Same or different?
09Aug06
I found this while surfing the net the other day. Are the two sentences below the same or different? Explain
- Everybody is innocent until proven guilty
- Nobody is guilty until proven to be not innocent.
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Filed under: Uncategorized | 5 Comments
(First I need to clarify the terms and my assumptions about them)1. "everybody" = the set of all persons.2. "is" = possesses the attribute of at the present time 3. "innocent" = not responsible for a particular crime 4. "until" = if not 5. "proven" = declared by a court of law 6. "guilty" = responsible for a particular crime 7. "nobody" means that the associated condition will not be true about any person.I will now rewrite the two statements:A) The set of all people are not responsible for a particular crime if not declared by a court of law to be responsible for a particular crime.B) It is true for no person that the person is responsible for a particular crime if not declared by a court of law to be not not responsible for a particular crime.Some semantics seem to be missing here:8. I assume that the implied crimes in the terms guilty and innocent are actually the same crime.9. In the context of these statements, I assume that guilt and innocence are not universal qualities but rather refer to a legal status– what people are considered by the government to be.10. I assume that "everybody" is a mistatement. I suspect that the author meant "anybody".Rewriting again (and simplifying to eliminate double negatives):A) It is true of any person that the person is considered by the government to be responsible for a particular crime only if declared by a court of law to be responsible for that crime.B) It is true for NO person that the person is considered by the government to be responsible for a particular crime if NOT declared by a court of law to be responsible for that crime.If the last double negative is eliminated from statement B, it becomes identical to statement A. The two statements are therefore identical.(However, I should point out that the original statement is a little off, at least in the United States. It should be that a person is presumed innocent until proven guilty, I think. This presumption is a statement about the burden of proof.)The fact that these statements appear to be logically identical does not necessarily mean that they must have the same truth value. This is because:1. Truth depends on context, and context may change, perhaps in the midst of the analysis.2. Truth is subjective, and two people may have different subjective interpretations of the two statements.
A more simple approach.Assumption: By definition of the words, innocence is the inverse of guilt. Therefore !guilty == innocent, and !innocent == guilty.Statement 1: innocent until proven guilty.Statement 2: !guilty until proven !innocent. >> innocent until proven guilty. Statement 1 == Statement 2. > QEDMatt Schulz
Here\’s an even simpler approach: "Trust me, they are the same." But sometimes simplicity isn\’t helpful.The point of the detailed analysis is to demonstrate skills of software testing, one of which is to identify and work with assumptions, another of which is to have awareness and control over the steps we take when we try to think logically. This is especially important when real people are talking to each other, because there are such layers of meaning in real speech.A professional logician would probably find much to nitpick about in my analysis, actually. I\’d like to see this problem in full symbolic logic form, with all assumptions and definitions analyzed to the maximum degree.– James
Thanks for this interesting question. While they are the same using formal logic pricipals, I don\’t think they are the same. My initial instinct is to think that it is a pretty big leap to assume that "Not Innocent" means the same as "Guilty". What about accomplices? They are not innocent, but they are also not guilty of the main crime in question. "Not Innocent" seems much less concrete than \’Guilty\’ which implies of a certain crime. It is possible in the second scenario that all people who aren\’t entirely innocent of all crime would be considered to be guilty.
I\’m now going back in your blog archive to see what other thought provoking treats your blog may hold.
(http://blog.testyredhead.com) That\’s a new blog inspired by the Cast 2007 tutorial that I saw you in, which is also why I\’m here checking out your blog.
Lanette – thanks for the comment. I haven\’t checked my blog in ages so I didn\’t know you had responded to a post.
I hope to give you more interesting and challenging puzzles over the next little while.
Did you start your blog right after CAST? Did we meet at CAST?