I agree with your example and think that it touches on something important. However, in this post, I did not claim that the counterfactual condition was the only condition required for information transfer. You are correct to say that the lamp signal would not constitute information to someone who was unaware of the plan. But this is because, in that situation, there are other conditions that have not been met. Since the other person seeing the lamp signal would not react differently to the different signals, there is no causal link between the signal and them. This is also required for information transfer. I tried to explain this idea a bit more in my subsequent post [LW · GW]. 

If you don't like the idea of information being physical, rather than epistemological, then maybe you can think of this post as asking the question 'what are the physical conditions that a system must satisfy in order to transmit epistemological information?'

Hi, thanks for your question. I have a big piece covering all of this in more detail which I plan to post in a couple of days once I've finished writing it. In the meantime, please accept this 'teaser' of a few problems in the prevailing conception (PC):

1. Dealing with hybrid systems. If we are operating in a regime where there are two contradictory sets of dynamical laws, we do not know what kind of evolution the system will follow. An example of such a system is one where both gravity (as governed by general relativity) and quantum mechanics are relevant. In such a cases, under the PC, it is difficult to make any predictions of what kind of behaviour systems will exhibit, since we lack the dynamical laws governing the system. However, by appealing to general counterfactual principles (the interoperability principle and the principle of locality), which cannot be stated in the PC, we can make predictions about such systems, even if we don't know the form of the dynamical laws.
2. The 2nd Law of Thermodynamics. Under the PC, the 2nd is difficult to express precisely, since all dynamical laws are reversible in time, but the 2nd law implies irreversible dynamics. This is normally dealt with by introducing some degree of imprecision or anthropocentrism (eg. through averaging or coarse graining, or describing the 2nd law in terms of our state of knowledge of the system). However, the 2nd law can be stated precisely as a counterfactual statement along the lines of 'it is impossible to engineer a cyclic process which converts heat entirely into work'.
3. The initial state problem. Under the PC, the state of a system can be explained in terms of its evolution, according to dynamical laws, from a previous state at an earlier time. This makes it difficult to explain early states of the universe: if a state can only be explained in terms of earlier states, then either the universe has an initial state, which we cannot explain (since there are no earlier state), or the universe does not have an initial state we have an infinite regress, explaining each state in terms of earlier states, going on forever. Neither of these options seem satisfactory.

I presume you are talking about the post What is Evidence [LW · GW]?

Yes, the ideas in that post are closely related to this one. I think that the main difference is that, in that post Eliezer is interested in epistemology whereas here I am interested in how the process works from a physics point of view. For example, in my post, there is no need for 'information' (as I am using the word) to be correlated with true beliefs.

I think I disagree with your characterisation of the split between 'objective' Shannon information and information as meaning, which requires interpretation.

As you point at the end of your comment, Shannon information requires you to know the probability distribution from which your data is drawn. And probabilities are reflections of your own state of knowledge, which is subjective. (Or at least subjectively objective [LW · GW], if you are using 'objective' in that sense, then I guess I agree.) For example, if Alice sends Bob a string '11111', we might be tempted to say that she has sent Bob 5 bits of information, but if Bob knows that Alice can only send two possible strings '00000' or '11111', then he would say that she has only sent one bit. All signals, not just what you call 'information as meaning' require some degree of interpretation. And this interpretation, I argue, requires knowing the possible signals that could be sent, even if they are not actually sent. These possible signals are what I am calling counterfactuals. 

I'm not sure I understand your point about conditionals vs counterfactuals.

AFAICS, that's just a special case of the inverse relationship between probability and(Shannon) information. If the lamp is stuck "on", the probability of an "on" signal is 1.000 and the information content is 0.000. So it's not fundamentally about counterfactuals at all.

I kind of agree with this, but it doesn't tell the whole story. Consider the case where, instead of being stuck 'on', the lamp flickers randomly and is on 50% of the time and off 50% of the time. In this case, you would not be able to use the lamp to send information, even though the probability of an 'on' signal is 0.5 and, in one sense, the Shannon entropy would be maximal. To send information requires that it is possible for you to change the signal sent by the lamp. This is what I was trying to get at in this post. Another way of thinking about it is to say that you must have a causal effect on the state of the signal. In both the case where the lamp is stuck on and the case where it is flickering uncontrollably, you have no causal link to the state of the signal. I tried to explain the link between counterfactuals, information and causality in the subsequent post [LW · GW].