St. Thomas Aquinas wrote in the Second Article to his thirteenth-century Summa Theologica that "the first indemonstrable principle is that one cannot at the same time affirm and deny the same thing." Appealing to Aristotle's Metaphysics, he says that "this principle is based on the nature of being and nonbeing, and all other principles are based on it." He quickly concludes that "the first precept of the natural law is that we should do and seek good, and shun evil."
Appealing to a law of non-contradiction is a standard trope in Western philosophy that forms the cornerstone of many logical arguments. But is this principle really inflexible? How do you know what you think you know about it?
Qualities such as heat and cold, wetness and dryness, etc., are opposites, but you never see them at their "pure" extremes. Instead, whenever they describe something in nature, they appear somewhere along a spectrum. To say that something is partly wet is also to say that it is partly dry. This looks like a potential case of affirming and denying the same thing. Indeed, it seems that there is some inevitable contradiction in any assessment you might make about the qualities of a thing, since your words are only rough approximations of the world they describe and nothing is ever a pure example of the categories you attach to it. You try to be mostly right, but you are always a little bit wrong. You could speak for hours or write hundreds of pages and never get at the full, exact meaning of what you are trying to convey.
Furthermore, when such observations are made, they typically involve an observer whose subjective appraisal taints the "fact of the matter." For you to say that something is hot is to imply that it is warmer than you might normally expect and also to suggest that you attach a value judgment to it: a pleasingly hot dinner, perhaps, or a scaldingly hot one. Otherwise, if there were nothing interesting to report, why would you be speaking about its temperature? So when you affirm or deny something about your dinner, you're also affirming or denying something about yourself and what you find noteworthy.
This sort of psychological reading of even the simplest factual assertions introduces a new level of complexity. The hard material world may not seem to admit contradictions, but the soft abstractions of humanity certainly do. Happiness and sadness are opposites, yet you can be happy and sad at the same time. You may affirm and deny your happiness simultaneously because you do not know yourself well, because you know yourself too well, or because you wish to influence what others believe about your mental status regardless of whether you are convinced it is true.
As another example, if you ask someone whether they like chocolate, they might reasonably assume you are offering them a small dessert following a meal. In that case, they probably do like chocolate. But they would not like to be forced to eat three pounds of chocolate in the middle of the night. So there are different senses in which they do and do not like chocolate. It's that crucial interpretation that makes your sentence appear (mostly) true or (mostly) false.
Thomas Aquinas wants to apply the "first indemonstrable principle" to the ethical realm. To get started here, you would have to agree that good and evil are opposites; that to be one is not to be the other. This is not as straightforward as one might suppose, since it is not obvious whether evil is merely the absence of good or whether evil is some positive trait in itself that somehow opposes or frustrates good. Good and evil might be on a spectrum just as wet and dry are. After all, anyone giving an honest assessment of themself would have to admit they are neither wholly good nor wholly evil.
This brings you to the psychological angle which cannot be removed from questions of good and evil. If you meet two beggars and only have one coin, how do you choose which one to feed, or whether to feed yourself instead? To choose one person leaves another in the lurch. There is no option uncontaminated by complexity and the possibility of competing ethical valuations. You cannot choose good in one area without choosing the absence of good in another area. And whether you've chosen good at all is arguably a matter of opinion. The beggar who receives the coin will affirm that you've chosen good, while the one who goes hungry will deny that you've done so. How should you evaluate yourself? Why should it be impossible that both beggars' assessments of you are true? Why must you affirm one and deny the other?
There is another problem with Western philosophy's fixation on the supposed law of non-contradiction. It is that arguments tend to reduce to only two sides. In the nineteenth century, Harriet Beecher Stowe, reflecting on Protestant-Catholic disputes about the proper reverence of the Virgin Mary, wrote in her essay "The Blessed Woman": "Truth has always had the fate of the shuttlecock between the conflicting battledoors of controversy." By this she implied that neither the typical Protestant nor Catholic argument captured what she saw as the real truth about Mary. In other words, the problem is that, when you frame your idea of what the argument is or should be, you tend to close off your imagination to solutions that lie outside the bounds of the argument you've just constructed.
Of course, there may be multiple religious opinions about all sorts of subjects, and many of these beliefs are compatible with each other. If one reduces these opinions to a simplistic debate about whether it is, or is not, proper to make a statue of the Virgin Mary, then one has framed the debate in a way that seems to force everyone to take sides - even those who are not Christian and should have no recommendation about the worship of Mary at all!
One would seem foolish, hypocritical, and untrustworthy if one went around publicly affirming and denying the very same statement. In this way, what Thomas Aquinas calls the "first indemonstrable principle" is somewhat of a social norm governing clear, reliable communication. Non-contradiction helps to manage useful pieces of information and creates boundaries in which people can respect each other. But it is not necessarily descriptive of the way things "actually are."
Fortunately, for many questions you are not called upon to affirm or deny anything at all. Most subjects to most people are irrelevant or beyond their ken. When you are asked to make a choice about some obscure or abstract question, you should be suspicious not just about which of two options is more correct, but about what motivates someone to ask someone to "pick sides" in the first place.
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