The key here is that Laplace's Demon doesn't know what an "otherwise" is. The Demon has no notion of possibility, no notion of an ability (something that "can" happen or that we "can" do). The Demon always knows what will happen and what we will do. If we want to know what will happen we can ask the Demon. But if we ask the Demon, "What can happen?", the Demon will not know what we are talking about. The Demon, being omniscient, has never had any reason to evolve the notion of a "possibility".

It is only because we are not omniscient, like Laplace's Demon, that we have evolved the notion of possibilities. The notion of possibility has these qualities:

1. A possibility exists solely within the imagination. We cannot drive a car across the possibility of a bridge. We can only drive across an actual bridge.
2. A possibility is an essential token for certain logical operations, such as planning, inventing, creating, and choosing. Without this token these operations become impossible. For example: We cannot build an actual bridge without first imagining a possible bridge.
3. Most possibilities will never happen. We may expect one possibility to happen, but we never expect them all to happen.
4. As soon as any possibility is realized, we cease calling it a "possibility" and immediately begin calling it an "actuality". A possibility is the opposite of an actuality.
5. There is a separate language and logic used when speaking in the context of possibilities versus the context of actualities. We smoothly switch from one context to the other when triggered by certain words. For example, when speaking of what "can" happen we are in the context of possibilities, but when speaking of what "is" or "will" happen, we are in the context of actualities.
6. When we know for certain what will happen, we do not use the word "can" or "possible" or "able" and other similar words. It is only when we do not know for certain what "will" happen that we switch to the context of possibilities and use words like "can" or "ability" or "could".

The choosing operation, like addition or subtraction, requires at least two inputs before it can begin. The inputs are called "options" and are logically assumed to be possible to choose. If we believe that we cannot choose an option or that we cannot carry out an option, then it is excluded for not being a "real" possibility. But any option that is choosable and realizable is considered a real possibility. There must, by logical necessity, be at least two real options before choosing can begin.

We must conclude from this that there will always be two inevitable outputs from every choosing operation: (1) The single option that we "will" choose and (2) at least one other option that we "could have" chosen but would not choose.

Thus, "could have done otherwise" will always be true, even though "would have done otherwise" will always be false.

Whenever we discuss what we "could have done", we are switching from the context of actualities to the context of possibilities, which leaves the real world behind and enters the imagination, where all possibilities exist. We are no longer speaking of what we "did" choose to do, but instead we are returning to that point in the past, where we had two or more things that we "could" choose to do. We may even be introducing to this imaginary scenario new possibilities which did not occur to us at the time. The point of this exercise is to evaluate our prior choices in order to make better choices in the future.