the concept of proof in that sense is quite subjective. Can’t one, then, find a more objective definition of the word “proof”? Well, so far no such definition has been found for the general notion of proof, but symbolic logic has done an admirable job in making absolutely precise the notion of “proof” for given axiom systems! - Raymond Smullyan
一个奇怪小岛上的逻辑问题Edgar Abercrombie was an anthropologist who was particularly interestedin the logic and sociology oflying and truth-telling. One day he decided tovisit the Island of Knights and Knaves, in which those called knightsalways tell the truth and knaves always lie. Furthermore, each inhabitant iseither a knight or a knave推理问题1：On the day of his arrival, Abercrombie came across three inhabitants,whom we will call A, B and CHe asked A: “Are you a knight or a knave?" A answered, but soindistinctly that Abercrombie could not understand what he said. Hethen asked B: What did he say?"B replied:He said that he is aknave." At this point, C piped up and said: “Don't believe that; it's alie!"Was C a knight or a knave?
一个奇怪小岛上的逻辑问题 Edgar Abercrombie was an anthropologist who was particularly interested in the logic and sociology of lying and truth-telling. One day he decided to visit the Island of Knights and Knaves，in which those called knights always tell the truth and knaves always lie. Furthermore, each inhabitant is either a knight or a knave. 推理问题1： On the day of his arrival, Abercrombie came across three inhabitants, whom we will call A, B and C. He asked A: “Are you a knight or a knave?” A answered, but so indistinctly that Abercrombie could not understand what he said. He then asked B: “What did he say?” B replied: “He said that he is a knave.” At this point, C piped up and said: “Don’t believe that; it’s a lie!” Was C a knight or a knave?
一个很可能的思考过程假设1.A或者是骑士（只说真话），或者是无赖（只说假话）二者必居其一。2.假如A是骑士，他不可能说自己是无赖，因为那不是事实。穷举3.假如A是无赖，也同样不可能说自己是无赖，因为那是真话。反证4.所以，A说的话不可能是“我是无赖”。5．因此，B说的不是事实，他必然是无赖。6.因此，C说的是事实。A可以是任何人，所以实7. 结论：C是骑士。际上到这里我们就知道这个岛上不会有任何人说自已是无赖
一个很可能的思考过程 1. A或者是骑士(只说真话)，或者是无赖(只说假话)， 二者必居其一。 2. 假如A是骑士，他不可能说自己是无赖，因为那不 是事实。 3. 假如A是无赖，也同样不可能说自己是无赖，因为 那是真话。 4. 所以，A说的话不可能是“我是无赖”。 5. 因此，B说的不是事实，他必然是无赖。 6. 因此，C说的是事实。 7. 结论：C是骑士。 A可以是任何人，所以实 际上到这里我们就知道这 个岛上不会有任何人说自 己是无赖。 穷举 反证 假设