Guest post by Samantha Eliza Benten

The Law of Non-Contradiction, as stated by Aristotle: "One cannot say of something that it is and that it is not in the same respect and at the same time."

Often, this is expressed in the formula: A ? ¬A, where "¬A" signifies "not A" or "not having quality A". (To prevent a common error, understand that it does NOT mean "the subset of everything except A." For example, to say that "an animal that is a cat cannot be, at the same time, a dog" is NOT an application of the law of non-contradiction. To say that "an animal that is a cat cannot, at the same time, also be a 'not cat'" IS to apply the law of non-contradiction.)

Worded a bit more clearly: Nothing can both have the quality of A and lack the quality of A at the same time. Before I get into the significant consequences this law of logic will have on morality, I'd like to begin with numerous examples of it applied to everyday life.

Imagine your kitchen table. Got the image in your head? Alright, does it have any black paint on it? Your answer to this must naturally be either yes or no. It cannot both have black paint on it and not have black paint on it, at the same time. Whether or not it also has red paint or silver paint or a wood finish on it is irrelevant. And if you decide to paint it red immediately on arriving home tonight, that also makes no difference. All that matters, as far as the law of non-contradiction is concerned, is that your kitchen table cannot both possess and lack the quality of having black paint on it at any given moment.

This law also applies to certain subatomic behavior. An electron behaves in one of two ways: as a particle or as a wave. The way I understand it (though I'm no quantum physicist), when it is seen as a particle, it has all of characteristics of being a particle and none of being a wave. When it is seen as a wave, it has all of characteristics of being a wave and none of being a particle. However, it cannot both possess and lack the quality of being a particle at the same time. Same goes for its wave form.

Now, sometimes the law of non-contradiction is only as good as the quality of our definitions. For example, the traditional qualities of a mammal (warm-blooded vertebrate having hair-covered skin, bearing live young, and nursing offspring with milk) accurately describe the vast majority of animals categorized this way. But the duck-billed platypus mixes and matches qualities from other animal families (having a duck bill and laying eggs). Given that our definition embodies so many qualities, it's harder to assert that the platypus is absolutely either a mammal or not a mammal. That creature defies logical law in the face of our definition. Of course, its evolutionary relationship to other animals has placed it solidly within the mammals, despite its not exactly fitting in all respects.

The same goes for a person's sex. Yes, the traditional definition, based on genetics and on genitalia, works for the vast majority of people. However, there are exceptions. Some people are born with XXY or XXX chromosomes. Some people are born with genitalia of both genders (hermaphrodites). To frame the question as "Is this person male or female?" is to ignore the law of non-contradiction. To break it down into two questions ("Does this person have or lack male characteristics?" and "Does this person have or lack female characteristics?") is the law of non-contradiction properly applied.

Another example comes from politics. Being conservative on some issues (fiscal policy, national security, etc) in no way prevents someone from holding more liberal views on other issues (gay marriage, for example). The terms liberal and conservative embody a slew of ideas, and there is a continuum of attitudes toward them, from dictator-like conservatism to anarchic liberalism, and everything in between. To say that each individual person must be either a conservative or not a conservative (by the law of excluded middle) is ludicrous, and doesn't describe life as people live it. Such laws of logic only work when we get into the nitty gritty details of particular instances. For example, it would be easier to say whether or not a person actively supports a conservative decision made by a particular politician. (Of course, even in those instances, people often admit complexity and/or doubt about their beliefs, or simply don't care.)

Yet, do these failures of definition mean the law of non-contradiction is flawed? Not in the least. All that is necessary to reinstate the legitimacy of the law is to break things down into individual characteristics or a particular example. The platypus cannot both possess and lack the capacity to lay eggs at the same time (whether it is hairy, duck-billed, etc. as well is irrelevant). A human being cannot both possess and lack a penis at the same time (whether said person also has female genitalia or two X chromosomes, is irrelevant). A human being cannot both have and lack a conservative opinion about a particular ruling at the same time (whether they also understand that ruling from the liberal, or other, perspective as well, or have no opinion at all, is irrelevant).