Oh, but I did refute you! Let's see. You claimed that the law of cause and effect is not explained by logic. I then counter-argued that logic and cause and effect are synonimous, and thus, it makes no sense to argue that it doesen't explain itself, because logic is a "language" that properties arbitrarily use to describe a pattern of interaction between themselves in an organized system. What this means, essentially, is that logic is axiomatic to the system it describes, and thus, does not need to justify itself. Let me give you and example: mathematics. It is bot axiomatic and abstract, because it describes truths that are only true if you accept that the axioms are irrefutable. In other words, mathematics can only possibly exist if you accept that there are numbers. But what are numbers? A pre-determined concept that limits are set, that units exist, and that the interaction between units can give rise to groups of units, etc. So, saying that the law of cause and effect does not explain logic is a tautalogy, based on trying to explain the rules of a system with the rules of the system.
I said the law of cause and effect contradicts itself, which is true if we assume that everything that happens must have been caused by something. Therefore, either you are arguing in favor of something that is illogical or you are using a different definition of causality all-together. Here are my objections.
objection 1: some effects do not require a cause. Quantum mechanics tells us that particles at the sub-atomic level behave without causation. You claim something must be responsible. However, no evidence for sub-quantum forces has ever been found. The forces ARE the result of quantum particles (e.g. strong forces are caused by gluons, not vice versa).
objection 2a: if everything that happens must have a cause, then each cause must have an earlier cause and so on. This means the chain of causes of your future actions extend backwards to before you were born. In essence, your whole life is predetermined and free will doesn't exist. If you object that any of these causes is an isolated event, then you are implying an uncaused cause which violates the "law of cause and effect."
objection 2b: if everything that happens must have a cause, then each cause must have an earlier cause and so on. This chain of causes may be traced back to the first cause. A familiar paradox arises - what caused the first cause? According to the "law of cause and effect," every cause must be caused by something else. If we assume there is an uncaused cause, then its premise is violated and the whole argument fails.
objection 3: the "law of cause and effect" postulates that a specific cause always leads to a specific effect (i.e. there may be some attribute X which always leads to some attribute Y). However, we have never observed two instances of X which led to two instances of Y. Every X is different in some respect from every other X. Likewise, every Y is different from every other Y. If you object that we may infer the same outcome when each X is exactly the same, then you are creating a definition for cause and effect that cannot be falsified. Since all you would have to do whenever someone challenges you is propose additional 'unknown' causes, this is not really a valid argument. It would be like me claiming "the universe was created by a black hole. We just don't understand all the factors that were involved" no matter how many objections are raised. Although this argument can never be falsified, it doesn't necessarily follow that it's true.