One of the thorny areas of logic which, to the best of my knowledge, is completely undeveloped is the concept of causation. Due to fairly recent advances in predicate logic, we now have a wide range of logical forms for expressing many concepts, as well as tools for logical manipulations, proofs, and so on. But thus far, there isn't any clear way to work with causation, and there's a pretty clear logical reason for that: causation doesn't exist.

That's a pretty extreme claim which demands proof, and I will do my best to lay out a convincing argument. Ultimately, causation is the same as morality or aesthetics. Ask someone if they know what causation is and they say yes, but ask them to define it and they falter.

Let's consider an example of this so-called causation. I push on a glass of water and the glass is knocked over. Common sense dictates that my pushing on the glass caused the glass to be knocked over. I yawn as I push on the glass. Does my yawn cause the glass to be knocked over? Does my yawn cause me to push on the glass? I yawn and push on the glass. My yawn causes me to push my hand forward, and pushing my hand forward causes the glass to be knocked over. My yawn causes the glass to be knocked over (common sense is quite handy here).

I have a light breakfast in the morning. Does having a light breakfast cause me to yawn? Does having a light breakfast cause the glass to be knocked over? Following this to its conclusion, we find that the Big Bang caused the glass of water to be knocked over. So everything that happens before the glass of water was knocked over caused the glass to be knocked over.

But there really isn't any reason to limit ourselves to events before the glass was knocked over. Time flows just as well backward as forward; the laws of physics that govern the behavior of everything in this universe work perfectly in either direction. We examine our universe with all of the physical laws reversed, and we can deduce similarly that everything after the glass of water was knocked over caused the glass to be knocked over. We can then repeat this for every event that ever happened and conclude that every event each causes every other event, at which point causation because rather meaningless as a concept.

Going further, there really isn't any reason for us to treat time specially; we can just reduce time to another dimension and represent the entire timeline of our universe as a single collection of 4-dimensional objects, at which point causation utterly disappears. The universe becomes analogous to a book, where everything that happens in the book's story simply exists. We can read parts of it in sequence, just as we experience all of the states of reality in sequence, and perceive the illusions of the passage of time and causality, but my pushing on the glass causes the glass to tip over just as much as the words "Bob let go of the ball" on the paper causes the existence of the words "The ball hit the floor" somewhere else on the paper.

Logical implication ("if A then B") is sometimes mistaken for causation, simply because causation is the mistaken form of logical implication. "If Bob is a human, then Bob is an animal", but clearly Bob being a human doesn't cause Bob to be an animal, it is merely a rule that describes the world. Likewise, "if I push on this glass then the glass is knocked over", and my pushing on the glass does not cause the glass to be knocked over, merely that the laws of physics dictate that one follows from the other. Causation doesn't exist. Thus, it follows logically that there is no way to express causation in formal logic.

Put another way, causation is a concept humans evolved to help make sense of logical implication in temporal sequence to better survive and reproduce.

So, causation is still a useful tool, just like morality, and if fatalism seems like a horrible idea, well, don't sweat the small stuff.