Here are some of the reasons why this adage is false:
By stating that you cannot prove a negative, you are making a negative statement that, if true, contradicts your statement. In other words, it's self-refuting.
If you cannot prove the statement, it's an arbitrary statement that has no basis and is not useful in any logical sense (i.e., it's nonsense).
There are many examples where this is not true. You can prove that 1 does not equal 0. You can prove that 2 is not greater than 3. You can prove that an equilateral triangle doesn't have any right angles. You can prove you don't have a million dollars in your pocket right now. You can prove that a flipped coin that lands on heads is not tails. You can prove that there isn't a rainbow-colored, fire-breathing unicorn sitting on your shoulder. You can prove you are not reading this article while having sex on the moon. You can prove you are not dead.
To have identity is, by definition, to have a single/the same identity. Therefore, if you can't prove a negative, you also can't prove a positive. (Or, another way to say it: every claim of positive knowledge is a claim that disproves all alternatives.) This is also referred to as the Aristotle's Law of Identity (aka A is A). For example, to prove that 1 = 1 is to disprove that 1 = 0.
Related to the law of identity and another one of the three classic laws of thought, the law of non-contradiction states that "contradictory propositions are not true simultaneously." Reality conforms to the law of non-contradiction (i.e., you can't have a certain attribute and not have the same attribute at the same time). Yet the law of non-contradiction is a negative statement and relies on negation. (There are controversial theories in quantum mechanics such as the Copenhagen interpretation which imply reality violates the law of non-contradiction, but they currently remain inconclusive and people can't seem to even precisely agree on "any concise statement which defines the full Copenhagen interpretation.")
You can't reasonably test every proposition. For example, to test the proposition that there aren't any such things as rainbow-colored unicorns, you would have to check every part of the universe at the same time. The best we can do is infer using inductive reasoning to make generalizations from what we do and can know.
Science is all about proving negatives, which can be done in as few as one experiment.
People make negative statements when they are unable to provide evidence of their beliefs (e.g., "can you prove that God doesn't exist?"). So, instead of retorting that you can't prove a negative, focus on the lack of evidence to test the proposition. Focus on the reasonability of doubt. The inability to invalidate a proposition does not make it true. That's the key.
James Randi Lecture @ Caltech - Cant Prove a Negative
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Original posting by Braincrave Second Life staff on Sep 27, 2011 at http://www.braincrave.com/viewblog.php?id=652
]]>Consider that x = 1 and y = 1. Therefore, we can properly say that x = y.
If x = y, then it must be true that multiplying both sides of the equation by x is also true. In other words, x * x = x * y or, more simply, x² = xy.
Continuing, when you subtract y² from both sides of the equation, the equation is still correct. In other words, x² - y² = xy - y².
Another way to write the equation x² - y² = xy - y² is through factoring: (x - y)(x y) = y(x - y).
To simplify the factored equation (x - y)(x y) = y(x - y), you can cross out/cancel the (x - y) on both sides of the equation, leaving you with (x y) = y.
As x = 1 and y = 1, when you substitute the values into the equation (x y) = y, you are left with the conclusion that (1 1) = 1 or, more simply, 2 = 1.
Relativists of the world unite! There are no absolutes!
Or... you can find which premise is wrong that yields the apparent contradiction here. Ergo, even if relativism still rules in people's minds, absolutism still rules nature.
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Original posting by Braincrave Second Life staff on Mar 1, 2011 at http://www.braincrave.com/viewblog.php?id=488
]]>FTA:
The history of chess goes back at least 1,400 years, where the game originated in India and Persia.
Chess hasn't changed much over the years. In fact, the last rule change was about 500 years ago.
It is believed that chess began as a way to get the royal children to think analytically and strategically.
The United States Chess Federation is 63 years old and boasts more than 90,000 members.
About 3 million chess sets are sold every year in the United States.
Yasser Seirawan, a top-ranked U.S. chess grandmaster is a Garfield High School graduate and co-founder of America's Foundation for Chess. He has also authored 13 books on chess.
At 2838 on the world-ranking list, Garry Kasparov is the highest-rated player in the world. The average tournament player is around 1750.
There are 169,518,829,100,544,000,000,000,000,000 ways to play the first ten moves in chess.
The word 'Checkmate' in comes from the Persian phrase 'Shah mat,' which means 'the king is dead.'
The first American chess tournament was held in New York in 1843.
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Original posting by Braincrave Second Life staff on Jan 18, 2011 at http://www.braincrave.com/viewblog.php?id=438
]]>FTV: "When people fill their mind with 4 hours a day of, for example Two and a Half Men, no disrespect, it shapes the neural pathways in such a way that they expect simple problems... You expect sitcom-sized problems that wrap up in 22 minutes, 3 commercial breaks, and a laugh track... No problem worth solving is that simple... What problem have you solved, ever, that was worth solving where you knew all of the given information in advance, or you didn't have a surplus of information and you had to filter it out, or you didn't have insufficient information and had to go find some? I'm sure we all agree that no problem worth solving is like that." Many of us will retire in a world that our children will run. If we do bad things to them now regarding teaching them how to think and giving them "paint-by-numbers classwork," we are going to get it back three-fold and destroy our own future and well-being.
TED - Dan Meyer: Math class needs a makeover: http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html (11.5-minute video)
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Original posting by Braincrave Second Life staff on May 15, 2010 at http://www.braincrave.com/viewblog.php?id=200
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