 Do you ever chuckle at people who see the face of Jesus on their toast? They find confirmation of their faith everywhere. It's a knot on their wooden table. A message in the clouds or a face at the bottom of their teacup. Rather than disparage them, I think we should try to understand their error. It's a simple methodological mistake. They actively seek out signs, and therefore they find them everywhere. This methodological error is not unique, I see it all the time, mostly from irrationalists who argue that contradictions exist. They seek out paradoxes and think that they find them everywhere. In fact, many irrationalists equate enlightenment with coming-to-terms with contradictions. The world is filled with so many contradictions, they say, that you have to be simple-minded not to see them. If you're familiar with my work, you know I'm not sympathetic to irrationalism. The most common arguments come from appeals to quantum physics or the Liar's paradox, but I've also frequently run into one argument that I've never seen properly addressed or labeled, so I've given it a proper name. The Bitter-Sweet Paradox. The Bitter-Sweet Paradox is yet another attempt to argue that contradictions exist. It goes like this. We experience paradoxes and contradictions all the time. Take the simple feelings of happiness and sadness. They are contradictory emotions. Happiness is the opposite of sadness, and sadness is the opposite of happiness. Yet we often feel happy and sad at the same time. The opposites are unified into a paradox that we experience. For example, say that your mother just died after battling cancer for a year. She was in agony day and night, but not anymore. What do you feel? Well, on the one hand, you feel awful because your mother died, but on the other hand, you feel happy because at least she isn't suffering anymore. So you feel happy-sad. This phenomena, the argument goes, is just as contradictory as seeing the color black-white or Schrodinger's cat being dead and alive at the same time. But since we clearly experience the state of happy-sad, paradoxes must exist. Put into a more abstract form, the argument goes like this. P and Q are opposites. Opposites are mutually exclusive. In Situation X, P and Q are both true at the same time. Therefore, contradictions exist. Now, there are a couple of errors nestled into this argument, both having to do with imprecise language. Specifically, we have to be clear what we mean by opposite versus mutually exclusive. The bittersweet paradox confuses the appearance of mutual exclusivity with actual mutual exclusivity. Strictly speaking, mutual exclusivity is a logical relationship between two things. It means there is no logical way that X and Y can be true at the same time. Consider the difference between these two examples. The first. I am happy right now. I am sad right now. I am happy and sad right now. Versus the second. I have two legs right now. I have no legs right now. I have two legs and no legs right now. Now, in the first example, the conclusion is possible. I can be happy and sad right now, as explained earlier. Happy and sad are only colloquially seen as opposites. There's nothing logically incompatible about them being unified together. But in the second example, the conclusion is not possible. I cannot have two legs and no legs at the same time. That's an actual contradiction. Having two legs is logically incompatible with having no legs. So this is precisely the error when people bring up the bittersweet paradox. They simply highlight what appear to be mutually exclusive phenomena, feeling happy and sad or cold and hot or tasting bitter and sweet at the same time. Now, we don't usually feel cold and hot at the same time, but that doesn't necessarily mean it's mutually exclusive. There is such a thing as having a cold sweat. It's kind of like entering a competition and getting in first place and last place at the same time. Have you experienced a paradox? Of course not. You could be the only one in the tournament. It doesn't happen very often, but it's not a logical contradiction. Consider one more example before moving on. 500 years ago, it would have seemed an absolute impossibility to say the following. I will be in Berlin on Sunday, and I will be in New York City on Sunday. It sounds contradictory, but with modern technology, there's no paradox or impossibility there. Anybody can fly from New York to Berlin in a day. This is why we need to be extremely careful in identifying actually mutually exclusive relationships. What might appear impossible could be commonplace in a few centuries. To avoid all possible confusion, we must dive deep into the weeds. Irrationalists flourish around murky language, whether they intend to or not, and we must join them in order to understand their errors. So we've established that the sentence I am happy and sad at the same time is not a contradiction. But watch what happens if we fiddle around a bit. Instead of using the term sad, let's call it not happy. Then, we can substitute one term for another and we're left with this sentence. I am happy and not happy at the same time. Ooh, now that sounds like a contradiction. If sadness is another term for not happiness, then how do you get around that paradox? You can imagine in a very real way that somebody could say I am happy and not happy at the same time without contradicting themselves. First, and perhaps most obviously, the terms sad and not happy aren't identical. Not happy is a negation. It's not something positive that you can be, which brings up the second error, an imprecise application of negation. In everyday language, putting a not before something turns it into a negation. If you want to be precise, this won't do because sometimes it leads to ambiguity. So for any statement X, an improper negation is to say not X. Usually it works, but for strict, careful philosophy, it doesn't. A proper negation is to say it is not the case that X. So a logical contradiction is not X and not X. Instead, to be perfectly precise, it is X and it is not the case that X. Now that might seem pedantic, but it's very important. So consider our happy and sad example. The sentence I am happy and I am not happy could possibly not be a contradiction if we're being vague. It's unclear what we mean by not happy, but the sentence I am happy and it is not the case that I am happy is indeed a logical contradiction. The first half of the proposition is properly negated by the second half, which means by necessity that if the first half is true, the second half is false. Consider another example to illustrate the importance of precise language. Say that you're standing halfway inside a doorway. Saying that half of me is inside the doorway is true. And saying that half of me is not inside the doorway is also true. Therefore saying half of me is inside and half of me is not inside the doorway is true. And you could see how some insistent irrationalist would try to turn this into a paradox. But proper, careful negation clears everything up. An actual contradiction would be half of me is inside the doorway and it is not the case that half of me is inside the doorway. If so the first part of the sentence is true then by logical necessity the second part must be false. If it's the case that half of you is inside the doorway then it is the case that half of you is inside the doorway. There's no ambiguity present. Now this might seem like elementary logic but it's applicable to every field of thought. Consider the ever popular argument for paradoxes from quantum physics. As I've gone into some detail about people loudly and inaccurately proclaim that quantum physics destroys classical logic. And it's actually rather easy to see why this is false. So according to standard theories in physics particles and waves are mutually exclusive. Yet in the famous double slit experiment light seems to exhibit properties of both waves and particles at the same time and in really weird ways. So weird that people have concluded wow reality itself is paradoxical and we have proof. Now unfortunately for the irrationalists this line of reasoning is flawed at a very basic level. Applying the simple principles that I just discussed resolves any apparent paradoxes. First of all to the extent that any two things are experienced or observed existing together it is a demonstration that they are not mutually exclusive obviously. So what needs to change is the theory that claims they're mutually exclusive. No different than the theories which insist that it is impossible to be in New York and Berlin on the same day. If people 500 years ago observed modern living they wouldn't conclude oh my gosh people can be in Berlin and New York at the same day reality is paradoxical. No they would think oh I guess my theory about what was mutually exclusive was wrong. And the same is true with quantum physics. If we've observed some phenomena which contradicts our theories our theories are wrong and you aren't witnessing a true contradiction. Perhaps waves and particles aren't mutually exclusive. They might be two parts of the same coin a waveical let's say. So carefully analyzing our concepts reveals a certain truth. Whether X and Y exist at the same time is never a question of whether two mutually exclusive things can be together. It's whether these two things are mutually exclusive. If two things are found together then they aren't mutually exclusive by definition and it isn't some hypothesis that's up for revision. To think otherwise is nonsensical and it's the central error in the bittersweet paradox. And you can help support the creation of a more rational world view. To read this article or to learn about my books check out steve-patterson.com