Logic in English
I thought I would write this up because of the frequency I see this stuff written wrongly. This time, I'll be focusing primarily on negations since that is what I see the most trouble with.Just to introduce some notation, "A and B" is a true statement when [i]all[/i] statements linked by "and" are true. If [i]a[/i] statement linked by "and" is not true then "A and B" is not true. I'll admit, this definition may seem complicated. It is so because it is a precise definition. Now compare this to "A or B", which is a true statement when [i]a[/i] statement linked by "or" is true and not a true statement when [i]all[/i] statements linked by "or" are not true. Take a moment to pause here and note how analogous "and" and "or" are and think about what a negation would do to them.(XZ(x P6G G#J)?
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I'll throw out some example sentences here: "I have shoes and an umbrella.", "Do you like red or blue?"/z)vM n_N
Their logical negations would then be: "I do not have shoes or an umbrella.", "Do you dislike red and blue?"
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Note the "and" changes to "or" and vice-versa. If, for example, you write "I do not have shoes and an umbrella." it would mean "I may have shoes or I may have an umbrella but I do not have both shoes and an umbrella." Likewise, "Do you dislike red or blue?" would be answered with affirmation if you don't like red, affirmation if you don't like blue and denial if you like both red and blue.
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To write them in prepositional logic, for those who are fine with it, if A is the preposition "I have shoes" and B "I have an umbrella", then the first sentence is taken to be of the form "A and B" and its negative is taken to be of the form "(not A) or (not B)". The second sentence works analogously.
The point of this, if you want to write a negative sentence where you would join a list of things with "and" in its positive form, join them with "or" in the negative form. If you want to write a negative sentence where you would join a list of things with "or" in its positive form, join them with "and" in the negative form.B(a s F ~ CI
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Now, there is still the negation of words like "everything", "something", "anything" and "nothing" to deal with. First, I'll give examples to clarify their meanings:o*GM}l _5Y%M(p5a W
"I know everything.": "All things are known by me."@0| `c9I
"I know something.": "There is a thing known by me."c_d9t~
"I know anything.": "All things are known by me."
"I know nothing." "There is not a thing known by me."[*SiM7p _
"I don't know everything.": "There is an unspecified thing that I do not know."
"I don't know something.": "There is a specific thing that I do not know."TF(M5tm(GE
"I don't know anything.": "All things are things that I do not know."*Cui*C"[!o N-m&]2]1R
"I don't know nothing.": This one's ambiguous. It uses a double negative, which logically cancels out, but is used for emphasis by the uneducated. So, it could mean "I know something" or "I know nothing" depending on who sees it.
Those examples may not be enough, so I'll explain a bit more: "everything" is universal in that it refers to all things as a whole, and "nothing" is universal in that it refers to all things but in a negative construct. "Something" is existential in that it refers to a thing, which may or may not be specific. "Anything" is completely non-specific. It can be used both as a universal term and an existential term. For instance, "I know anything" is universal, where "Give me anything" is existential. The exact difference is a bit hard to describe. I'll have to think about it more.
Now go back and look at the definitions of "and" and "or". I italicized "all" and "a" for a reason. "All" is universal, and "a" is existential. The negation of universal and exisistential works exactly like the negation of "and" and "or". With these words, there is not always a clear opposite, so it's best to look at what you are refering to, i.e. something universal or existential, negating that, then picking the word which matches that meaning closest.
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I'll break here to see if anyone actually followed this or if it is at all useful. I'm sure I could come up with more of this stuff if it's helpful. Great info. Thanks for sharing with us. useful,thanks I read this many times and finally go through.J X9]2hE5KZy:F0{q
Thanks a lot, it is very useful for me, especialy for those attorney letters or legle terms I'm reading these days. [quote]�­帖由 [i]maebus[/i] 于 2007-2-3 15:30 发表
"I don't know nothing.": This one's ambiguous. It uses a double negative, which logically cancels out, but is used for emphasis by the uneducated. So, it could mean "I know something" or "I know nothing" depending on who sees it.2s,@~f/}
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Thank you. This has bothered me a long time. very instructive article!
回复 #4 anohi 的帖子
Good luck reading legalese. Be warned that "or" has a different meaning in legalese; in regular English "A or B" is inclusive of the "A and B" case (i.e. if both A and B are true then "A or B" is true) but is often used to suggest either A or B (i.e. both A and B are not expected to be true). Legalese uses the exclusive definition: "A or B" is not true when both A and B are true. They denote the inclusive or by "and/or".5q0x/@5lB] Yu9uThere's mathematical notation to describe all of these ands and ors unambiguously but I think it would be even more confusing to introduce it... Hopefully that description of "or" in legal context is clear. Thanks! Interesting::z1
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