# Aristotle's laws of thought - examples **URL:** \ **Category:** Factual Questions\ **Created:** [May 7, 2015, 6:17pm UTC](https://boards.straightdope.com/t/aristotles-laws-of-thought-examples/719502 "2015-05-07T18:17:47Z")\ **Posts on this page:** 7\ **Page:** 1
**Author:** ![blood63](https://avatars.discourse-cdn.com/v4/letter/b/97f17d/32.png) [@blood63](https://boards.straightdope.com/u/blood63)\ **Post date:** [May 7, 2015, 6:17pm UTC](https://boards.straightdope.com/t/aristotles-laws-of-thought-examples/719502/1 "2015-05-07T18:17:47Z")
I need some good examples to help distinguish between the law of noncontradiction and the law of the excluded middle. Can anyone help? ---
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [May 7, 2015, 6:35pm UTC](https://boards.straightdope.com/t/aristotles-laws-of-thought-examples/719502/2 "2015-05-07T18:35:56Z")
They complement each other. The law of noncontradiction says that something cannot be both x and ~x simultaneously. BUT is there something that is neither x or ~x? The law of the excluded middle says no, something is always either x or ~x. Let me give you an example that gives the two concept a workout. What is the opposite of red? Artist would say it’s green. Can something (monochromatic to make it easy) be red and green at the same time? No - but it is possible to be not red and not green athe the same time. Like for example yellow. So law of noncontradiction holds but the excluded middle doesn’t. Of course the logician says that the opposite of red is not red so blue, green yellow, brown, black, white, etc. all fall in that not-red arena. But where does that put [red-orange](https://www.google.com/search?sa=G&q=fluorescent+neon+orange&tbm=isch&tbs=simg:CAQSiAEahQELEKjU2AQaAggIDAsQsIynCBpeClwIAxIm_1wi0AihHzwHyAvgI_1giyArUCoCuIJ9cooSuzKusn5zboNqU0nTcaMBvwQhbcjDw37_1jMIhYB6ur59C1p1lL8SFPxIIAjnSj-Zc8eBV_1ZMDEsC6gqi1gdoAwLEI6u_1ggaCgoICAESBNGPP18M&ei=dbBLVbRtgvGgBObKgLAC&ved=0CBoQwg4oAA&biw=1366&bih=657)? ---
**Author:** ![blood63](https://avatars.discourse-cdn.com/v4/letter/b/97f17d/32.png) [@blood63](https://boards.straightdope.com/u/blood63)\ **Post date:** [May 8, 2015, 1:03am UTC](https://boards.straightdope.com/t/aristotles-laws-of-thought-examples/719502/3 "2015-05-08T01:03:09Z")
That really helps. Thanks. > [@Saint\_Cad](#): > > They complement each other. The law of neoncontradiction says that something cannot be both x and ~x simultaneously. BUT is there something that is neither x or ~x? The law of the excluded middle says no, something is always either x or ~x. > > Let me give you an example that gives the two concept a workout. What is the opposite of red? Artist would say it’s green. Can something (monochromatic to make it easy) be red and green at the same time? No - but it is possible to be not red and not green athe the same time. Like for example yellow. So law of noncontradiction holds but the excluded middle doesn’t. > > Of course the logician says that the opposite of red is not red so blue, green yellow, brown, black, white, etc. all fall in that not-red arena. But where does that put [red-orange](https://www.google.com/search?sa=G&q=fluorescent+neon+orange&tbm=isch&tbs=simg:CAQSiAEahQELEKjU2AQaAggIDAsQsIynCBpeClwIAxIm_1wi0AihHzwHyAvgI_1giyArUCoCuIJ9cooSuzKusn5zboNqU0nTcaMBvwQhbcjDw37_1jMIhYB6ur59C1p1lL8SFPxIIAjnSj-Zc8eBV_1ZMDEsC6gqi1gdoAwLEI6u_1ggaCgoICAESBNGPP18M&ei=dbBLVbRtgvGgBObKgLAC&ved=0CBoQwg4oAA&biw=1366&bih=657)? ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [May 8, 2015, 2:37am UTC](https://boards.straightdope.com/t/aristotles-laws-of-thought-examples/719502/4 "2015-05-08T02:37:21Z")
I can help you with your question and I can’t help you, but I am going to do neither. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [May 8, 2015, 1:45pm UTC](https://boards.straightdope.com/t/aristotles-laws-of-thought-examples/719502/5 "2015-05-08T13:45:42Z")
If visualizing helps you, imagine a bar divided into two different colored sections. //////////\\\\\ The law of non-contradiction says they can’t overlap: /////XXXXX\\\ The law of the excluded middle says there can’t be a gap between: //////////\_\_\_\_\_\\\\\ ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [May 8, 2015, 1:49pm UTC](https://boards.straightdope.com/t/aristotles-laws-of-thought-examples/719502/6 "2015-05-08T13:49:23Z")
Another example: If you flip a coin, it has to come up either heads or tails. If it’s heads, the law of non-contradiction tells you that it can’t be tails. It can’t be both heads and not-heads. If it isn’t heads, the law of the excluded middle tells you it must be tails. It has to be either heads or not-heads; there is no “middle” alternative. ---
**Author:** ![ftg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ftg/32/2801_2.png) [@ftg](https://boards.straightdope.com/u/ftg)\ **Post date:** [May 8, 2015, 1:59pm UTC](https://boards.straightdope.com/t/aristotles-laws-of-thought-examples/719502/7 "2015-05-08T13:59:33Z")
Take two classics statements: “This statement is false.” “This statement is true.” The first is neither true nor false. The second is both true and false. In some sense. Ideally, we want a formal logic to be unable to express either of them. (But if your formal logic is powerful enough to express significant things, you can’t avoid the [problem](http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems) entirely.)