Logic0921 - Propositional logic 1. 2. 3. Symbolic method...

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Symbolic method The strength of modern logic con- sists mainly in the use of symbols (modeled upon math). Ex. A puzzle attributed to Euclid A mule and a donkey were talking. The mule said, “I’m carrying more than you. In fact, if you gave me one of your sacks, then I would have twice as many as you. If I gave you a sack, our loads would be equal.” How many sacks was each an- imal carrying?
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The puzzle reduces to solving linear equations with two variables: M+1=2(D-1), M-1=D+1 (1-line solution) But how could Euclid solve the puzzle without using any algebraic symbols? One possible scenario would be to give the following informal (non-symbolic) reason- ing. P Giving one sack makes two-sacks difference. Therefore, Donkey’s giving one and instead Mule’s giving one make the total difference of 4 sacks. That would be the difference
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Or try a geometric solution. P AB = total loads in sacks P The right part is carried by Mule (originally BF); the left part by Donkey (AF). P If Donkey gave one sack to Mule, F -> D and AD = DE = EB. P
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This note was uploaded on 02/04/2010 for the course HSS Hss105 taught by Professor Yeelee during the Fall '09 term at Korea Advanced Institute of Science and Technology.

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Logic0921 - Propositional logic 1. 2. 3. Symbolic method...

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